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7-cubic honeycomb
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<h2 id="related-honeycombs">Related honeycombs</h2> <p>The [4,35,4], , Coxeter group generates 255 permutations of uniform tessellations, 135 with unique symmetry and 134 with unique geometry. The <a href="/facts/Expansion_(geometry)/eMpoRlnm">expanded</a> 7-cubic honeycomb is geometrically identical to the 7-cubic honeycomb. </p><p>The <i>7-cubic honeycomb</i> can be <a href="/facts/Alternation_(geometry)/H2nVs4xj">alternated</a> into the <a href="/facts/7-demicubic_honeycomb/QYm4RCGK">7-demicubic honeycomb</a>, replacing the 7-cubes with <a href="/facts/7-demicube/fGVUTvTI">7-demicubes</a>, and the alternated gaps are filled by <a href="/facts/7-orthoplex/mIJa3rQp">7-orthoplex</a> facets. </p> <h3>Quadritruncated 7-cubic honeycomb</h3> <p>A quadritruncated 7-cubic honeycomb, , contains all <a href="/facts/Tritruncated_7-orthoplex/51j7Iq3F">tritruncated 7-orthoplex</a> facets and is the <a href="/facts/Voronoi_tessellation/AhQY5LD8">Voronoi tessellation</a> of the <a href="/facts/7-demicube_honeycomb/QYm4RCGK">D7* lattice</a>. Facets can be identically colored from a doubled C ~ 7 {\displaystyle {\tilde {C}}_{7}} ×2, [[4,35,4]] symmetry, alternately colored from C ~ 7 {\displaystyle {\tilde {C}}_{7}} , [4,35,4] symmetry, three colors from B ~ 7 {\displaystyle {\tilde {B}}_{7}} , [4,34,31,1] symmetry, and 4 colors from D ~ 7 {\displaystyle {\tilde {D}}_{7}} , [31,1,33,31,1] symmetry. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_regular_polytopes/Kng25Ymq">List of regular polytopes</a></li></ul> <ul><li><a href="/facts/Coxeter/D2l5jWGG">Coxeter, H.S.M.</a> <i><a href="/facts/Regular_Polytopes_(book)/jomuRNha">Regular Polytopes</a></i>, (3rd edition, 1973), Dover edition, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-61480-8 p. 296, Table II: Regular honeycombs</li> <li>Kaleidoscopes: Selected Writings of <a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">H. S. M. Coxeter</a>, 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">[1]</a> <ul><li>(Paper 24) H.S.M. Coxeter, <i>Regular and Semi-Regular Polytopes III</i>, [Math. Zeit. 200 (1988) 3-45]</li></ul></li></ul> <table><tbody><tr><th colspan="7"><ul><li>v</li><li>t</li><li>e</li></ul>Fundamental convex <a href="/facts/Regular_honeycomb/Kng25Ymq">regular</a> and <a href="/facts/Uniform_honeycomb/fGXtrgGF">uniform honeycombs</a> in dimensions 2–9</th></tr><tr><th>Space</th><th><a href="/facts/Coxeter_group/bgzHFm1Q">Family</a></th><td> A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} </td><td> C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} </td><td> B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} </td><td> D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} </td><td> G ~ 2 {\displaystyle {\tilde {G}}_{2}} / F ~ 4 {\displaystyle {\tilde {F}}_{4}} / E ~ n − 1 {\displaystyle {\tilde {E}}_{n-1}} </td></tr><tr><th>E2</th><th><a href="/facts/Uniform_tiling/QVK02ksI">Uniform tiling</a></th><td><a href="/facts/Triangular_tiling/Jx8f8Krh">0[3]</a></td><td><a href="/facts/Square_tiling/3ym86mvv">δ3</a></td><td><a href="/facts/Square_tiling/3ym86mvv">hδ3</a></td><td><a href="/facts/Square_tiling/3ym86mvv">qδ3</a></td><td><a href="/facts/Hexagonal_tiling/HwG5F0YH">Hexagonal</a></td></tr><tr><th>E3</th><th><a href="/facts/Uniform_convex_honeycomb/78IkTl7A">Uniform convex honeycomb</a></th><td><a href="/facts/Tetrahedral-octahedral_honeycomb/mX4CxSvp">0[4]</a></td><td><a href="/facts/Cubic_honeycomb/eMxySFur">δ4</a></td><td><a href="/facts/Tetrahedral-octahedral_honeycomb/mX4CxSvp">hδ4</a></td><td><a href="/facts/Quarter_cubic_honeycomb/22qQazbw">qδ4</a></td><td></td></tr><tr><th>E4</th><th><a href="/facts/Uniform_4-honeycomb/mqxsoqwY">Uniform 4-honeycomb</a></th><td><a href="/facts/5-cell_honeycomb/YgY6eSTr">0[5]</a></td><td><a href="/facts/Tesseractic_honeycomb/fpucRJJn">δ5</a></td><td><a href="/facts/16-cell_honeycomb/lbktV8Nr">hδ5</a></td><td><a href="/facts/Rectified_tesseractic_honeycomb/P266Jc7y">qδ5</a></td><td><a href="/facts/24-cell_honeycomb/foFoK5YX">24-cell honeycomb</a></td></tr><tr><th>E5</th><th><a href="/facