Uniform 8-polytope

<h2 id="regular-8-polytopes">Regular 8-polytopes</h2>
<p>Regular 8-polytopes can be represented by the <a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbol</a> {p,q,r,s,t,u,v}, with v {p,q,r,s,t,u} 7-polytope <a href="/facts/Facet_(mathematics)/IreRHGJ7">facets</a> around each <a href="/facts/Peak_(geometry)/T2E6BTU4">peak</a>.
</p><p>There are exactly three such <a href="/facts/List_of_regular_polytopes/Kng25Ymq">convex regular 8-polytopes</a>:
</p>
<ol><li>{3,3,3,3,3,3,3} - <a href="/facts/8-simplex/QUhcnmk2">8-simplex</a></li>
<li>{4,3,3,3,3,3,3} - <a href="/facts/8-cube/vEpKH3le">8-cube</a></li>
<li>{3,3,3,3,3,3,4} - <a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a></li></ol>
<p>There are no nonconvex regular 8-polytopes.
</p>
<h2 id="characteristics">Characteristics</h2>
<p>The topology of any given 8-polytope is defined by its <a href="/facts/Betti_number/r42Y8k6f">Betti numbers</a> and <a href="/facts/Torsion_coefficient_(topology)/r42Y8k6f">torsion coefficients</a>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p><p>The value of the <a href="/facts/Euler_characteristic/JCjzWUr2">Euler characteristic</a> used to characterise polyhedra does not generalize usefully to higher dimensions, and is zero for all 8-polytopes, whatever their underlying topology. This inadequacy of the Euler characteristic to reliably distinguish between different topologies in higher dimensions led to the discovery of the more sophisticated Betti numbers.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p><p>Similarly, the notion of orientability of a polyhedron is insufficient to characterise the surface twistings of toroidal polytopes, and this led to the use of torsion coefficients.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p>
<h2 id="uniform-8-polytopes-by-fundamental-coxeter-groups">Uniform 8-polytopes by fundamental Coxeter groups</h2>
<p>Uniform 8-polytopes with reflective symmetry can be generated by these four Coxeter groups, represented by permutations of rings of the <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagrams</a>:
</p>
<table><tbody><tr><th>#</th><th colspan="3"><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></th><th>Forms</th></tr><tr><td>1</td><td>A8</td><td>[37]</td><td></td><td>135</td></tr><tr><td>2</td><td>BC8</td><td>[4,36]</td><td></td><td>255</td></tr><tr><td>3</td><td>D8</td><td>[35,1,1]</td><td></td><td>191 (64 unique)</td></tr><tr><td>4</td><td><a href="/facts/E8_(mathematics)/NEaKT71H">E8</a></td><td>[34,2,1]</td><td></td><td>255</td></tr></tbody></table>
<p>Selected regular and uniform 8-polytopes from each family include:
</p>
<ol><li><a href="/facts/Simplex/0FCfNRN8">Simplex</a> family: A8 [37] - 
<ul><li>135 uniform 8-polytopes as permutations of rings in the group diagram, including one regular:
<ol><li>{37} - <a href="/facts/8-simplex/QUhcnmk2">8-simplex</a> or ennea-9-tope or enneazetton - </li></ol></li></ul></li>
<li><a href="/facts/Hypercube/q2mRPbIz">Hypercube</a>/<a href="/facts/Orthoplex/erk0byF6">orthoplex</a> family: B8 [4,36] - 
<ul><li>255 uniform 8-polytopes as permutations of rings in the group diagram, including two regular ones:
<ol><li>{4,36} - <a href="/facts/8-cube/vEpKH3le">8-cube</a> or <i>octeract</i>- </li>
<li>{36,4} - <a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a> or <i>octacross</i> - </li></ol></li></ul></li>
<li><a href="/facts/Demihypercube/ackHKsEa">Demihypercube</a> D8 family: [35,1,1] - 
<ul><li>191 uniform 8-polytopes as permutations of rings in the group diagram, including:
<ol><li>{3,35,1} - <a href="/facts/8-demicube/sWAomIhw">8-demicube</a> or <i>demiocteract</i>, 151 - ; also as h{4,36} .</li>
<li>{3,3,3,3,3,31,1} - <a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a>, 511 - </li></ol></li></ul></li>
<li><a href="/facts/Semiregular_E-polytope/vv3lWMYd">E-polytope family</a> E8 family: [34,1,1] - 
<ul><li>255 uniform 8-polytopes as permutations of rings in the group diagram, including:
<ol><li>{3,3,3,3,32,1} - <a href="/facts/Thorold_Gosset/3wvHtGPn">Thorold Gosset</a>'s semiregular <a href="/facts/Gosset_4_21_polytope/QFGglCkk">421</a>, </li>
<li>{3,34,2} - the uniform <a href="/facts/Gosset_1_42_polytope/DTgYDddB">142</a>, ,</li>
<li>{3,3,34,1} - the uniform <a href="/facts/Gosset_2_41_polytope/R9z0wNUz">241</a>, </li></ol></li></ul></li></ol>
<h3>Uniform prismatic forms</h3>
<p>There are many <a href="/facts/Uniform_polytope/nFcNAzLy">uniform</a> <a href="/facts/Prismatic_polytope/baIRRkCy">prismatic</a> families, including:
</p>
<table><tbody><tr><th colspan="12">Uniform 8-polytope prism families</th></tr><tr><th>#</th><th colspan="2"><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></th><th><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></th></tr><tr><th colspan="4">7+1</th></tr><tr><td>1</td><td>A7A1</td><td>[3,3,3,3,3,3]×[ ]</td><td></td></tr><tr><td>2</td><td>B7A1</td><td>[4,3,3,3,3,3]×[ ]</td><td></td></tr><tr><td>3</td><td>D7A1</td><td>[34,1,1]×[ ]</td><td></td></tr><tr><td>4</td><td><a href="/facts/E7_(mathematics)/KjFez9PW">E7</a>A1</td><td>[33,2,1]×[ ]</td><td></td></tr><tr><th colspan="4">6+2</th></tr><tr><td>1</td><td>A6I2(p)</td><td>[3,3,3,3,3]×[p]</td><td></td></tr><tr><td>2</td><td>B6I2(p)</td><td>[4,3,3,3,3]×[p]</td><td></td></tr><tr><td>3</td><td>D6I2(p)</td><td>[33,1,1]×[p]</td><td></td></tr><tr><td>4</td><td>E6I2(p)</td><td>[3,3,3,3,3]×[p]</td><td></td></tr><tr><th colspan="4">6+1+1</th></tr><tr><td>1</td><td>A6A1A1</td><td>[3,3,3,3,3]×[ ]x[ ]</td><td></td></tr><tr><td>2</td><td>B6A1A1</td><td>[4,3,3,3,3]×[ ]x[ ]</td><td></td></tr><tr><td>3</td><td>D6A1A1</td><td>[33,1,1]×[ ]x[ ]</td><td></td></tr><tr><td>4</td><td>E6A1A1</td><td>[3,3,3,3,3]×[ ]x[ ]</td><td></td></tr><tr><th colspan="4">5+3</th></tr><tr><td>1</td><td>A5A3</td><td>[34]×[3,3]</td><td></td></tr><tr><td>2</td><td>B5A3</td><td>[4,33]×[3,3]</td><td></td></tr><tr><td>3</td><td>D5A3</td><td>[32,1,1]×[3,3]</td><td></td></tr><tr><td>4</td><td>A5B3</td><td>[34]×[4,3]</td><td></td></tr><tr><td>5</td><td>B5B3</td><td>[4,33]×[4,3]</td><td></td></tr><tr><td>6</td><td>D5B3</td><td>[32,1,1]×[4,3]</td><td></td></tr><tr><td>7</td><td>A5H3</td><td>[34]×[5,3]</td><td></td></tr><tr><td>8</td><td>B5H3</td><td>[4,33]×[5,3]</td><td></td></tr><tr><td>9</td><td>D5H3</td><td>[32,1,1]×[5,3]</td><td></td></tr><tr><th colspan="4">5+2+1</th></tr><tr><td>1</td><td>A5I2(p)A1</td><td>[3,3,3]×[p]×[ ]</td><td></td></tr><tr><td>2</td><td>B5I2(p)A1</td><td>[4,3,3]×[p]×[ ]</td><td></td></tr><tr><td>3</td><td>D5I2(p)A1</td><td>[32,1,1]×[p]×[ ]</td><td></td></tr><tr><th colspan="4">5+1+1+1</th></tr><tr><td>1</td><td>A5A1A1A1</td><td>[3,3,3]×[ ]×[ ]×[ ]</td><td></td></tr><tr><td>2</td><td>B5A1A1A1</td><td>[4,3,3]×[ ]×[ ]×[ ]</td><td></td></tr><tr><td>3</td><td>D5A1A1A1</td><td>[32,1,1]×[ ]×[ ]×[ ]</td><td></td></tr><tr><th colspan="4">4+4</th></tr><tr><td>1</td><td>A4A4</td><td>[3,3,3]×[3,3,3]</td><td></td></tr><tr><td>2</td><td>B4A4</td><td>[4,3,3]×[3,3,3]</td><td></td></tr><tr><td>3</td><td>D4A4</td><td>[31,1,1]×[3,3,3]</td><td></td></tr><tr><td>4</td><td>F4A4</td><td>[3,4,3]×[3,3,3]</td><td></td></tr><tr><td>5</td><td>H4A4</td><td>[5,3,3]×[3,3,3]</td><td></td></tr><tr><td>6</td><td>B4B4</td><td>[4,3,3]×[4,3,3]</td><td></td></tr><tr><td>7</td><td>D4B4</td><td>[31,1,1]×[4,3,3]</td><td></td></tr><tr><td>8</td><td>F4B4</td><td>[3,4,3]×[4,3,3]</td><td></td></tr><tr><td>9</td><td>H4B4</td><td>[5,3,3]×[4,3,3]</td><td></td></tr><tr><td>10</td><td>D4D4</td><td>[31,1,1]×[31,1,1]</td><td></td></tr><tr><td>11</td><td>F4D4</td><td>[3,4,3]×[31,1,1]</td><td></td></tr><tr><td>12</td><td>H4D4</td><td>[5,3,3]×[31,1,1]</td><td></td></tr><tr><td>13</td><td>F4×F4</td><td>[3,4,3]×[3,4,3]</td><td></td></tr><tr><td>14</td><td>H4×F4</td><td>[5,3,3]×[3,4,3]</td><td></td></tr><tr><td>15</td><td>H4H4</td><td>[5,3,3]×[5,3,3]</td><td></td></tr><tr><th colspan="4">4+3+1</th></tr><tr><td>1</td><td>A4A3A1</td><td>[3,3,3]×[3,3]×[ ]</td><td></td></tr><tr><td>2</td><td>A4B3A1</td><td>[3,3,3]×[4,3]×[ ]</td><td></td></tr><tr><td>3</td><td>A4H3A1</td><td>[3,3,3]×[5,3]×[ ]</td><td></td></tr><tr><td>4</td><td>B4A3A1</td><td>[4,3,3]×[3,3]×[ ]</td><td></td></tr><tr><td>5</td><td>B4B3A1</td><td>[4,3,3]×[4,3]×[ ]</td><td></td></tr><tr><td>6</td><td>B4H3A1</td><td>[4,3,3]×[5,3]×[ ]</td><td></td></tr><tr><td>7</td><td>H4A3A1</td><td>[5,3,3]×[3,3]×[ ]</td><td></td></tr><tr><td>8</td><td>H4B3A1</td><td>[5,3,3]×[4,3]×[ ]</td><td></td></tr><tr><td>9</td><td>H4H3A1</td><td>[5,3,3]×[5,3]×[ ]</td><td></td></tr><tr><td>10</td><td>F4A3A1</td><td>[3,4,3]×[3,3]×[ ]</td><td></td></tr><tr><td>11</td><td>F4B3A1</td><td>[3,4,3]×[4,3]×[ ]</td><td></td></tr><tr><td>12</td><td>F4H3A1</td><td>[3,4,3]×[5,3]×[ ]</td><td></td></tr><tr><td>13</td><td>D4A3A1</td><td>[31,1,1]×[3,3]×[ ]</td><td></td></tr><tr><td>14</td><td>D4B3A1</td><td>[31,1,1]×[4,3]×[ ]</td><td></td></tr><tr><td>15</td><td>D4H3A1</td><td>[31,1,1]×[5,3]×[ ]</td><td></td></tr><tr><th colspan="4">4+2+2</th></tr><tr><td>...</td></tr><tr><th colspan="4">4+2+1+1</th></tr><tr><td>...</td></tr><tr><th colspan="4">4+1+1+1+1</th></tr><tr><td>...</td></tr><tr><th colspan="4">3+3+2</th></tr><tr><th>1</th><td>A3A3I2(p)</td><td>[3,3]×[3,3]×[p]</td><td></td></tr><tr><th>2</th><td>B3A3I2(p)</td><td>[4,3]×[3,3]×[p]</td><td></td></tr><tr><th>3</th><td>H3A3I2(p)</td><td>[5,3]×[3,3]×[p]</td><td></td></tr><tr><th>4</th><td>B3B3I2(p)</td><td>[4,3]×[4,3]×[p]</td><td></td></tr><tr><th>5</th><td>H3B3I2(p)</td><td>[5,3]×[4,3]×[p]</td><td></td></tr><tr><th>6</th><td>H3H3I2(p)</td><td>[5,3]×[5,3]×[p]</td><td></td></tr><tr><th colspan="4">3+3+1+1</th></tr><tr><th>1</th><td>A32A12</td><td>[3,3]×[3,3]×[ ]×[ ]</td><td></td></tr><tr><th>2</th><td>B3A3A12</td><td>[4,3]×[3,3]×[ ]×[ ]</td><td></td></tr><tr><th>3</th><td>H3A3A12</td><td>[5,3]×[3,3]×[ ]×[ ]</td><td></td></tr><tr><th>4</th><td>B3B3A12</td><td>[4,3]×[4,3]×[ ]×[ ]</td><td></td></tr><tr><th>5</th><td>H3B3A12</td><td>[5,3]×[4,3]×[ ]×[ ]</td><td></td></tr><tr><th>6</th><td>H3H3A12</td><td>[5,3]×[5,3]×[ ]×[ ]</td><td></td></tr><tr><th colspan="4">3+2+2+1</th></tr><tr><td>1</td><td>A3I2(p)I2(q)A1</td><td>[3,3]×[p]×[q]×[ ]</td><td></td></tr><tr><td>2</td><td>B3I2(p)I2(q)A1</td><td>[4,3]×[p]×[q]×[ ]</td><td></td></tr><tr><td>3</td><td>H3I2(p)I2(q)A1</td><td>[5,3]×[p]×[q]×[ ]</td><td></td></tr><tr><th colspan="4">3+2+1+1+1</th></tr><tr><td>1</td><td>A3I2(p)A13</td><td>[3,3]×[p]×[ ]x[ ]×[ ]</td><td></td></tr><tr><td>2</td><td>B3I2(p)A13</td><td>[4,3]×[p]×[ ]x[ ]×[ ]</td><td></td></tr><tr><td>3</td><td>H3I2(p)A13</td><td>[5,3]×[p]×[ ]x[ ]×[ ]</td><td></td></tr><tr><th colspan="4">3+1+1+1+1+1</th></tr><tr><td>1</td><td>A3A15</td><td>[3,3]×[ ]x[ ]×[ ]x[ ]×[ ]</td><td></td></tr><tr><td>2</td><td>B3A15</td><td>[4,3]×[ ]x[ ]×[ ]x[ ]×[ ]</td><td></td></tr><tr><td>3</td><td>H3A15</td><td>[5,3]×[ ]x[ ]×[ ]x[ ]×[ ]</td><td></td></tr><tr><th colspan="4">2+2+2+2</th></tr><tr><td>1</td><td>I2(p)I2(q)I2(r)I2(s)</td><td>[p]×[q]×[r]×[s]</td><td></td></tr><tr><th colspan="4">2+2+2+1+1</th></tr><tr><td>1</td><td>I2(p)I2(q)I2(r)A12</td><td>[p]×[q]×[r]×[ ]×[ ]</td><td></td></tr><tr><th colspan="4">2+2+1+1+1+1</th></tr><tr><td>2</td><td>I2(p)I2(q)A14</td><td>[p]×[q]×[ ]×[ ]×[ ]×[ ]</td><td></td></tr><tr><th colspan="4">2+1+1+1+1+1+1</th></tr><tr><td>1</td><td>I2(p)A16</td><td>[p]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]</td><td></td></tr><tr><th colspan="4">1+1+1+1+1+1+1+1</th></tr><tr><td>1</td><td>A18</td><td>[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]×[ ]</td><td></td></tr></tbody></table>
<h3>The A8 family</h3>
<p>The A8 family has symmetry of order 362880 (9 <a href="/facts/Factorial/kkfy1Bwe">factorial</a>).
</p><p>There are 135 forms based on all permutations of the <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagrams</a> with one or more rings. (128+8-1 cases) These are all enumerated below. Bowers-style acronym names are given in parentheses for cross-referencing.
</p><p>See also a <a href="/facts/List_of_8-simplex_polytopes/ujwSbssj">list of 8-simplex polytopes</a> for symmetric <a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a> graphs of these polytopes.
</p>
<table><tbody><tr><th colspan="13">A8 uniform polytopes</th></tr><tr><th rowspan="2">#</th><th rowspan="2"><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></th><th rowspan="2">Truncationindices</th><th rowspan="2"><a href="/facts/Norman_Johnson_(mathematician)/bQtL9w56">Johnson name</a></th><th rowspan="2">Basepoint</th><th colspan="8">Element counts</th></tr><tr><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th><th>0</th></tr><tr><th>1</th><td></td><td>t0</td><td><a href="/facts/8-simplex/QUhcnmk2">8-simplex</a> (ene)</td><td>(0,0,0,0,0,0,0,0,1)</td><td>9</td><td>36</td><td>84</td><td>126</td><td>126</td><td>84</td><td>36</td><td>9</td></tr><tr><th>2</th><td></td><td>t1</td><td><a href="/facts/Rectified_8-simplex/SozS9o74">Rectified 8-simplex</a> (rene)</td><td>(0,0,0,0,0,0,0,1,1)</td><td>18</td><td>108</td><td>336</td><td>630</td><td>576</td><td>588</td><td>252</td><td>36</td></tr><tr><th>3</th><td></td><td>t2</td><td><a href="/facts/Birectified_8-simplex/SozS9o74">Birectified 8-simplex</a> (bene)</td><td>(0,0,0,0,0,0,1,1,1)</td><td>18</td><td>144</td><td>588</td><td>1386</td><td>2016</td><td>1764</td><td>756</td><td>84</td></tr><tr><th>4</th><td></td><td>t3</td><td><a href="/facts/Trirectified_8-simplex/SozS9o74">Trirectified 8-simplex</a> (trene)</td><td>(0,0,0,0,0,1,1,1,1)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1260</td><td>126</td></tr><tr><th>5</th><td></td><td>t0,1</td><td><a href="/facts/Truncated_8-simplex/aQ2TjRuJ">Truncated 8-simplex</a> (tene)</td><td>(0,0,0,0,0,0,0,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>288</td><td>72</td></tr><tr><th>6</th><td></td><td>t0,2</td><td><a href="/facts/Cantellated_8-simplex/BBMyy5Gm">Cantellated 8-simplex</a></td><td>(0,0,0,0,0,0,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1764</td><td>252</td></tr><tr><th>7</th><td></td><td>t1,2</td><td><a href="/facts/Bitruncated_8-simplex/aQ2TjRuJ">Bitruncated 8-simplex</a></td><td>(0,0,0,0,0,0,1,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1008</td><td>252</td></tr><tr><th>8</th><td></td><td>t0,3</td><td><a href="/facts/Runcinated_8-simplex/eucoYK9b">Runcinated 8-simplex</a></td><td>(0,0,0,0,0,1,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4536</td><td>504</td></tr><tr><th>9</th><td></td><td>t1,3</td><td><a href="/facts/Bicantellated_8-simplex/BBMyy5Gm">Bicantellated 8-simplex</a></td><td>(0,0,0,0,0,1,1,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5292</td><td>756</td></tr><tr><th>10</th><td></td><td>t2,3</td><td><a href="/facts/Tritruncated_8-simplex/aQ2TjRuJ">Tritruncated 8-simplex</a></td><td>(0,0,0,0,0,1,2,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2016</td><td>504</td></tr><tr><th>11</th><td></td><td>t0,4</td><td><a href="/facts/Stericated_8-simplex/5YrBlfyj">Stericated 8-simplex</a></td><td>(0,0,0,0,1,1,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6300</td><td>630</td></tr><tr><th>12</th><td></td><td>t1,4</td><td><a href="/facts/Biruncinated_8-simplex/eucoYK9b">Biruncinated 8-simplex</a></td><td>(0,0,0,0,1,1,1,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11340</td><td>1260</td></tr><tr><th>13</th><td></td><td>t2,4</td><td><a href="/facts/Tricantellated_8-simplex/BBMyy5Gm">Tricantellated 8-simplex</a></td><td>(0,0,0,0,1,1,2,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8820</td><td>1260</td></tr><tr><th>14</th><td></td><td>t3,4</td><td><a href="/facts/Quadritruncated_8-simplex/aQ2TjRuJ">Quadritruncated 8-simplex</a></td><td>(0,0,0,0,1,2,2,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2520</td><td>630</td></tr><tr><th>15</th><td></td><td>t0,5</td><td><a href="/facts/Pentellated_8-simplex/Wd4EzKld">Pentellated 8-simplex</a></td><td>(0,0,0,1,1,1,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5040</td><td>504</td></tr><tr><th>16</th><td></td><td>t1,5</td><td><a href="/facts/Bistericated_8-simplex/5YrBlfyj">Bistericated 8-simplex</a></td><td>(0,0,0,1,1,1,1,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12600</td><td>1260</td></tr><tr><th>17</th><td></td><td>t2,5</td><td><a href="/facts/Triruncinated_8-simplex/eucoYK9b">Triruncinated 8-simplex</a></td><td>(0,0,0,1,1,1,2,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>15120</td><td>1680</td></tr><tr><th>18</th><td></td><td>t0,6</td><td><a href="/facts/Hexicated_8-simplex/30whwsV8">Hexicated 8-simplex</a></td><td>(0,0,1,1,1,1,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2268</td><td>252</td></tr><tr><th>19</th><td></td><td>t1,6</td><td><a href="/facts/Bipentellated_8-simplex/Wd4EzKld">Bipentellated 8-simplex</a></td><td>(0,0,1,1,1,1,1,2,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7560</td><td>756</td></tr><tr><th>20</th><td></td><td>t0,7</td><td><a href="/facts/Heptellated_8-simplex/VX5EgAv7">Heptellated 8-simplex</a></td><td>(0,1,1,1,1,1,1,1,2)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>504</td><td>72</td></tr><tr><th>21</th><td></td><td>t0,1,2</td><td><a href="/facts/Cantitruncated_8-simplex/BBMyy5Gm">Cantitruncated 8-simplex</a></td><td>(0,0,0,0,0,0,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2016</td><td>504</td></tr><tr><th>22</th><td></td><td>t0,1,3</td><td><a href="/facts/Runcitruncated_8-simplex/eucoYK9b">Runcitruncated 8-simplex</a></td><td>(0,0,0,0,0,1,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>9828</td><td>1512</td></tr><tr><th>23</th><td></td><td>t0,2,3</td><td><a href="/facts/Runcicantellated_8-simplex/eucoYK9b">Runcicantellated 8-simplex</a></td><td>(0,0,0,0,0,1,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6804</td><td>1512</td></tr><tr><th>24</th><td></td><td>t1,2,3</td><td><a href="/facts/Bicantitruncated_8-simplex/BBMyy5Gm">Bicantitruncated 8-simplex</a></td><td>(0,0,0,0,0,1,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6048</td><td>1512</td></tr><tr><th>25</th><td></td><td>t0,1,4</td><td><a href="/facts/Steritruncated_8-simplex/5YrBlfyj">Steritruncated 8-simplex</a></td><td>(0,0,0,0,1,1,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>20160</td><td>2520</td></tr><tr><th>26</th><td></td><td>t0,2,4</td><td><a href="/facts/Stericantellated_8-simplex/5YrBlfyj">Stericantellated 8-simplex</a></td><td>(0,0,0,0,1,1,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>26460</td><td>3780</td></tr><tr><th>27</th><td></td><td>t1,2,4</td><td><a href="/facts/Biruncitruncated_8-simplex/eucoYK9b">Biruncitruncated 8-simplex</a></td><td>(0,0,0,0,1,1,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>22680</td><td>3780</td></tr><tr><th>28</th><td></td><td>t0,3,4</td><td><a href="/facts/Steriruncinated_8-simplex/5YrBlfyj">Steriruncinated 8-simplex</a></td><td>(0,0,0,0,1,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12600</td><td>2520</td></tr><tr><th>29</th><td></td><td>t1,3,4</td><td><a href="/facts/Biruncicantellated_8-simplex/eucoYK9b">Biruncicantellated 8-simplex</a></td><td>(0,0,0,0,1,2,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>18900</td><td>3780</td></tr><tr><th>30</th><td></td><td>t2,3,4</td><td><a href="/facts/Tricantitruncated_8-simplex/BBMyy5Gm">Tricantitruncated 8-simplex</a></td><td>(0,0,0,0,1,2,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>10080</td><td>2520</td></tr><tr><th>31</th><td></td><td>t0,1,5</td><td>Pentitruncated 8-simplex</td><td>(0,0,0,1,1,1,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>21420</td><td>2520</td></tr><tr><th>32</th><td></td><td>t0,2,5</td><td>Penticantellated 8-simplex</td><td>(0,0,0,1,1,1,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>42840</td><td>5040</td></tr><tr><th>33</th><td></td><td>t1,2,5</td><td><a href="/facts/Bisteritruncated_8-simplex/5YrBlfyj">Bisteritruncated 8-simplex</a></td><td>(0,0,0,1,1,1,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>35280</td><td>5040</td></tr><tr><th>34</th><td></td><td>t0,3,5</td><td>Pentiruncinated 8-simplex</td><td>(0,0,0,1,1,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>37800</td><td>5040</td></tr><tr><th>35</th><td></td><td>t1,3,5</td><td><a href="/facts/Bistericantellated_8-simplex/5YrBlfyj">Bistericantellated 8-simplex</a></td><td>(0,0,0,1,1,2,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>52920</td><td>7560</td></tr><tr><th>36</th><td></td><td>t2,3,5</td><td>Triruncitruncated 8-simplex</td><td>(0,0,0,1,1,2,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>27720</td><td>5040</td></tr><tr><th>37</th><td></td><td>t0,4,5</td><td>Pentistericated 8-simplex</td><td>(0,0,0,1,2,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>13860</td><td>2520</td></tr><tr><th>38</th><td></td><td>t1,4,5</td><td><a href="/facts/Bisteriruncinated_8-simplex/5YrBlfyj">Bisteriruncinated 8-simplex</a></td><td>(0,0,0,1,2,2,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>30240</td><td>5040</td></tr><tr><th>39</th><td></td><td>t0,1,6</td><td>Hexitruncated 8-simplex</td><td>(0,0,1,1,1,1,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12096</td><td>1512</td></tr><tr><th>40</th><td></td><td>t0,2,6</td><td>Hexicantellated 8-simplex</td><td>(0,0,1,1,1,1,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>34020</td><td>3780</td></tr><tr><th>41</th><td></td><td>t1,2,6</td><td>Bipentitruncated 8-simplex</td><td>(0,0,1,1,1,1,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>26460</td><td>3780</td></tr><tr><th>42</th><td></td><td>t0,3,6</td><td>Hexiruncinated 8-simplex</td><td>(0,0,1,1,1,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>45360</td><td>5040</td></tr><tr><th>43</th><td></td><td>t1,3,6</td><td>Bipenticantellated 8-simplex</td><td>(0,0,1,1,1,2,2,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>60480</td><td>7560</td></tr><tr><th>44</th><td></td><td>t0,4,6</td><td>Hexistericated 8-simplex</td><td>(0,0,1,1,2,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>30240</td><td>3780</td></tr><tr><th>45</th><td></td><td>t0,5,6</td><td>Hexipentellated 8-simplex</td><td>(0,0,1,2,2,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>9072</td><td>1512</td></tr><tr><th>46</th><td></td><td>t0,1,7</td><td>Heptitruncated 8-simplex</td><td>(0,1,1,1,1,1,1,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3276</td><td>504</td></tr><tr><th>47</th><td></td><td>t0,2,7</td><td>Hepticantellated 8-simplex</td><td>(0,1,1,1,1,1,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12852</td><td>1512</td></tr><tr><th>48</th><td></td><td>t0,3,7</td><td>Heptiruncinated 8-simplex</td><td>(0,1,1,1,1,2,2,2,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23940</td><td>2520</td></tr><tr><th>49</th><td></td><td>t0,1,2,3</td><td><a href="/facts/Runcicantitruncated_8-simplex/eucoYK9b">Runcicantitruncated 8-simplex</a></td><td>(0,0,0,0,0,1,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12096</td><td>3024</td></tr><tr><th>50</th><td></td><td>t0,1,2,4</td><td><a href="/facts/Stericantitruncated_8-simplex/5YrBlfyj">Stericantitruncated 8-simplex</a></td><td>(0,0,0,0,1,1,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>45360</td><td>7560</td></tr><tr><th>51</th><td></td><td>t0,1,3,4</td><td><a href="/facts/Steriruncitruncated_8-simplex/5YrBlfyj">Steriruncitruncated 8-simplex</a></td><td>(0,0,0,0,1,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>34020</td><td>7560</td></tr><tr><th>52</th><td></td><td>t0,2,3,4</td><td><a href="/facts/Steriruncicantellated_8-simplex/5YrBlfyj">Steriruncicantellated 8-simplex</a></td><td>(0,0,0,0,1,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>34020</td><td>7560</td></tr><tr><th>53</th><td></td><td>t1,2,3,4</td><td><a href="/facts/Biruncicantitruncated_8-simplex/eucoYK9b">Biruncicantitruncated 8-simplex</a></td><td>(0,0,0,0,1,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>30240</td><td>7560</td></tr><tr><th>54</th><td></td><td>t0,1,2,5</td><td>Penticantitruncated 8-simplex</td><td>(0,0,0,1,1,1,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>70560</td><td>10080</td></tr><tr><th>55</th><td></td><td>t0,1,3,5</td><td>Pentiruncitruncated 8-simplex</td><td>(0,0,0,1,1,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>98280</td><td>15120</td></tr><tr><th>56</th><td></td><td>t0,2,3,5</td><td>Pentiruncicantellated 8-simplex</td><td>(0,0,0,1,1,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>90720</td><td>15120</td></tr><tr><th>57</th><td></td><td>t1,2,3,5</td><td><a href="/facts/Bistericantitruncated_8-simplex/5YrBlfyj">Bistericantitruncated 8-simplex</a></td><td>(0,0,0,1,1,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>83160</td><td>15120</td></tr><tr><th>58</th><td></td><td>t0,1,4,5</td><td>Pentisteritruncated 8-simplex</td><td>(0,0,0,1,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>50400</td><td>10080</td></tr><tr><th>59</th><td></td><td>t0,2,4,5</td><td>Pentistericantellated 8-simplex</td><td>(0,0,0,1,2,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>83160</td><td>15120</td></tr><tr><th>60</th><td></td><td>t1,2,4,5</td><td><a href="/facts/Bisteriruncitruncated_8-simplex/5YrBlfyj">Bisteriruncitruncated 8-simplex</a></td><td>(0,0,0,1,2,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>68040</td><td>15120</td></tr><tr><th>61</th><td></td><td>t0,3,4,5</td><td>Pentisteriruncinated 8-simplex</td><td>(0,0,0,1,2,3,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>50400</td><td>10080</td></tr><tr><th>62</th><td></td><td>t1,3,4,5</td><td><a href="/facts/Bisteriruncicantellated_8-simplex/5YrBlfyj">Bisteriruncicantellated 8-simplex</a></td><td>(0,0,0,1,2,3,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>75600</td><td>15120</td></tr><tr><th>63</th><td></td><td>t2,3,4,5</td><td><a href="/facts/Triruncicantitruncated_8-simplex/eucoYK9b">Triruncicantitruncated 8-simplex</a></td><td>(0,0,0,1,2,3,4,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>40320</td><td>10080</td></tr><tr><th>64</th><td></td><td>t0,1,2,6</td><td>Hexicantitruncated 8-simplex</td><td>(0,0,1,1,1,1,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>52920</td><td>7560</td></tr><tr><th>65</th><td></td><td>t0,1,3,6</td><td>Hexiruncitruncated 8-simplex</td><td>(0,0,1,1,1,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>113400</td><td>15120</td></tr><tr><th>66</th><td></td><td>t0,2,3,6</td><td>Hexiruncicantellated 8-simplex</td><td>(0,0,1,1,1,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>98280</td><td>15120</td></tr><tr><th>67</th><td></td><td>t1,2,3,6</td><td>Bipenticantitruncated 8-simplex</td><td>(0,0,1,1,1,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>90720</td><td>15120</td></tr><tr><th>68</th><td></td><td>t0,1,4,6</td><td>Hexisteritruncated 8-simplex</td><td>(0,0,1,1,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>105840</td><td>15120</td></tr><tr><th>69</th><td></td><td>t0,2,4,6</td><td>Hexistericantellated 8-simplex</td><td>(0,0,1,1,2,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>158760</td><td>22680</td></tr><tr><th>70</th><td></td><td>t1,2,4,6</td><td>Bipentiruncitruncated 8-simplex</td><td>(0,0,1,1,2,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>136080</td><td>22680</td></tr><tr><th>71</th><td></td><td>t0,3,4,6</td><td>Hexisteriruncinated 8-simplex</td><td>(0,0,1,1,2,3,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>90720</td><td>15120</td></tr><tr><th>72</th><td></td><td>t1,3,4,6</td><td>Bipentiruncicantellated 8-simplex</td><td>(0,0,1,1,2,3,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>136080</td><td>22680</td></tr><tr><th>73</th><td></td><td>t0,1,5,6</td><td>Hexipentitruncated 8-simplex</td><td>(0,0,1,2,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>41580</td><td>7560</td></tr><tr><th>74</th><td></td><td>t0,2,5,6</td><td>Hexipenticantellated 8-simplex</td><td>(0,0,1,2,2,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>98280</td><td>15120</td></tr><tr><th>75</th><td></td><td>t1,2,5,6</td><td>Bipentisteritruncated 8-simplex</td><td>(0,0,1,2,2,2,3,4,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>75600</td><td>15120</td></tr><tr><th>76</th><td></td><td>t0,3,5,6</td><td>Hexipentiruncinated 8-simplex</td><td>(0,0,1,2,2,3,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>98280</td><td>15120</td></tr><tr><th>77</th><td></td><td>t0,4,5,6</td><td>Hexipentistericated 8-simplex</td><td>(0,0,1,2,3,3,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>41580</td><td>7560</td></tr><tr><th>78</th><td></td><td>t0,1,2,7</td><td>Hepticantitruncated 8-simplex</td><td>(0,1,1,1,1,1,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>18144</td><td>3024</td></tr><tr><th>79</th><td></td><td>t0,1,3,7</td><td>Heptiruncitruncated 8-simplex</td><td>(0,1,1,1,1,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>56700</td><td>7560</td></tr><tr><th>80</th><td></td><td>t0,2,3,7</td><td>Heptiruncicantellated 8-simplex</td><td>(0,1,1,1,1,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>45360</td><td>7560</td></tr><tr><th>81</th><td></td><td>t0,1,4,7</td><td>Heptisteritruncated 8-simplex</td><td>(0,1,1,1,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80640</td><td>10080</td></tr><tr><th>82</th><td></td><td>t0,2,4,7</td><td>Heptistericantellated 8-simplex</td><td>(0,1,1,1,2,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>113400</td><td>15120</td></tr><tr><th>83</th><td></td><td>t0,3,4,7</td><td>Heptisteriruncinated 8-simplex</td><td>(0,1,1,1,2,3,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>60480</td><td>10080</td></tr><tr><th>84</th><td></td><td>t0,1,5,7</td><td>Heptipentitruncated 8-simplex</td><td>(0,1,1,2,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>56700</td><td>7560</td></tr><tr><th>85</th><td></td><td>t0,2,5,7</td><td>Heptipenticantellated 8-simplex</td><td>(0,1,1,2,2,2,3,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>120960</td><td>15120</td></tr><tr><th>86</th><td></td><td>t0,1,6,7</td><td>Heptihexitruncated 8-simplex</td><td>(0,1,2,2,2,2,2,3,4)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>18144</td><td>3024</td></tr><tr><th>87</th><td></td><td>t0,1,2,3,4</td><td><a href="/facts/Steriruncicantitruncated_8-simplex/5YrBlfyj">Steriruncicantitruncated 8-simplex</a></td><td>(0,0,0,0,1,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>60480</td><td>15120</td></tr><tr><th>88</th><td></td><td>t0,1,2,3,5</td><td>Pentiruncicantitruncated 8-simplex</td><td>(0,0,0,1,1,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>166320</td><td>30240</td></tr><tr><th>89</th><td></td><td>t0,1,2,4,5</td><td>Pentistericantitruncated 8-simplex</td><td>(0,0,0,1,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>136080</td><td>30240</td></tr><tr><th>90</th><td></td><td>t0,1,3,4,5</td><td>Pentisteriruncitruncated 8-simplex</td><td>(0,0,0,1,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>136080</td><td>30240</td></tr><tr><th>91</th><td></td><td>t0,2,3,4,5</td><td>Pentisteriruncicantellated 8-simplex</td><td>(0,0,0,1,2,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>136080</td><td>30240</td></tr><tr><th>92</th><td></td><td>t1,2,3,4,5</td><td><a href="/facts/Bisteriruncicantitruncated_8-simplex/5YrBlfyj">Bisteriruncicantitruncated 8-simplex</a></td><td>(0,0,0,1,2,3,4,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>120960</td><td>30240</td></tr><tr><th>93</th><td></td><td>t0,1,2,3,6</td><td>Hexiruncicantitruncated 8-simplex</td><td>(0,0,1,1,1,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>181440</td><td>30240</td></tr><tr><th>94</th><td></td><td>t0,1,2,4,6</td><td>Hexistericantitruncated 8-simplex</td><td>(0,0,1,1,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>272160</td><td>45360</td></tr><tr><th>95</th><td></td><td>t0,1,3,4,6</td><td>Hexisteriruncitruncated 8-simplex</td><td>(0,0,1,1,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>249480</td><td>45360</td></tr><tr><th>96</th><td></td><td>t0,2,3,4,6</td><td>Hexisteriruncicantellated 8-simplex</td><td>(0,0,1,1,2,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>249480</td><td>45360</td></tr><tr><th>97</th><td></td><td>t1,2,3,4,6</td><td>Bipentiruncicantitruncated 8-simplex</td><td>(0,0,1,1,2,3,4,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>226800</td><td>45360</td></tr><tr><th>98</th><td></td><td>t0,1,2,5,6</td><td>Hexipenticantitruncated 8-simplex</td><td>(0,0,1,2,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>151200</td><td>30240</td></tr><tr><th>99</th><td></td><td>t0,1,3,5,6</td><td>Hexipentiruncitruncated 8-simplex</td><td>(0,0,1,2,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>249480</td><td>45360</td></tr><tr><th>100</th><td></td><td>t0,2,3,5,6</td><td>Hexipentiruncicantellated 8-simplex</td><td>(0,0,1,2,2,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>226800</td><td>45360</td></tr><tr><th>101</th><td></td><td>t1,2,3,5,6</td><td>Bipentistericantitruncated 8-simplex</td><td>(0,0,1,2,2,3,4,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>204120</td><td>45360</td></tr><tr><th>102</th><td></td><td>t0,1,4,5,6</td><td>Hexipentisteritruncated 8-simplex</td><td>(0,0,1,2,3,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>151200</td><td>30240</td></tr><tr><th>103</th><td></td><td>t0,2,4,5,6</td><td>Hexipentistericantellated 8-simplex</td><td>(0,0,1,2,3,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>249480</td><td>45360</td></tr><tr><th>104</th><td></td><td>t0,3,4,5,6</td><td>Hexipentisteriruncinated 8-simplex</td><td>(0,0,1,2,3,4,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>151200</td><td>30240</td></tr><tr><th>105</th><td></td><td>t0,1,2,3,7</td><td>Heptiruncicantitruncated 8-simplex</td><td>(0,1,1,1,1,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>83160</td><td>15120</td></tr><tr><th>106</th><td></td><td>t0,1,2,4,7</td><td>Heptistericantitruncated 8-simplex</td><td>(0,1,1,1,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>196560</td><td>30240</td></tr><tr><th>107</th><td></td><td>t0,1,3,4,7</td><td>Heptisteriruncitruncated 8-simplex</td><td>(0,1,1,1,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>166320</td><td>30240</td></tr><tr><th>108</th><td></td><td>t0,2,3,4,7</td><td>Heptisteriruncicantellated 8-simplex</td><td>(0,1,1,1,2,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>166320</td><td>30240</td></tr><tr><th>109</th><td></td><td>t0,1,2,5,7</td><td>Heptipenticantitruncated 8-simplex</td><td>(0,1,1,2,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>196560</td><td>30240</td></tr><tr><th>110</th><td></td><td>t0,1,3,5,7</td><td>Heptipentiruncitruncated 8-simplex</td><td>(0,1,1,2,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>294840</td><td>45360</td></tr><tr><th>111</th><td></td><td>t0,2,3,5,7</td><td>Heptipentiruncicantellated 8-simplex</td><td>(0,1,1,2,2,3,4,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>272160</td><td>45360</td></tr><tr><th>112</th><td></td><td>t0,1,4,5,7</td><td>Heptipentisteritruncated 8-simplex</td><td>(0,1,1,2,3,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>166320</td><td>30240</td></tr><tr><th>113</th><td></td><td>t0,1,2,6,7</td><td>Heptihexicantitruncated 8-simplex</td><td>(0,1,2,2,2,2,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>83160</td><td>15120</td></tr><tr><th>114</th><td></td><td>t0,1,3,6,7</td><td>Heptihexiruncitruncated 8-simplex</td><td>(0,1,2,2,2,3,3,4,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>196560</td><td>30240</td></tr><tr><th>115</th><td></td><td>t0,1,2,3,4,5</td><td>Pentisteriruncicantitruncated 8-simplex</td><td>(0,0,0,1,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>241920</td><td>60480</td></tr><tr><th>116</th><td></td><td>t0,1,2,3,4,6</td><td>Hexisteriruncicantitruncated 8-simplex</td><td>(0,0,1,1,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>453600</td><td>90720</td></tr><tr><th>117</th><td></td><td>t0,1,2,3,5,6</td><td>Hexipentiruncicantitruncated 8-simplex</td><td>(0,0,1,2,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>408240</td><td>90720</td></tr><tr><th>118</th><td></td><td>t0,1,2,4,5,6</td><td>Hexipentistericantitruncated 8-simplex</td><td>(0,0,1,2,3,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>408240</td><td>90720</td></tr><tr><th>119</th><td></td><td>t0,1,3,4,5,6</td><td>Hexipentisteriruncitruncated 8-simplex</td><td>(0,0,1,2,3,4,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>408240</td><td>90720</td></tr><tr><th>120</th><td></td><td>t0,2,3,4,5,6</td><td>Hexipentisteriruncicantellated 8-simplex</td><td>(0,0,1,2,3,4,5,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>408240</td><td>90720</td></tr><tr><th>121</th><td></td><td>t1,2,3,4,5,6</td><td>Bipentisteriruncicantitruncated 8-simplex</td><td>(0,0,1,2,3,4,5,6,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>362880</td><td>90720</td></tr><tr><th>122</th><td></td><td>t0,1,2,3,4,7</td><td>Heptisteriruncicantitruncated 8-simplex</td><td>(0,1,1,1,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>302400</td><td>60480</td></tr><tr><th>123</th><td></td><td>t0,1,2,3,5,7</td><td>Heptipentiruncicantitruncated 8-simplex</td><td>(0,1,1,2,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>498960</td><td>90720</td></tr><tr><th>124</th><td></td><td>t0,1,2,4,5,7</td><td>Heptipentistericantitruncated 8-simplex</td><td>(0,1,1,2,3,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>453600</td><td>90720</td></tr><tr><th>125</th><td></td><td>t0,1,3,4,5,7</td><td>Heptipentisteriruncitruncated 8-simplex</td><td>(0,1,1,2,3,4,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>453600</td><td>90720</td></tr><tr><th>126</th><td></td><td>t0,2,3,4,5,7</td><td>Heptipentisteriruncicantellated 8-simplex</td><td>(0,1,1,2,3,4,5,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>453600</td><td>90720</td></tr><tr><th>127</th><td></td><td>t0,1,2,3,6,7</td><td>Heptihexiruncicantitruncated 8-simplex</td><td>(0,1,2,2,2,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>302400</td><td>60480</td></tr><tr><th>128</th><td></td><td>t0,1,2,4,6,7</td><td>Heptihexistericantitruncated 8-simplex</td><td>(0,1,2,2,3,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>498960</td><td>90720</td></tr><tr><th>129</th><td></td><td>t0,1,3,4,6,7</td><td>Heptihexisteriruncitruncated 8-simplex</td><td>(0,1,2,2,3,4,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>453600</td><td>90720</td></tr><tr><th>130</th><td></td><td>t0,1,2,5,6,7</td><td>Heptihexipenticantitruncated 8-simplex</td><td>(0,1,2,3,3,3,4,5,6)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>302400</td><td>60480</td></tr><tr><th>131</th><td></td><td>t0,1,2,3,4,5,6</td><td>Hexipentisteriruncicantitruncated 8-simplex</td><td>(0,0,1,2,3,4,5,6,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>725760</td><td>181440</td></tr><tr><th>132</th><td></td><td>t0,1,2,3,4,5,7</td><td>Heptipentisteriruncicantitruncated 8-simplex</td><td>(0,1,1,2,3,4,5,6,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>816480</td><td>181440</td></tr><tr><th>133</th><td></td><td>t0,1,2,3,4,6,7</td><td>Heptihexisteriruncicantitruncated 8-simplex</td><td>(0,1,2,2,3,4,5,6,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>816480</td><td>181440</td></tr><tr><th>134</th><td></td><td>t0,1,2,3,5,6,7</td><td>Heptihexipentiruncicantitruncated 8-simplex</td><td>(0,1,2,3,3,4,5,6,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>816480</td><td>181440</td></tr><tr><th>135</th><td></td><td>t0,1,2,3,4,5,6,7</td><td><a href="/facts/Omnitruncated_8-simplex/VX5EgAv7">Omnitruncated 8-simplex</a></td><td>(0,1,2,3,4,5,6,7,8)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1451520</td><td>362880</td></tr></tbody></table>
<h3>The B8 family</h3>
<p>The B8 family has symmetry of order 10321920 (8 <a href="/facts/Factorial/kkfy1Bwe">factorial</a> x 28). There are 255 forms based on all permutations of the <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagrams</a> with one or more rings.
</p><p>See also a <a href="/facts/List_of_B8_polytopes/Ac3tV8hG">list of B8 polytopes</a> for symmetric <a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a> graphs of these polytopes.
</p>
<table><tbody><tr><th colspan="13">B8 uniform polytopes</th></tr><tr><th rowspan="2">#</th><th rowspan="2"><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></th><th rowspan="2"><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläflisymbol</a></th><th rowspan="2">Name</th><th colspan="8">Element counts</th></tr><tr><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th><th>0</th></tr><tr><th>1</th><td></td><td>t0{36,4}</td><td><a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a>Diacosipentacontahexazetton (ek)</td><td>256</td><td>1024</td><td>1792</td><td>1792</td><td>1120</td><td>448</td><td>112</td><td>16</td></tr><tr><th>2</th><td></td><td>t1{36,4}</td><td><a href="/facts/Rectified_8-orthoplex/CRmQvbIL">Rectified 8-orthoplex</a>Rectified diacosipentacontahexazetton (rek)</td><td>272</td><td>3072</td><td>8960</td><td>12544</td><td>10080</td><td>4928</td><td>1344</td><td>112</td></tr><tr><th>3</th><td></td><td>t2{36,4}</td><td><a href="/facts/Birectified_8-orthoplex/CRmQvbIL">Birectified 8-orthoplex</a>Birectified diacosipentacontahexazetton (bark)</td><td>272</td><td>3184</td><td>16128</td><td>34048</td><td>36960</td><td>22400</td><td>6720</td><td>448</td></tr><tr><th>4</th><td></td><td>t3{36,4}</td><td><a href="/facts/Trirectified_8-orthoplex/CRmQvbIL">Trirectified 8-orthoplex</a>Trirectified diacosipentacontahexazetton (tark)</td><td>272</td><td>3184</td><td>16576</td><td>48384</td><td>71680</td><td>53760</td><td>17920</td><td>1120</td></tr><tr><th>5</th><td></td><td>t3{4,36}</td><td><a href="/facts/Trirectified_8-cube/Gvwn9bHr">Trirectified 8-cube</a>Trirectified octeract (tro)</td><td>272</td><td>3184</td><td>16576</td><td>47712</td><td>80640</td><td>71680</td><td>26880</td><td>1792</td></tr><tr><th>6</th><td></td><td>t2{4,36}</td><td><a href="/facts/Birectified_8-cube/Gvwn9bHr">Birectified 8-cube</a>Birectified octeract (bro)</td><td>272</td><td>3184</td><td>14784</td><td>36960</td><td>55552</td><td>50176</td><td>21504</td><td>1792</td></tr><tr><th>7</th><td></td><td>t1{4,36}</td><td><a href="/facts/Rectified_8-cube/Gvwn9bHr">Rectified 8-cube</a>Rectified octeract (recto)</td><td>272</td><td>2160</td><td>7616</td><td>15456</td><td>19712</td><td>16128</td><td>7168</td><td>1024</td></tr><tr><th>8</th><td></td><td>t0{4,36}</td><td><a href="/facts/8-cube/vEpKH3le">8-cube</a>Octeract (octo)</td><td>16</td><td>112</td><td>448</td><td>1120</td><td>1792</td><td>1792</td><td>1024</td><td>256</td></tr><tr><th>9</th><td></td><td>t0,1{36,4}</td><td><a href="/facts/Truncated_8-orthoplex/6ndRPvfy">Truncated 8-orthoplex</a>Truncated diacosipentacontahexazetton (tek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1456</td><td>224</td></tr><tr><th>10</th><td></td><td>t0,2{36,4}</td><td><a href="/facts/Cantellated_8-orthoplex/M93v3h3c">Cantellated 8-orthoplex</a>Small rhombated diacosipentacontahexazetton (srek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14784</td><td>1344</td></tr><tr><th>11</th><td></td><td>t1,2{36,4}</td><td><a href="/facts/Bitruncated_8-orthoplex/6ndRPvfy">Bitruncated 8-orthoplex</a>Bitruncated diacosipentacontahexazetton (batek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8064</td><td>1344</td></tr><tr><th>12</th><td></td><td>t0,3{36,4}</td><td>Runcinated 8-orthoplexSmall prismated diacosipentacontahexazetton (spek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>60480</td><td>4480</td></tr><tr><th>13</th><td></td><td>t1,3{36,4}</td><td>Bicantellated 8-orthoplexSmall birhombated diacosipentacontahexazetton (sabork)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>67200</td><td>6720</td></tr><tr><th>14</th><td></td><td>t2,3{36,4}</td><td><a href="/facts/Tritruncated_8-orthoplex/6ndRPvfy">Tritruncated 8-orthoplex</a>Tritruncated diacosipentacontahexazetton (tatek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>24640</td><td>4480</td></tr><tr><th>15</th><td></td><td>t0,4{36,4}</td><td>Stericated 8-orthoplexSmall cellated diacosipentacontahexazetton (scak)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>125440</td><td>8960</td></tr><tr><th>16</th><td></td><td>t1,4{36,4}</td><td>Biruncinated 8-orthoplexSmall biprismated diacosipentacontahexazetton (sabpek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>215040</td><td>17920</td></tr><tr><th>17</th><td></td><td>t2,4{36,4}</td><td>Tricantellated 8-orthoplexSmall trirhombated diacosipentacontahexazetton (satrek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>161280</td><td>17920</td></tr><tr><th>18</th><td></td><td>t3,4{4,36}</td><td><a href="/facts/Quadritruncated_8-cube/8Bsbj6Nw">Quadritruncated 8-cube</a>Octeractidiacosipentacontahexazetton (oke)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>44800</td><td>8960</td></tr><tr><th>19</th><td></td><td>t0,5{36,4}</td><td>Pentellated 8-orthoplexSmall terated diacosipentacontahexazetton (setek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>134400</td><td>10752</td></tr><tr><th>20</th><td></td><td>t1,5{36,4}</td><td>Bistericated 8-orthoplexSmall bicellated diacosipentacontahexazetton (sibcak)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>322560</td><td>26880</td></tr><tr><th>21</th><td></td><td>t2,5{4,36}</td><td>Triruncinated 8-cubeSmall triprismato-octeractidiacosipentacontahexazetton (sitpoke)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>376320</td><td>35840</td></tr><tr><th>22</th><td></td><td>t2,4{4,36}</td><td>Tricantellated 8-cubeSmall trirhombated octeract (satro)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>215040</td><td>26880</td></tr><tr><th>23</th><td></td><td>t2,3{4,36}</td><td><a href="/facts/Tritruncated_8-cube/8Bsbj6Nw">Tritruncated 8-cube</a>Tritruncated octeract (tato)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>48384</td><td>10752</td></tr><tr><th>24</th><td></td><td>t0,6{36,4}</td><td>Hexicated 8-orthoplexSmall petated diacosipentacontahexazetton (supek)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>64512</td><td>7168</td></tr><tr><th>25</th><td></td><td>t1,6{4,36}</td><td>Bipentellated 8-cubeSmall biteri-octeractidiacosipentacontahexazetton (sabtoke)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>215040</td><td>21504</td></tr><tr><th>26</th><td></td><td>t1,5{4,36}</td><td>Bistericated 8-cubeSmall bicellated octeract (sobco)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>358400</td><td>35840</td></tr><tr><th>27</th><td></td><td>t1,4{4,36}</td><td>Biruncinated 8-cubeSmall biprismated octeract (sabepo)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>322560</td><td>35840</td></tr><tr><th>28</th><td></td><td>t1,3{4,36}</td><td>Bicantellated 8-cubeSmall birhombated octeract (subro)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>150528</td><td>21504</td></tr><tr><th>29</th><td></td><td>t1,2{4,36}</td><td><a href="/facts/Bitruncated_8-cube/8Bsbj6Nw">Bitruncated 8-cube</a>Bitruncated octeract (bato)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>28672</td><td>7168</td></tr><tr><th>30</th><td></td><td>t0,7{4,36}</td><td>Heptellated 8-cubeSmall exi-octeractidiacosipentacontahexazetton (saxoke)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14336</td><td>2048</td></tr><tr><th>31</th><td></td><td>t0,6{4,36}</td><td>Hexicated 8-cubeSmall petated octeract (supo)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>64512</td><td>7168</td></tr><tr><th>32</th><td></td><td>t0,5{4,36}</td><td>Pentellated 8-cubeSmall terated octeract (soto)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>143360</td><td>14336</td></tr><tr><th>33</th><td></td><td>t0,4{4,36}</td><td>Stericated 8-cubeSmall cellated octeract (soco)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>179200</td><td>17920</td></tr><tr><th>34</th><td></td><td>t0,3{4,36}</td><td>Runcinated 8-cubeSmall prismated octeract (sopo)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>129024</td><td>14336</td></tr><tr><th>35</th><td></td><td>t0,2{4,36}</td><td>Cantellated 8-cubeSmall rhombated octeract (soro)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>50176</td><td>7168</td></tr><tr><th>36</th><td></td><td>t0,1{4,36}</td><td><a href="/facts/Truncated_8-cube/8Bsbj6Nw">Truncated 8-cube</a>Truncated octeract (tocto)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8192</td><td>2048</td></tr><tr><th>37</th><td></td><td>t0,1,2{36,4}</td><td>Cantitruncated 8-orthoplexGreat rhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>16128</td><td>2688</td></tr><tr><th>38</th><td></td><td>t0,1,3{36,4}</td><td>Runcitruncated 8-orthoplexPrismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>127680</td><td>13440</td></tr><tr><th>39</th><td></td><td>t0,2,3{36,4}</td><td>Runcicantellated 8-orthoplexPrismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>80640</td><td>13440</td></tr><tr><th>40</th><td></td><td>t1,2,3{36,4}</td><td>Bicantitruncated 8-orthoplexGreat birhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>73920</td><td>13440</td></tr><tr><th>41</th><td></td><td>t0,1,4{36,4}</td><td>Steritruncated 8-orthoplexCellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>394240</td><td>35840</td></tr><tr><th>42</th><td></td><td>t0,2,4{36,4}</td><td>Stericantellated 8-orthoplexCellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>483840</td><td>53760</td></tr><tr><th>43</th><td></td><td>t1,2,4{36,4}</td><td>Biruncitruncated 8-orthoplexBiprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>430080</td><td>53760</td></tr><tr><th>44</th><td></td><td>t0,3,4{36,4}</td><td>Steriruncinated 8-orthoplexCelliprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>215040</td><td>35840</td></tr><tr><th>45</th><td></td><td>t1,3,4{36,4}</td><td>Biruncicantellated 8-orthoplexBiprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>322560</td><td>53760</td></tr><tr><th>46</th><td></td><td>t2,3,4{36,4}</td><td>Tricantitruncated 8-orthoplexGreat trirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>179200</td><td>35840</td></tr><tr><th>47</th><td></td><td>t0,1,5{36,4}</td><td>Pentitruncated 8-orthoplexTeritruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>564480</td><td>53760</td></tr><tr><th>48</th><td></td><td>t0,2,5{36,4}</td><td>Penticantellated 8-orthoplexTerirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1075200</td><td>107520</td></tr><tr><th>49</th><td></td><td>t1,2,5{36,4}</td><td>Bisteritruncated 8-orthoplexBicellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>913920</td><td>107520</td></tr><tr><th>50</th><td></td><td>t0,3,5{36,4}</td><td>Pentiruncinated 8-orthoplexTeriprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>913920</td><td>107520</td></tr><tr><th>51</th><td></td><td>t1,3,5{36,4}</td><td>Bistericantellated 8-orthoplexBicellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>161280</td></tr><tr><th>52</th><td></td><td>t2,3,5{36,4}</td><td>Triruncitruncated 8-orthoplexTriprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>698880</td><td>107520</td></tr><tr><th>53</th><td></td><td>t0,4,5{36,4}</td><td>Pentistericated 8-orthoplexTericellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>322560</td><td>53760</td></tr><tr><th>54</th><td></td><td>t1,4,5{36,4}</td><td>Bisteriruncinated 8-orthoplexBicelliprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>698880</td><td>107520</td></tr><tr><th>55</th><td></td><td>t2,3,5{4,36}</td><td>Triruncitruncated 8-cubeTriprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>645120</td><td>107520</td></tr><tr><th>56</th><td></td><td>t2,3,4{4,36}</td><td>Tricantitruncated 8-cubeGreat trirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>241920</td><td>53760</td></tr><tr><th>57</th><td></td><td>t0,1,6{36,4}</td><td>Hexitruncated 8-orthoplexPetitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>344064</td><td>43008</td></tr><tr><th>58</th><td></td><td>t0,2,6{36,4}</td><td>Hexicantellated 8-orthoplexPetirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td><td>107520</td></tr><tr><th>59</th><td></td><td>t1,2,6{36,4}</td><td>Bipentitruncated 8-orthoplexBiteritruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>752640</td><td>107520</td></tr><tr><th>60</th><td></td><td>t0,3,6{36,4}</td><td>Hexiruncinated 8-orthoplexPetiprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>143360</td></tr><tr><th>61</th><td></td><td>t1,3,6{36,4}</td><td>Bipenticantellated 8-orthoplexBiterirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1720320</td><td>215040</td></tr><tr><th>62</th><td></td><td>t1,4,5{4,36}</td><td>Bisteriruncinated 8-cubeBicelliprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>143360</td></tr><tr><th>63</th><td></td><td>t0,4,6{36,4}</td><td>Hexistericated 8-orthoplexPeticellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>107520</td></tr><tr><th>64</th><td></td><td>t1,3,6{4,36}</td><td>Bipenticantellated 8-cubeBiterirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1720320</td><td>215040</td></tr><tr><th>65</th><td></td><td>t1,3,5{4,36}</td><td>Bistericantellated 8-cubeBicellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1505280</td><td>215040</td></tr><tr><th>66</th><td></td><td>t1,3,4{4,36}</td><td>Biruncicantellated 8-cubeBiprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>537600</td><td>107520</td></tr><tr><th>67</th><td></td><td>t0,5,6{36,4}</td><td>Hexipentellated 8-orthoplexPetiterated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>258048</td><td>43008</td></tr><tr><th>68</th><td></td><td>t1,2,6{4,36}</td><td>Bipentitruncated 8-cubeBiteritruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>752640</td><td>107520</td></tr><tr><th>69</th><td></td><td>t1,2,5{4,36}</td><td>Bisteritruncated 8-cubeBicellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1003520</td><td>143360</td></tr><tr><th>70</th><td></td><td>t1,2,4{4,36}</td><td>Biruncitruncated 8-cubeBiprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>645120</td><td>107520</td></tr><tr><th>71</th><td></td><td>t1,2,3{4,36}</td><td>Bicantitruncated 8-cubeGreat birhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>172032</td><td>43008</td></tr><tr><th>72</th><td></td><td>t0,1,7{36,4}</td><td>Heptitruncated 8-orthoplexExitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>93184</td><td>14336</td></tr><tr><th>73</th><td></td><td>t0,2,7{36,4}</td><td>Hepticantellated 8-orthoplexExirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>365568</td><td>43008</td></tr><tr><th>74</th><td></td><td>t0,5,6{4,36}</td><td>Hexipentellated 8-cubePetiterated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>258048</td><td>43008</td></tr><tr><th>75</th><td></td><td>t0,3,7{36,4}</td><td>Heptiruncinated 8-orthoplexExiprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>680960</td><td>71680</td></tr><tr><th>76</th><td></td><td>t0,4,6{4,36}</td><td>Hexistericated 8-cubePeticellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>107520</td></tr><tr><th>77</th><td></td><td>t0,4,5{4,36}</td><td>Pentistericated 8-cubeTericellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>394240</td><td>71680</td></tr><tr><th>78</th><td></td><td>t0,3,7{4,36}</td><td>Heptiruncinated 8-cubeExiprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>680960</td><td>71680</td></tr><tr><th>79</th><td></td><td>t0,3,6{4,36}</td><td>Hexiruncinated 8-cubePetiprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>143360</td></tr><tr><th>80</th><td></td><td>t0,3,5{4,36}</td><td>Pentiruncinated 8-cubeTeriprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1075200</td><td>143360</td></tr><tr><th>81</th><td></td><td>t0,3,4{4,36}</td><td>Steriruncinated 8-cubeCelliprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>358400</td><td>71680</td></tr><tr><th>82</th><td></td><td>t0,2,7{4,36}</td><td>Hepticantellated 8-cubeExirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>365568</td><td>43008</td></tr><tr><th>83</th><td></td><td>t0,2,6{4,36}</td><td>Hexicantellated 8-cubePetirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td><td>107520</td></tr><tr><th>84</th><td></td><td>t0,2,5{4,36}</td><td>Penticantellated 8-cubeTerirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1218560</td><td>143360</td></tr><tr><th>85</th><td></td><td>t0,2,4{4,36}</td><td>Stericantellated 8-cubeCellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>752640</td><td>107520</td></tr><tr><th>86</th><td></td><td>t0,2,3{4,36}</td><td>Runcicantellated 8-cubePrismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>193536</td><td>43008</td></tr><tr><th>87</th><td></td><td>t0,1,7{4,36}</td><td>Heptitruncated 8-cubeExitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>93184</td><td>14336</td></tr><tr><th>88</th><td></td><td>t0,1,6{4,36}</td><td>Hexitruncated 8-cubePetitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>344064</td><td>43008</td></tr><tr><th>89</th><td></td><td>t0,1,5{4,36}</td><td>Pentitruncated 8-cubeTeritruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>609280</td><td>71680</td></tr><tr><th>90</th><td></td><td>t0,1,4{4,36}</td><td>Steritruncated 8-cubeCellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>573440</td><td>71680</td></tr><tr><th>91</th><td></td><td>t0,1,3{4,36}</td><td>Runcitruncated 8-cubePrismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>279552</td><td>43008</td></tr><tr><th>92</th><td></td><td>t0,1,2{4,36}</td><td>Cantitruncated 8-cubeGreat rhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>57344</td><td>14336</td></tr><tr><th>93</th><td></td><td>t0,1,2,3{36,4}</td><td>Runcicantitruncated 8-orthoplexGreat prismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>147840</td><td>26880</td></tr><tr><th>94</th><td></td><td>t0,1,2,4{36,4}</td><td>Stericantitruncated 8-orthoplexCelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>107520</td></tr><tr><th>95</th><td></td><td>t0,1,3,4{36,4}</td><td>Steriruncitruncated 8-orthoplexCelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>591360</td><td>107520</td></tr><tr><th>96</th><td></td><td>t0,2,3,4{36,4}</td><td>Steriruncicantellated 8-orthoplexCelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>591360</td><td>107520</td></tr><tr><th>97</th><td></td><td>t1,2,3,4{36,4}</td><td>Biruncicantitruncated 8-orthoplexGreat biprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>537600</td><td>107520</td></tr><tr><th>98</th><td></td><td>t0,1,2,5{36,4}</td><td>Penticantitruncated 8-orthoplexTerigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1827840</td><td>215040</td></tr><tr><th>99</th><td></td><td>t0,1,3,5{36,4}</td><td>Pentiruncitruncated 8-orthoplexTeriprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2419200</td><td>322560</td></tr><tr><th>100</th><td></td><td>t0,2,3,5{36,4}</td><td>Pentiruncicantellated 8-orthoplexTeriprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2257920</td><td>322560</td></tr><tr><th>101</th><td></td><td>t1,2,3,5{36,4}</td><td>Bistericantitruncated 8-orthoplexBicelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2096640</td><td>322560</td></tr><tr><th>102</th><td></td><td>t0,1,4,5{36,4}</td><td>Pentisteritruncated 8-orthoplexTericellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>103</th><td></td><td>t0,2,4,5{36,4}</td><td>Pentistericantellated 8-orthoplexTericellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1935360</td><td>322560</td></tr><tr><th>104</th><td></td><td>t1,2,4,5{36,4}</td><td>Bisteriruncitruncated 8-orthoplexBicelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>322560</td></tr><tr><th>105</th><td></td><td>t0,3,4,5{36,4}</td><td>Pentisteriruncinated 8-orthoplexTericelliprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>106</th><td></td><td>t1,3,4,5{36,4}</td><td>Bisteriruncicantellated 8-orthoplexBicelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1774080</td><td>322560</td></tr><tr><th>107</th><td></td><td>t2,3,4,5{4,36}</td><td>Triruncicantitruncated 8-cubeGreat triprismato-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td><td>215040</td></tr><tr><th>108</th><td></td><td>t0,1,2,6{36,4}</td><td>Hexicantitruncated 8-orthoplexPetigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1505280</td><td>215040</td></tr><tr><th>109</th><td></td><td>t0,1,3,6{36,4}</td><td>Hexiruncitruncated 8-orthoplexPetiprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>430080</td></tr><tr><th>110</th><td></td><td>t0,2,3,6{36,4}</td><td>Hexiruncicantellated 8-orthoplexPetiprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>111</th><td></td><td>t1,2,3,6{36,4}</td><td>Bipenticantitruncated 8-orthoplexBiterigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td></tr><tr><th>112</th><td></td><td>t0,1,4,6{36,4}</td><td>Hexisteritruncated 8-orthoplexPeticellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3010560</td><td>430080</td></tr><tr><th>113</th><td></td><td>t0,2,4,6{36,4}</td><td>Hexistericantellated 8-orthoplexPeticellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4515840</td><td>645120</td></tr><tr><th>114</th><td></td><td>t1,2,4,6{36,4}</td><td>Bipentiruncitruncated 8-orthoplexBiteriprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>645120</td></tr><tr><th>115</th><td></td><td>t0,3,4,6{36,4}</td><td>Hexisteriruncinated 8-orthoplexPeticelliprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td></tr><tr><th>116</th><td></td><td>t1,3,4,6{4,36}</td><td>Bipentiruncicantellated 8-cubeBiteriprismatorhombi-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>645120</td></tr><tr><th>117</th><td></td><td>t1,3,4,5{4,36}</td><td>Bisteriruncicantellated 8-cubeBicelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2150400</td><td>430080</td></tr><tr><th>118</th><td></td><td>t0,1,5,6{36,4}</td><td>Hexipentitruncated 8-orthoplexPetiteritruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>119</th><td></td><td>t0,2,5,6{36,4}</td><td>Hexipenticantellated 8-orthoplexPetiterirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>120</th><td></td><td>t1,2,5,6{4,36}</td><td>Bipentisteritruncated 8-cubeBitericellitrunki-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2150400</td><td>430080</td></tr><tr><th>121</th><td></td><td>t0,3,5,6{36,4}</td><td>Hexipentiruncinated 8-orthoplexPetiteriprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>122</th><td></td><td>t1,2,4,6{4,36}</td><td>Bipentiruncitruncated 8-cubeBiteriprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>645120</td></tr><tr><th>123</th><td></td><td>t1,2,4,5{4,36}</td><td>Bisteriruncitruncated 8-cubeBicelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1935360</td><td>430080</td></tr><tr><th>124</th><td></td><td>t0,4,5,6{36,4}</td><td>Hexipentistericated 8-orthoplexPetitericellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>125</th><td></td><td>t1,2,3,6{4,36}</td><td>Bipenticantitruncated 8-cubeBiterigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td></tr><tr><th>126</th><td></td><td>t1,2,3,5{4,36}</td><td>Bistericantitruncated 8-cubeBicelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>127</th><td></td><td>t1,2,3,4{4,36}</td><td>Biruncicantitruncated 8-cubeGreat biprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>215040</td></tr><tr><th>128</th><td></td><td>t0,1,2,7{36,4}</td><td>Hepticantitruncated 8-orthoplexExigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>516096</td><td>86016</td></tr><tr><th>129</th><td></td><td>t0,1,3,7{36,4}</td><td>Heptiruncitruncated 8-orthoplexExiprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td></tr><tr><th>130</th><td></td><td>t0,2,3,7{36,4}</td><td>Heptiruncicantellated 8-orthoplexExiprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td></tr><tr><th>131</th><td></td><td>t0,4,5,6{4,36}</td><td>Hexipentistericated 8-cubePetitericellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>132</th><td></td><td>t0,1,4,7{36,4}</td><td>Heptisteritruncated 8-orthoplexExicellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2293760</td><td>286720</td></tr><tr><th>133</th><td></td><td>t0,2,4,7{36,4}</td><td>Heptistericantellated 8-orthoplexExicellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>430080</td></tr><tr><th>134</th><td></td><td>t0,3,5,6{4,36}</td><td>Hexipentiruncinated 8-cubePetiteriprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>135</th><td></td><td>t0,3,4,7{4,36}</td><td>Heptisteriruncinated 8-cubeExicelliprismato-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1720320</td><td>286720</td></tr><tr><th>136</th><td></td><td>t0,3,4,6{4,36}</td><td>Hexisteriruncinated 8-cubePeticelliprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td></tr><tr><th>137</th><td></td><td>t0,3,4,5{4,36}</td><td>Pentisteriruncinated 8-cubeTericelliprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1433600</td><td>286720</td></tr><tr><th>138</th><td></td><td>t0,1,5,7{36,4}</td><td>Heptipentitruncated 8-orthoplexExiteritruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td></tr><tr><th>139</th><td></td><td>t0,2,5,7{4,36}</td><td>Heptipenticantellated 8-cubeExiterirhombi-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3440640</td><td>430080</td></tr><tr><th>140</th><td></td><td>t0,2,5,6{4,36}</td><td>Hexipenticantellated 8-cubePetiterirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>141</th><td></td><td>t0,2,4,7{4,36}</td><td>Heptistericantellated 8-cubeExicellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>430080</td></tr><tr><th>142</th><td></td><td>t0,2,4,6{4,36}</td><td>Hexistericantellated 8-cubePeticellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4515840</td><td>645120</td></tr><tr><th>143</th><td></td><td>t0,2,4,5{4,36}</td><td>Pentistericantellated 8-cubeTericellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>144</th><td></td><td>t0,2,3,7{4,36}</td><td>Heptiruncicantellated 8-cubeExiprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td></tr><tr><th>145</th><td></td><td>t0,2,3,6{4,36}</td><td>Hexiruncicantellated 8-cubePetiprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>146</th><td></td><td>t0,2,3,5{4,36}</td><td>Pentiruncicantellated 8-cubeTeriprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td></tr><tr><th>147</th><td></td><td>t0,2,3,4{4,36}</td><td>Steriruncicantellated 8-cubeCelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td><td>215040</td></tr><tr><th>148</th><td></td><td>t0,1,6,7{4,36}</td><td>Heptihexitruncated 8-cubeExipetitrunki-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>516096</td><td>86016</td></tr><tr><th>149</th><td></td><td>t0,1,5,7{4,36}</td><td>Heptipentitruncated 8-cubeExiteritruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td></tr><tr><th>150</th><td></td><td>t0,1,5,6{4,36}</td><td>Hexipentitruncated 8-cubePetiteritruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td></tr><tr><th>151</th><td></td><td>t0,1,4,7{4,36}</td><td>Heptisteritruncated 8-cubeExicellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2293760</td><td>286720</td></tr><tr><th>152</th><td></td><td>t0,1,4,6{4,36}</td><td>Hexisteritruncated 8-cubePeticellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3010560</td><td>430080</td></tr><tr><th>153</th><td></td><td>t0,1,4,5{4,36}</td><td>Pentisteritruncated 8-cubeTericellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1433600</td><td>286720</td></tr><tr><th>154</th><td></td><td>t0,1,3,7{4,36}</td><td>Heptiruncitruncated 8-cubeExiprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td></tr><tr><th>155</th><td></td><td>t0,1,3,6{4,36}</td><td>Hexiruncitruncated 8-cubePetiprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>430080</td></tr><tr><th>156</th><td></td><td>t0,1,3,5{4,36}</td><td>Pentiruncitruncated 8-cubeTeriprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td></tr><tr><th>157</th><td></td><td>t0,1,3,4{4,36}</td><td>Steriruncitruncated 8-cubeCelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td><td>215040</td></tr><tr><th>158</th><td></td><td>t0,1,2,7{4,36}</td><td>Hepticantitruncated 8-cubeExigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>516096</td><td>86016</td></tr><tr><th>159</th><td></td><td>t0,1,2,6{4,36}</td><td>Hexicantitruncated 8-cubePetigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1505280</td><td>215040</td></tr><tr><th>160</th><td></td><td>t0,1,2,5{4,36}</td><td>Penticantitruncated 8-cubeTerigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2007040</td><td>286720</td></tr><tr><th>161</th><td></td><td>t0,1,2,4{4,36}</td><td>Stericantitruncated 8-cubeCelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td></tr><tr><th>162</th><td></td><td>t0,1,2,3{4,36}</td><td>Runcicantitruncated 8-cubeGreat prismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>344064</td><td>86016</td></tr><tr><th>163</th><td></td><td>t0,1,2,3,4{36,4}</td><td>Steriruncicantitruncated 8-orthoplexGreat cellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1075200</td><td>215040</td></tr><tr><th>164</th><td></td><td>t0,1,2,3,5{36,4}</td><td>Pentiruncicantitruncated 8-orthoplexTerigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4193280</td><td>645120</td></tr><tr><th>165</th><td></td><td>t0,1,2,4,5{36,4}</td><td>Pentistericantitruncated 8-orthoplexTericelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>645120</td></tr><tr><th>166</th><td></td><td>t0,1,3,4,5{36,4}</td><td>Pentisteriruncitruncated 8-orthoplexTericelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>645120</td></tr><tr><th>167</th><td></td><td>t0,2,3,4,5{36,4}</td><td>Pentisteriruncicantellated 8-orthoplexTericelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>645120</td></tr><tr><th>168</th><td></td><td>t1,2,3,4,5{36,4}</td><td>Bisteriruncicantitruncated 8-orthoplexGreat bicellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2903040</td><td>645120</td></tr><tr><th>169</th><td></td><td>t0,1,2,3,6{36,4}</td><td>Hexiruncicantitruncated 8-orthoplexPetigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5160960</td><td>860160</td></tr><tr><th>170</th><td></td><td>t0,1,2,4,6{36,4}</td><td>Hexistericantitruncated 8-orthoplexPeticelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7741440</td><td>1290240</td></tr><tr><th>171</th><td></td><td>t0,1,3,4,6{36,4}</td><td>Hexisteriruncitruncated 8-orthoplexPeticelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>172</th><td></td><td>t0,2,3,4,6{36,4}</td><td>Hexisteriruncicantellated 8-orthoplexPeticelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>173</th><td></td><td>t1,2,3,4,6{36,4}</td><td>Bipentiruncicantitruncated 8-orthoplexBiterigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6451200</td><td>1290240</td></tr><tr><th>174</th><td></td><td>t0,1,2,5,6{36,4}</td><td>Hexipenticantitruncated 8-orthoplexPetiterigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>175</th><td></td><td>t0,1,3,5,6{36,4}</td><td>Hexipentiruncitruncated 8-orthoplexPetiteriprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>176</th><td></td><td>t0,2,3,5,6{36,4}</td><td>Hexipentiruncicantellated 8-orthoplexPetiteriprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6451200</td><td>1290240</td></tr><tr><th>177</th><td></td><td>t1,2,3,5,6{36,4}</td><td>Bipentistericantitruncated 8-orthoplexBitericelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td></tr><tr><th>178</th><td></td><td>t0,1,4,5,6{36,4}</td><td>Hexipentisteritruncated 8-orthoplexPetitericellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>179</th><td></td><td>t0,2,4,5,6{36,4}</td><td>Hexipentistericantellated 8-orthoplexPetitericellirhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>180</th><td></td><td>t1,2,3,5,6{4,36}</td><td>Bipentistericantitruncated 8-cubeBitericelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td></tr><tr><th>181</th><td></td><td>t0,3,4,5,6{36,4}</td><td>Hexipentisteriruncinated 8-orthoplexPetitericelliprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>182</th><td></td><td>t1,2,3,4,6{4,36}</td><td>Bipentiruncicantitruncated 8-cubeBiterigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6451200</td><td>1290240</td></tr><tr><th>183</th><td></td><td>t1,2,3,4,5{4,36}</td><td>Bisteriruncicantitruncated 8-cubeGreat bicellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3440640</td><td>860160</td></tr><tr><th>184</th><td></td><td>t0,1,2,3,7{36,4}</td><td>Heptiruncicantitruncated 8-orthoplexExigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>185</th><td></td><td>t0,1,2,4,7{36,4}</td><td>Heptistericantitruncated 8-orthoplexExicelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>186</th><td></td><td>t0,1,3,4,7{36,4}</td><td>Heptisteriruncitruncated 8-orthoplexExicelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>187</th><td></td><td>t0,2,3,4,7{36,4}</td><td>Heptisteriruncicantellated 8-orthoplexExicelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>188</th><td></td><td>t0,3,4,5,6{4,36}</td><td>Hexipentisteriruncinated 8-cubePetitericelliprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>189</th><td></td><td>t0,1,2,5,7{36,4}</td><td>Heptipenticantitruncated 8-orthoplexExiterigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>190</th><td></td><td>t0,1,3,5,7{36,4}</td><td>Heptipentiruncitruncated 8-orthoplexExiteriprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8386560</td><td>1290240</td></tr><tr><th>191</th><td></td><td>t0,2,3,5,7{36,4}</td><td>Heptipentiruncicantellated 8-orthoplexExiteriprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7741440</td><td>1290240</td></tr><tr><th>192</th><td></td><td>t0,2,4,5,6{4,36}</td><td>Hexipentistericantellated 8-cubePetitericellirhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>193</th><td></td><td>t0,1,4,5,7{36,4}</td><td>Heptipentisteritruncated 8-orthoplexExitericellitruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>194</th><td></td><td>t0,2,3,5,7{4,36}</td><td>Heptipentiruncicantellated 8-cubeExiteriprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7741440</td><td>1290240</td></tr><tr><th>195</th><td></td><td>t0,2,3,5,6{4,36}</td><td>Hexipentiruncicantellated 8-cubePetiteriprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6451200</td><td>1290240</td></tr><tr><th>196</th><td></td><td>t0,2,3,4,7{4,36}</td><td>Heptisteriruncicantellated 8-cubeExicelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>197</th><td></td><td>t0,2,3,4,6{4,36}</td><td>Hexisteriruncicantellated 8-cubePeticelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>198</th><td></td><td>t0,2,3,4,5{4,36}</td><td>Pentisteriruncicantellated 8-cubeTericelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>860160</td></tr><tr><th>199</th><td></td><td>t0,1,2,6,7{36,4}</td><td>Heptihexicantitruncated 8-orthoplexExipetigreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>200</th><td></td><td>t0,1,3,6,7{36,4}</td><td>Heptihexiruncitruncated 8-orthoplexExipetiprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>201</th><td></td><td>t0,1,4,5,7{4,36}</td><td>Heptipentisteritruncated 8-cubeExitericellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>202</th><td></td><td>t0,1,4,5,6{4,36}</td><td>Hexipentisteritruncated 8-cubePetitericellitruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>203</th><td></td><td>t0,1,3,6,7{4,36}</td><td>Heptihexiruncitruncated 8-cubeExipetiprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>204</th><td></td><td>t0,1,3,5,7{4,36}</td><td>Heptipentiruncitruncated 8-cubeExiteriprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8386560</td><td>1290240</td></tr><tr><th>205</th><td></td><td>t0,1,3,5,6{4,36}</td><td>Hexipentiruncitruncated 8-cubePetiteriprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>206</th><td></td><td>t0,1,3,4,7{4,36}</td><td>Heptisteriruncitruncated 8-cubeExicelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>207</th><td></td><td>t0,1,3,4,6{4,36}</td><td>Hexisteriruncitruncated 8-cubePeticelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7096320</td><td>1290240</td></tr><tr><th>208</th><td></td><td>t0,1,3,4,5{4,36}</td><td>Pentisteriruncitruncated 8-cubeTericelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>860160</td></tr><tr><th>209</th><td></td><td>t0,1,2,6,7{4,36}</td><td>Heptihexicantitruncated 8-cubeExipetigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>210</th><td></td><td>t0,1,2,5,7{4,36}</td><td>Heptipenticantitruncated 8-cubeExiterigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>211</th><td></td><td>t0,1,2,5,6{4,36}</td><td>Hexipenticantitruncated 8-cubePetiterigreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td></tr><tr><th>212</th><td></td><td>t0,1,2,4,7{4,36}</td><td>Heptistericantitruncated 8-cubeExicelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5591040</td><td>860160</td></tr><tr><th>213</th><td></td><td>t0,1,2,4,6{4,36}</td><td>Hexistericantitruncated 8-cubePeticelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>7741440</td><td>1290240</td></tr><tr><th>214</th><td></td><td>t0,1,2,4,5{4,36}</td><td>Pentistericantitruncated 8-cubeTericelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>860160</td></tr><tr><th>215</th><td></td><td>t0,1,2,3,7{4,36}</td><td>Heptiruncicantitruncated 8-cubeExigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td></tr><tr><th>216</th><td></td><td>t0,1,2,3,6{4,36}</td><td>Hexiruncicantitruncated 8-cubePetigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5160960</td><td>860160</td></tr><tr><th>217</th><td></td><td>t0,1,2,3,5{4,36}</td><td>Pentiruncicantitruncated 8-cubeTerigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4730880</td><td>860160</td></tr><tr><th>218</th><td></td><td>t0,1,2,3,4{4,36}</td><td>Steriruncicantitruncated 8-cubeGreat cellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1720320</td><td>430080</td></tr><tr><th>219</th><td></td><td>t0,1,2,3,4,5{36,4}</td><td>Pentisteriruncicantitruncated 8-orthoplexGreat terated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td></tr><tr><th>220</th><td></td><td>t0,1,2,3,4,6{36,4}</td><td>Hexisteriruncicantitruncated 8-orthoplexPetigreatocellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>221</th><td></td><td>t0,1,2,3,5,6{36,4}</td><td>Hexipentiruncicantitruncated 8-orthoplexPetiterigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>222</th><td></td><td>t0,1,2,4,5,6{36,4}</td><td>Hexipentistericantitruncated 8-orthoplexPetitericelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>223</th><td></td><td>t0,1,3,4,5,6{36,4}</td><td>Hexipentisteriruncitruncated 8-orthoplexPetitericelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>224</th><td></td><td>t0,2,3,4,5,6{36,4}</td><td>Hexipentisteriruncicantellated 8-orthoplexPetitericelliprismatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>225</th><td></td><td>t1,2,3,4,5,6{4,36}</td><td>Bipentisteriruncicantitruncated 8-cubeGreat biteri-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>10321920</td><td>2580480</td></tr><tr><th>226</th><td></td><td>t0,1,2,3,4,7{36,4}</td><td>Heptisteriruncicantitruncated 8-orthoplexExigreatocellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8601600</td><td>1720320</td></tr><tr><th>227</th><td></td><td>t0,1,2,3,5,7{36,4}</td><td>Heptipentiruncicantitruncated 8-orthoplexExiterigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14192640</td><td>2580480</td></tr><tr><th>228</th><td></td><td>t0,1,2,4,5,7{36,4}</td><td>Heptipentistericantitruncated 8-orthoplexExitericelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>229</th><td></td><td>t0,1,3,4,5,7{36,4}</td><td>Heptipentisteriruncitruncated 8-orthoplexExitericelliprismatotruncated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>230</th><td></td><td>t0,2,3,4,5,7{4,36}</td><td>Heptipentisteriruncicantellated 8-cubeExitericelliprismatorhombi-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>231</th><td></td><td>t0,2,3,4,5,6{4,36}</td><td>Hexipentisteriruncicantellated 8-cubePetitericelliprismatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>232</th><td></td><td>t0,1,2,3,6,7{36,4}</td><td>Heptihexiruncicantitruncated 8-orthoplexExipetigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8601600</td><td>1720320</td></tr><tr><th>233</th><td></td><td>t0,1,2,4,6,7{36,4}</td><td>Heptihexistericantitruncated 8-orthoplexExipeticelligreatorhombated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14192640</td><td>2580480</td></tr><tr><th>234</th><td></td><td>t0,1,3,4,6,7{4,36}</td><td>Heptihexisteriruncitruncated 8-cubeExipeticelliprismatotrunki-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>235</th><td></td><td>t0,1,3,4,5,7{4,36}</td><td>Heptipentisteriruncitruncated 8-cubeExitericelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>236</th><td></td><td>t0,1,3,4,5,6{4,36}</td><td>Hexipentisteriruncitruncated 8-cubePetitericelliprismatotruncated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>237</th><td></td><td>t0,1,2,5,6,7{4,36}</td><td>Heptihexipenticantitruncated 8-cubeExipetiterigreatorhombi-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8601600</td><td>1720320</td></tr><tr><th>238</th><td></td><td>t0,1,2,4,6,7{4,36}</td><td>Heptihexistericantitruncated 8-cubeExipeticelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14192640</td><td>2580480</td></tr><tr><th>239</th><td></td><td>t0,1,2,4,5,7{4,36}</td><td>Heptipentistericantitruncated 8-cubeExitericelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>240</th><td></td><td>t0,1,2,4,5,6{4,36}</td><td>Hexipentistericantitruncated 8-cubePetitericelligreatorhombated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>241</th><td></td><td>t0,1,2,3,6,7{4,36}</td><td>Heptihexiruncicantitruncated 8-cubeExipetigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8601600</td><td>1720320</td></tr><tr><th>242</th><td></td><td>t0,1,2,3,5,7{4,36}</td><td>Heptipentiruncicantitruncated 8-cubeExiterigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14192640</td><td>2580480</td></tr><tr><th>243</th><td></td><td>t0,1,2,3,5,6{4,36}</td><td>Hexipentiruncicantitruncated 8-cubePetiterigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>11612160</td><td>2580480</td></tr><tr><th>244</th><td></td><td>t0,1,2,3,4,7{4,36}</td><td>Heptisteriruncicantitruncated 8-cubeExigreatocellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>8601600</td><td>1720320</td></tr><tr><th>245</th><td></td><td>t0,1,2,3,4,6{4,36}</td><td>Hexisteriruncicantitruncated 8-cubePetigreatocellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>12902400</td><td>2580480</td></tr><tr><th>246</th><td></td><td>t0,1,2,3,4,5{4,36}</td><td>Pentisteriruncicantitruncated 8-cubeGreat terated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6881280</td><td>1720320</td></tr><tr><th>247</th><td></td><td>t0,1,2,3,4,5,6{36,4}</td><td>Hexipentisteriruncicantitruncated 8-orthoplexGreat petated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>20643840</td><td>5160960</td></tr><tr><th>248</th><td></td><td>t0,1,2,3,4,5,7{36,4}</td><td>Heptipentisteriruncicantitruncated 8-orthoplexExigreatoterated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>249</th><td></td><td>t0,1,2,3,4,6,7{36,4}</td><td>Heptihexisteriruncicantitruncated 8-orthoplexExipetigreatocellated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>250</th><td></td><td>t0,1,2,3,5,6,7{36,4}</td><td>Heptihexipentiruncicantitruncated 8-orthoplexExipetiterigreatoprismated diacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>251</th><td></td><td>t0,1,2,3,5,6,7{4,36}</td><td>Heptihexipentiruncicantitruncated 8-cubeExipetiterigreatoprismated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>252</th><td></td><td>t0,1,2,3,4,6,7{4,36}</td><td>Heptihexisteriruncicantitruncated 8-cubeExipetigreatocellated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>253</th><td></td><td>t0,1,2,3,4,5,7{4,36}</td><td>Heptipentisteriruncicantitruncated 8-cubeExigreatoterated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23224320</td><td>5160960</td></tr><tr><th>254</th><td></td><td>t0,1,2,3,4,5,6{4,36}</td><td>Hexipentisteriruncicantitruncated 8-cubeGreat petated octeract</td><td></td><td></td><td></td><td></td><td></td><td></td><td>20643840</td><td>5160960</td></tr><tr><th>255</th><td></td><td>t0,1,2,3,4,5,6,7{4,36}</td><td>Omnitruncated 8-cubeGreat exi-octeractidiacosipentacontahexazetton</td><td></td><td></td><td></td><td></td><td></td><td></td><td>41287680</td><td>10321920</td></tr></tbody></table>
<h3>The D8 family</h3>
<p>The D8 family has symmetry of order 5,160,960 (8 <a href="/facts/Factorial/kkfy1Bwe">factorial</a> x 27).
</p><p>This family has 191 Wythoffian uniform polytopes, from <i>3x64-1</i> permutations of the D8 <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a> with one or more rings. 127 (2x64-1) are repeated from the B8 family and 64 are unique to this family, all listed below.
</p><p>See <a href="/facts/List_of_D8_polytopes/BVhPD0rG">list of D8 polytopes</a> for Coxeter plane graphs of these polytopes.
</p>
<table><tbody><tr><th colspan="15">D8 uniform polytopes</th></tr><tr><th rowspan="2">#</th><th rowspan="2"><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></th><th rowspan="2">Name</th><th rowspan="2">Base point(Alternately signed)</th><th colspan="8">Element counts</th><th rowspan="2">Circumrad</th></tr><tr><th>7</th><th>6</th><th>5</th><th>4</th><th>3</th><th>2</th><th>1</th><th>0</th></tr><tr><th>1</th><td>= </td><td><a href="/facts/8-demicube/sWAomIhw">8-demicube</a>h{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,1,1,1)</td><td>144</td><td>1136</td><td>4032</td><td>8288</td><td>10752</td><td>7168</td><td>1792</td><td>128</td><td>1.0000000</td></tr><tr><th>2</th><td>= </td><td><a href="/facts/Cantic_8-cube/80Lj88aQ">cantic 8-cube</a>h2{4,3,3,3,3,3,3}</td><td>(1,1,3,3,3,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>23296</td><td>3584</td><td>2.6457512</td></tr><tr><th>3</th><td>= </td><td><a href="/facts/Runcic_8-cube/M93v3h3c">runcic 8-cube</a>h3{4,3,3,3,3,3,3}</td><td>(1,1,1,3,3,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>64512</td><td>7168</td><td>2.4494896</td></tr><tr><th>4</th><td>= </td><td><a href="/facts/Steric_8-cube/M93v3h3c">steric 8-cube</a>h4{4,3,3,3,3,3,3}</td><td>(1,1,1,1,3,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>98560</td><td>8960</td><td>2.2360678</td></tr><tr><th>5</th><td>= </td><td><a href="/facts/Pentic_8-cube/M93v3h3c">pentic 8-cube</a>h5{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,3,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>89600</td><td>7168</td><td>1.9999999</td></tr><tr><th>6</th><td>= </td><td><a href="/facts/Hexic_8-cube/M93v3h3c">hexic 8-cube</a>h6{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,1,3,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>48384</td><td>3584</td><td>1.7320508</td></tr><tr><th>7</th><td>= </td><td><a href="/facts/Heptic_8-cube/M93v3h3c">heptic 8-cube</a>h7{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,1,1,3)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>14336</td><td>1024</td><td>1.4142135</td></tr><tr><th>8</th><td>= </td><td>runcicantic 8-cubeh2,3{4,3,3,3,3,3,3}</td><td>(1,1,3,5,5,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>86016</td><td>21504</td><td>4.1231055</td></tr><tr><th>9</th><td>= </td><td>stericantic 8-cubeh2,4{4,3,3,3,3,3,3}</td><td>(1,1,3,3,5,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>349440</td><td>53760</td><td>3.8729835</td></tr><tr><th>10</th><td>= </td><td>steriruncic 8-cubeh3,4{4,3,3,3,3,3,3}</td><td>(1,1,1,3,5,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>179200</td><td>35840</td><td>3.7416575</td></tr><tr><th>11</th><td>= </td><td>penticantic 8-cubeh2,5{4,3,3,3,3,3,3}</td><td>(1,1,3,3,3,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>573440</td><td>71680</td><td>3.6055512</td></tr><tr><th>12</th><td>= </td><td>pentiruncic 8-cubeh3,5{4,3,3,3,3,3,3}</td><td>(1,1,1,3,3,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>537600</td><td>71680</td><td>3.4641016</td></tr><tr><th>13</th><td>= </td><td>pentisteric 8-cubeh4,5{4,3,3,3,3,3,3}</td><td>(1,1,1,1,3,5,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>232960</td><td>35840</td><td>3.3166249</td></tr><tr><th>14</th><td>= </td><td>hexicantic 8-cubeh2,6{4,3,3,3,3,3,3}</td><td>(1,1,3,3,3,3,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>456960</td><td>53760</td><td>3.3166249</td></tr><tr><th>15</th><td>= </td><td>hexicruncic 8-cubeh3,6{4,3,3,3,3,3,3}</td><td>(1,1,1,3,3,3,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>645120</td><td>71680</td><td>3.1622777</td></tr><tr><th>16</th><td>= </td><td>hexisteric 8-cubeh4,6{4,3,3,3,3,3,3}</td><td>(1,1,1,1,3,3,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>483840</td><td>53760</td><td>3</td></tr><tr><th>17</th><td>= </td><td>hexipentic 8-cubeh5,6{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,3,5,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>182784</td><td>21504</td><td>2.8284271</td></tr><tr><th>18</th><td>= </td><td>hepticantic 8-cubeh2,7{4,3,3,3,3,3,3}</td><td>(1,1,3,3,3,3,3,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>172032</td><td>21504</td><td>3</td></tr><tr><th>19</th><td>= </td><td>heptiruncic 8-cubeh3,7{4,3,3,3,3,3,3}</td><td>(1,1,1,3,3,3,3,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>340480</td><td>35840</td><td>2.8284271</td></tr><tr><th>20</th><td>= </td><td>heptsteric 8-cubeh4,7{4,3,3,3,3,3,3}</td><td>(1,1,1,1,3,3,3,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>376320</td><td>35840</td><td>2.6457512</td></tr><tr><th>21</th><td>= </td><td>heptipentic 8-cubeh5,7{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,3,3,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>236544</td><td>21504</td><td>2.4494898</td></tr><tr><th>22</th><td>= </td><td>heptihexic 8-cubeh6,7{4,3,3,3,3,3,3}</td><td>(1,1,1,1,1,1,3,5)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>78848</td><td>7168</td><td>2.236068</td></tr><tr><th>23</th><td>= </td><td>steriruncicantic 8-cubeh2,3,4{4,36}</td><td>(1,1,3,5,7,7,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>430080</td><td>107520</td><td>5.3851647</td></tr><tr><th>24</th><td>= </td><td>pentiruncicantic 8-cubeh2,3,5{4,36}</td><td>(1,1,3,5,5,7,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1182720</td><td>215040</td><td>5.0990195</td></tr><tr><th>25</th><td>= </td><td>pentistericantic 8-cubeh2,4,5{4,36}</td><td>(1,1,3,3,5,7,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1075200</td><td>215040</td><td>4.8989797</td></tr><tr><th>26</th><td>= </td><td>pentisterirunic 8-cubeh3,4,5{4,36}</td><td>(1,1,1,3,5,7,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>716800</td><td>143360</td><td>4.7958317</td></tr><tr><th>27</th><td>= </td><td>hexiruncicantic 8-cubeh2,3,6{4,36}</td><td>(1,1,3,5,5,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td><td>4.7958317</td></tr><tr><th>28</th><td>= </td><td>hexistericantic 8-cubeh2,4,6{4,36}</td><td>(1,1,3,3,5,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2096640</td><td>322560</td><td>4.5825758</td></tr><tr><th>29</th><td>= </td><td>hexisterirunic 8-cubeh3,4,6{4,36}</td><td>(1,1,1,3,5,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td><td>4.472136</td></tr><tr><th>30</th><td>= </td><td>hexipenticantic 8-cubeh2,5,6{4,36}</td><td>(1,1,3,3,3,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1290240</td><td>215040</td><td>4.3588991</td></tr><tr><th>31</th><td>= </td><td>hexipentirunic 8-cubeh3,5,6{4,36}</td><td>(1,1,1,3,3,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1397760</td><td>215040</td><td>4.2426405</td></tr><tr><th>32</th><td>= </td><td>hexipentisteric 8-cubeh4,5,6{4,36}</td><td>(1,1,1,1,3,5,7,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>698880</td><td>107520</td><td>4.1231055</td></tr><tr><th>33</th><td>= </td><td>heptiruncicantic 8-cubeh2,3,7{4,36}</td><td>(1,1,3,5,5,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>591360</td><td>107520</td><td>4.472136</td></tr><tr><th>34</th><td>= </td><td>heptistericantic 8-cubeh2,4,7{4,36}</td><td>(1,1,3,3,5,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1505280</td><td>215040</td><td>4.2426405</td></tr><tr><th>35</th><td>= </td><td>heptisterruncic 8-cubeh3,4,7{4,36}</td><td>(1,1,1,3,5,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>860160</td><td>143360</td><td>4.1231055</td></tr><tr><th>36</th><td>= </td><td>heptipenticantic 8-cubeh2,5,7{4,36}</td><td>(1,1,3,3,3,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td><td>4</td></tr><tr><th>37</th><td>= </td><td>heptipentiruncic 8-cubeh3,5,7{4,36}</td><td>(1,1,1,3,3,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1612800</td><td>215040</td><td>3.8729835</td></tr><tr><th>38</th><td>= </td><td>heptipentisteric 8-cubeh4,5,7{4,36}</td><td>(1,1,1,1,3,5,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>752640</td><td>107520</td><td>3.7416575</td></tr><tr><th>39</th><td>= </td><td>heptihexicantic 8-cubeh2,6,7{4,36}</td><td>(1,1,3,3,3,3,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>752640</td><td>107520</td><td>3.7416575</td></tr><tr><th>40</th><td>= </td><td>heptihexiruncic 8-cubeh3,6,7{4,36}</td><td>(1,1,1,3,3,3,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1146880</td><td>143360</td><td>3.6055512</td></tr><tr><th>41</th><td>= </td><td>heptihexisteric 8-cubeh4,6,7{4,36}</td><td>(1,1,1,1,3,3,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>913920</td><td>107520</td><td>3.4641016</td></tr><tr><th>42</th><td>= </td><td>heptihexipentic 8-cubeh5,6,7{4,36}</td><td>(1,1,1,1,1,3,5,7)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>365568</td><td>43008</td><td>3.3166249</td></tr><tr><th>43</th><td>= </td><td>pentisteriruncicantic 8-cubeh2,3,4,5{4,36}</td><td>(1,1,3,5,7,9,9,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1720320</td><td>430080</td><td>6.4031243</td></tr><tr><th>44</th><td>= </td><td>hexisteriruncicantic 8-cubeh2,3,4,6{4,36}</td><td>(1,1,3,5,7,7,9,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>645120</td><td>6.0827627</td></tr><tr><th>45</th><td>= </td><td>hexipentiruncicantic 8-cubeh2,3,5,6{4,36}</td><td>(1,1,3,5,5,7,9,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2903040</td><td>645120</td><td>5.8309517</td></tr><tr><th>46</th><td>= </td><td>hexipentistericantic 8-cubeh2,4,5,6{4,36}</td><td>(1,1,3,3,5,7,9,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3225600</td><td>645120</td><td>5.6568542</td></tr><tr><th>47</th><td>= </td><td>hexipentisteriruncic 8-cubeh3,4,5,6{4,36}</td><td>(1,1,1,3,5,7,9,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2150400</td><td>430080</td><td>5.5677648</td></tr><tr><th>48</th><td>= </td><td>heptsteriruncicantic 8-cubeh2,3,4,7{4,36}</td><td>(1,1,3,5,7,7,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2150400</td><td>430080</td><td>5.7445626</td></tr><tr><th>49</th><td>= </td><td>heptipentiruncicantic 8-cubeh2,3,5,7{4,36}</td><td>(1,1,3,5,5,7,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3548160</td><td>645120</td><td>5.4772258</td></tr><tr><th>50</th><td>= </td><td>heptipentistericantic 8-cubeh2,4,5,7{4,36}</td><td>(1,1,3,3,5,7,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3548160</td><td>645120</td><td>5.291503</td></tr><tr><th>51</th><td>= </td><td>heptipentisteriruncic 8-cubeh3,4,5,7{4,36}</td><td>(1,1,1,3,5,7,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td><td>5.1961527</td></tr><tr><th>52</th><td>= </td><td>heptihexiruncicantic 8-cubeh2,3,6,7{4,36}</td><td>(1,1,3,5,5,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2150400</td><td>430080</td><td>5.1961527</td></tr><tr><th>53</th><td>= </td><td>heptihexistericantic 8-cubeh2,4,6,7{4,36}</td><td>(1,1,3,3,5,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3870720</td><td>645120</td><td>5</td></tr><tr><th>54</th><td>= </td><td>heptihexisteriruncic 8-cubeh3,4,6,7{4,36}</td><td>(1,1,1,3,5,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2365440</td><td>430080</td><td>4.8989797</td></tr><tr><th>55</th><td>= </td><td>heptihexipenticantic 8-cubeh2,5,6,7{4,36}</td><td>(1,1,3,3,3,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>430080</td><td>4.7958317</td></tr><tr><th>56</th><td>= </td><td>heptihexipentiruncic 8-cubeh3,5,6,7{4,36}</td><td>(1,1,1,3,3,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2795520</td><td>430080</td><td>4.6904159</td></tr><tr><th>57</th><td>= </td><td>heptihexipentisteric 8-cubeh4,5,6,7{4,36}</td><td>(1,1,1,1,3,5,7,9)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1397760</td><td>215040</td><td>4.5825758</td></tr><tr><th>58</th><td>= </td><td>hexipentisteriruncicantic 8-cubeh2,3,4,5,6{4,36}</td><td>(1,1,3,5,7,9,11,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5160960</td><td>1290240</td><td>7.1414285</td></tr><tr><th>59</th><td>= </td><td>heptipentisteriruncicantic 8-cubeh2,3,4,5,7{4,36}</td><td>(1,1,3,5,7,9,9,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td><td>6.78233</td></tr><tr><th>60</th><td>= </td><td>heptihexisteriruncicantic 8-cubeh2,3,4,6,7{4,36}</td><td>(1,1,3,5,7,7,9,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td><td>6.480741</td></tr><tr><th>61</th><td>= </td><td>heptihexipentiruncicantic 8-cubeh2,3,5,6,7{4,36}</td><td>(1,1,3,5,5,7,9,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5806080</td><td>1290240</td><td>6.244998</td></tr><tr><th>62</th><td>= </td><td>heptihexipentistericantic 8-cubeh2,4,5,6,7{4,36}</td><td>(1,1,3,3,5,7,9,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6451200</td><td>1290240</td><td>6.0827627</td></tr><tr><th>63</th><td>= </td><td>heptihexipentisteriruncic 8-cubeh3,4,5,6,7{4,36}</td><td>(1,1,1,3,5,7,9,11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4300800</td><td>860160</td><td>6.0000000</td></tr><tr><th>64</th><td>= </td><td>heptihexipentisteriruncicantic 8-cubeh2,3,4,5,6,7{4,36}</td><td>(1,1,3,5,7,9,11,13)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2580480</td><td>10321920</td><td>7.5498347</td></tr></tbody></table>
<h3>The E8 family</h3>
<p>The E8 family has symmetry order 696,729,600.
</p><p>There are 255 forms based on all permutations of the <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagrams</a> with one or more rings. Eight forms are shown below, 4 single-ringed, 3 truncations (2 rings), and the final omnitruncation are given below. Bowers-style acronym names are given for cross-referencing.
</p><p>See also <a href="/facts/List_of_E8_polytopes/JhQgUPS4">list of E8 polytopes</a> for Coxeter plane graphs of this family.
</p>
<table><tbody><tr><th colspan="15">E8 uniform polytopes</th></tr><tr><th rowspan="2">#</th><th rowspan="2"><a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a></th><th rowspan="2">Names</th><th colspan="8">Element counts</th></tr><tr><th>7-faces</th><th>6-faces</th><th>5-faces</th><th>4-faces</th><th>Cells</th><th>Faces</th><th>Edges</th><th>Vertices</th></tr><tr><td>1</td><td></td><td><a href="/facts/Gosset_4_21_polytope/QFGglCkk">421</a> (fy)</td><td>19440</td><td>207360</td><td>483840</td><td>483840</td><td>241920</td><td>60480</td><td>6720</td><td>240</td></tr><tr><td>2</td><td></td><td>Truncated 421 (tiffy)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>188160</td><td>13440</td></tr><tr><td>3</td><td></td><td><a href="/facts/Rectified_4_21_polytope/QFGglCkk">Rectified 421</a> (riffy)</td><td>19680</td><td>375840</td><td>1935360</td><td>3386880</td><td>2661120</td><td>1028160</td><td>181440</td><td>6720</td></tr><tr><td>4</td><td></td><td><a href="/facts/Birectified_4_21_polytope/QFGglCkk">Birectified 421</a> (borfy)</td><td>19680</td><td>382560</td><td>2600640</td><td>7741440</td><td>9918720</td><td>5806080</td><td>1451520</td><td>60480</td></tr><tr><td>5</td><td></td><td><a href="/facts/Trirectified_4_21_polytope/QFGglCkk">Trirectified 421</a> (torfy)</td><td>19680</td><td>382560</td><td>2661120</td><td>9313920</td><td>16934400</td><td>14515200</td><td>4838400</td><td>241920</td></tr><tr><td>6</td><td></td><td><a href="/facts/Rectified_1_42_polytope/DTgYDddB">Rectified 142</a> (buffy)</td><td>19680</td><td>382560</td><td>2661120</td><td>9072000</td><td>16934400</td><td>16934400</td><td>7257600</td><td>483840</td></tr><tr><td>7</td><td></td><td><a href="/facts/Rectified_2_41_polytope/R9z0wNUz">Rectified 241</a> (robay)</td><td>19680</td><td>313440</td><td>1693440</td><td>4717440</td><td>7257600</td><td>5322240</td><td>1451520</td><td>69120</td></tr><tr><td>8</td><td></td><td><a href="/facts/2_41_polytope/R9z0wNUz">241</a> (bay)</td><td>17520</td><td>144960</td><td>544320</td><td>1209600</td><td>1209600</td><td>483840</td><td>69120</td><td>2160</td></tr><tr><td>9</td><td></td><td>Truncated 241</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>138240</td></tr><tr><td>10</td><td></td><td><a href="/facts/1_42_polytope/DTgYDddB">142</a> (bif)</td><td>2400</td><td>106080</td><td>725760</td><td>2298240</td><td>3628800</td><td>2419200</td><td>483840</td><td>17280</td></tr><tr><td>11</td><td></td><td>Truncated 142</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>967680</td></tr><tr><td>12</td><td></td><td>Omnitruncated 421</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>696729600</td></tr></tbody></table>
<h2 id="regular-and-uniform-honeycombs">Regular and uniform honeycombs</h2>

<p>There are five fundamental affine <a href="/facts/Coxeter_groups/bgzHFm1Q">Coxeter groups</a> that generate regular and uniform tessellations in 7-space:
</p>
<table><tbody><tr><th>#</th><th colspan="2"><a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a></th><th><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></th><th>Forms</th></tr><tr><td>1</td><td>                                                                        A                ~                                                          7                                {\displaystyle {\tilde {A}}_{7}}  </td><td>[3[8]]</td><td></td><td>29</td></tr><tr><td>2</td><td>                                                                        C                ~                                                          7                                {\displaystyle {\tilde {C}}_{7}}  </td><td>[4,35,4]</td><td></td><td>135</td></tr><tr><td>3</td><td>                                                                        B                ~                                                          7                                {\displaystyle {\tilde {B}}_{7}}  </td><td>[4,34,31,1]</td><td></td><td>191 (64 new)</td></tr><tr><td>4</td><td>                                                                        D                ~                                                          7                                {\displaystyle {\tilde {D}}_{7}}  </td><td>[31,1,33,31,1]</td><td></td><td>77 (10 new)</td></tr><tr><td>5</td><td>                                                                        E                ~                                                          7                                {\displaystyle {\tilde {E}}_{7}}  </td><td>[33,3,1]</td><td></td><td>143</td></tr></tbody></table>
<p>Regular and uniform tessellations include:
</p>
<ul><li>
  
    
      
        
          
            
              
                A
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {A}}_{7}}
  
 29 uniquely ringed forms, including:
<ul><li><a href="/facts/7-simplex_honeycomb/dq8hy2lI">7-simplex honeycomb</a>: {3[8]} </li></ul></li>
<li>
  
    
      
        
          
            
              
                C
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {C}}_{7}}
  
 135 uniquely ringed forms, including:
<ul><li>Regular <a href="/facts/7-cube_honeycomb/Im2bVBf7">7-cube honeycomb</a>: {4,34,4} = {4,34,31,1},  = </li></ul></li>
<li>
  
    
      
        
          
            
              
                B
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {B}}_{7}}
  
 191 uniquely ringed forms, 127 shared with 
  
    
      
        
          
            
              
                C
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {C}}_{7}}
  
, and 64 new, including:
<ul><li><a href="/facts/7-demicube_honeycomb/QYm4RCGK">7-demicube honeycomb</a>: h{4,34,4} = {31,1,34,4},  = </li></ul></li>
<li>
  
    
      
        
          
            
              
                D
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {D}}_{7}}
  
, [31,1,33,31,1]: 77 unique ring permutations, and 10 are new, the first Coxeter called a <a href="/facts/Quarter_7-cubic_honeycomb/GjVHMBLq">quarter 7-cubic honeycomb</a>.
<ul><li>, , , , , , , , , </li></ul></li>
<li>
  
    
      
        
          
            
              
                E
                ~
              
            
          
          
            7
          
        
      
    
    {\displaystyle {\tilde {E}}_{7}}
  
 143 uniquely ringed forms, including:
<ul><li><a href="/facts/1_33_honeycomb/tYL93yF1">133 honeycomb</a>: {3,33,3}, </li>
<li><a href="/facts/3_31_honeycomb/VlInrcea">331 honeycomb</a>: {3,3,3,33,1}, </li></ul></li></ul>
<h3>Regular and uniform hyperbolic honeycombs</h3>
<p>There are no compact hyperbolic Coxeter groups of rank 8, groups that can generate honeycombs with all finite facets, and a finite <a href="/facts/Vertex_figure/3u2ySK0C">vertex figure</a>. However, there are <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">4 paracompact hyperbolic Coxeter groups</a> of rank 8, each generating uniform honeycombs in 7-space as permutations of rings of the Coxeter diagrams.
</p>
<table><tbody><tr><td>                                                                        P                ¯                                                          7                                {\displaystyle {\bar {P}}_{7}}   = [3,3[7]]:</td><td>                                                                        Q                ¯                                                          7                                {\displaystyle {\bar {Q}}_{7}}   = [31,1,32,32,1]: </td><td>                                                                        S                ¯                                                          7                                {\displaystyle {\bar {S}}_{7}}   = [4,33,32,1]: </td><td>                                                                        T                ¯                                                          7                                {\displaystyle {\bar {T}}_{7}}   = [33,2,2]:</td></tr></tbody></table>

<ul><li><a href="/facts/Thorold_Gosset/3wvHtGPn">T. Gosset</a>: <i>On the Regular and Semi-Regular Figures in Space of n Dimensions</i>, <a href="/facts/Messenger_of_Mathematics/anb7QjuX">Messenger of Mathematics</a>, Macmillan, 1900</li>
<li><a href="/facts/Alicia_Boole_Stott/FoqXBA5T">A. Boole Stott</a>: <i>Geometrical deduction of semiregular from regular polytopes and space fillings</i>, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910</li>
<li><a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">H.S.M. Coxeter</a>:
<ul><li>H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: <i>Uniform Polyhedra</i>, Philosophical Transactions of the Royal Society of London, Londne, 1954</li>
<li>H.S.M. Coxeter, <i>Regular Polytopes</i>, 3rd Edition, Dover New York, 1973</li></ul></li>
<li>Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-471-01003-6 <a href="http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html">Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter</a>
<ul><li>(Paper 22) H.S.M. Coxeter, <i>Regular and Semi Regular Polytopes I</i>, [Math. Zeit. 46 (1940) 380–407, MR 2,10]</li>
<li>(Paper 23) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes II</i>, [Math. Zeit. 188 (1985) 559-591]</li>
<li>(Paper 24) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes III</i>, [Math. Zeit. 200 (1988) 3-45]</li></ul></li>
<li><a href="/facts/Norman_Johnson_(mathematician)/bQtL9w56">N.W. Johnson</a>: <i>The Theory of Uniform Polytopes and Honeycombs</i>, Ph.D. Dissertation, University of Toronto, 1966</li>
<li>Klitzing, Richard. <a href="https://bendwavy.org/klitzing/dimensions/polyzetta.htm">"8D uniform polytopes (polyzetta)"</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.steelpillow.com/polyhedra/ditela.html">Polytope names</a></li>
<li><a href="http://www.polytope.net/hedrondude/topes.htm">Polytopes of Various Dimensions</a></li>
<li><a href="http://tetraspace.alkaline.org/glossary.htm">Multi-dimensional Glossary</a></li></ul>
<table><tbody><tr><th colspan="13"><ul><li>v</li><li>t</li><li>e</li></ul>Fundamental convex <a href="/facts/Regular_polytope/RYTnEF6Q">regular</a> and <a href="/facts/Uniform_polytope/nFcNAzLy">uniform polytopes</a> in dimensions 2–10</th></tr><tr><th><a href="/facts/Coxeter_group/bgzHFm1Q">Family</a></th><td><a href="/facts/Simple_Lie_group/LkHTNYU9"><i>A</i><i>n</i></a></td><td><a href="/facts/Simple_Lie_group/LkHTNYU9"><i>B</i><i>n</i></a></td><td><i>I</i>2(p) / <a href="/facts/Simple_Lie_group/LkHTNYU9"><i>D</i><i>n</i></a></td><td><a href="/facts/E6_(mathematics)/U9YEMtWj"><i>E</i>6</a> / <a href="/facts/E7_(mathematics)/KjFez9PW"><i>E</i>7</a> / <a href="/facts/E8_(mathematics)/NEaKT71H"><i>E</i>8</a> / <a href="/facts/F4_(mathematics)/30H8CQ8v"><i>F</i>4</a> / <a href="/facts/G2_(mathematics)/Bka4pKjQ"><i>G</i>2</a></td><td><a href="/facts/H4_(mathematics)/bgzHFm1Q">Hn</a></td></tr><tr><th><a href="/facts/Regular_polygon/ws89Nhpt">Regular polygon</a></th><td><a href="/facts/Equilateral_triangle/MJomsYDS">Triangle</a></td><td><a href="/facts/Square/JHJeMvmL">Square</a></td><td><a href="/facts/Regular_polygon/ws89Nhpt">p-gon</a></td><td><a href="/facts/Hexagon/DPzuCzWE">Hexagon</a></td><td><a href="/facts/Pentagon/jeHEARHH">Pentagon</a></td></tr><tr><th><a href="/facts/Uniform_polyhedron/PHnprqRC">Uniform polyhedron</a></th><td><a href="/facts/Tetrahedron/7mkSrl6j">Tetrahedron</a></td><td><a href="/facts/Octahedron/G38q92xW">Octahedron</a> • <a href="/facts/Cube/65lUaAqN">Cube</a></td><td><a href="/facts/Tetrahedron/7mkSrl6j">Demicube</a></td><td></td><td><a href="/facts/Regular_dodecahedron/xClYqhcp">Dodecahedron</a> • <a href="/facts/Regular_icosahedron/1U93vmXV">Icosahedron</a></td></tr><tr><th><a href="/facts/Uniform_polychoron/NHxomMxC">Uniform polychoron</a></th><td><a href="/facts/5-cell/Rh6lwDcc">Pentachoron</a></td><td><a href="/facts/16-cell/X0YAfobw">16-cell</a> • <a href="/facts/Tesseract/tlqouBoU">Tesseract</a></td><td><a href="/facts/16-cell/X0YAfobw">Demitesseract</a></td><td><a href="/facts/24-cell/tfoGnlAD">24-cell</a></td><td><a href="/facts/120-cell/W4nroBjJ">120-cell</a> • <a href="/facts/600-cell/tNBtDUe9">600-cell</a></td></tr><tr><th><a href="/facts/Uniform_5-polytope/mqxsoqwY">Uniform 5-polytope</a></th><td><a href="/facts/5-simplex/KIfBFfhl">5-simplex</a></td><td><a href="/facts/5-orthoplex/vU1TvdQ1">5-orthoplex</a> • <a href="/facts/5-cube/XABdhjof">5-cube</a></td><td><a href="/facts/5-demicube/zvCeNbU2">5-demicube</a></td><td></td><td></td></tr><tr><th><a href="/facts/Uniform_6-polytope/pxqFTw2F">Uniform 6-polytope</a></th><td><a href="/facts/6-simplex/mInfSIeH">6-simplex</a></td><td><a href="/facts/6-orthoplex/eGV6o0ol">6-orthoplex</a> • <a href="/facts/6-cube/xN74tdD0">6-cube</a></td><td><a href="/facts/6-demicube/1oTufnFp">6-demicube</a></td><td><a href="/facts/1_22_polytope/7XXjWGQ8">122</a> • <a href="/facts/2_21_polytope/nF3nYaQk">221</a></td><td></td></tr><tr><th><a href="/facts/Uniform_7-polytope/suCJSvTN">Uniform 7-polytope</a></th><td><a href="/facts/7-simplex/6DwtPplH">7-simplex</a></td><td><a href="/facts/7-orthoplex/mIJa3rQp">7-orthoplex</a> • <a href="/facts/7-cube/4af1W7tq">7-cube</a></td><td><a href="/facts/7-demicube/fGVUTvTI">7-demicube</a></td><td><a href="/facts/1_32_polytope/um16Pd2V">132</a> • <a href="/facts/2_31_polytope/zkjkKJ6X">231</a> • <a href="/facts/3_21_polytope/AEUzwA1A">321</a></td><td></td></tr><tr><th>Uniform 8-polytope</th><td><a href="/facts/8-simplex/QUhcnmk2">8-simplex</a></td><td><a href="/facts/8-orthoplex/dXFkXtPn">8-orthoplex</a> • <a href="/facts/8-cube/vEpKH3le">8-cube</a></td><td><a href="/facts/8-demicube/sWAomIhw">8-demicube</a></td><td><a href="/facts/1_42_polytope/DTgYDddB">142</a> • <a href="/facts/2_41_polytope/R9z0wNUz">241</a> • <a href="/facts/4_21_polytope/QFGglCkk">421</a></td><td></td></tr><tr><th><a href="/facts/Uniform_9-polytope/UdFL9ns2">Uniform 9-polytope</a></th><td><a href="/facts/9-simplex/dHV7qhxN">9-simplex</a></td><td><a href="/facts/9-orthoplex/D7LjUcAh">9-orthoplex</a> • <a href="/facts/9-cube/RNgCPzoM">9-cube</a></td><td><a href="/facts/9-demicube/dkTpfqss">9-demicube</a></td><td></td><td></td></tr><tr><th><a href="/facts/Uniform_10-polytope/Qc5NglV8">Uniform 10-polytope</a></th><td><a href="/facts/10-simplex/oeft7Qjn">10-simplex</a></td><td><a href="/facts/10-orthoplex/x6ysTC9U">10-orthoplex</a> • <a href="/facts/10-cube/mmmyBfJJ">10-cube</a></td><td><a href="/facts/10-demicube/TskxfLy9">10-demicube</a></td><td></td><td></td></tr><tr><th>Uniform <i>n</i>-<a href="/facts/Polytope/a76nXrL0">polytope</a></th><td><i>n</i>-<a href="/facts/Simplex/0FCfNRN8">simplex</a></td><td><i>n</i>-<a href="/facts/Cross-polytope/erk0byF6">orthoplex</a> • <i>n</i>-<a href="/facts/Hypercube/q2mRPbIz">cube</a></td><td><i>n</i>-<a href="/facts/Demihypercube/ackHKsEa">demicube</a></td><td><a href="/facts/Uniform_1_k2_polytope/eqTstjgl">1k2</a> • <a href="/facts/Uniform_2_k1_polytope/pQv1I7AC">2k1</a> • <a href="/facts/Uniform_k_21_polytope/vv3lWMYd">k21</a></td><td><i>n</i>-<a href="/facts/Pentagonal_polytope/4uxePdKt">pentagonal polytope</a></td></tr><tr><th colspan="13">Topics: <a href="/facts/Polytope_families/Gun0RgmR">Polytope families</a> • <a href="/facts/Regular_polytope/RYTnEF6Q">Regular polytope</a> • <a href="/facts/List_of_regular_polytopes_and_compounds/Kng25Ymq">List of regular polytopes and compounds</a></th></tr></tbody></table>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Richeson, D.; Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy, Princeton, 2008. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Richeson, D.; Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy, Princeton, 2008. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Richeson, D.; Euler's Gem: The Polyhedron Formula and the Birth of Topoplogy, Princeton, 2008. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Uniform 8-polytope open-in-new

Uniform 8-polytope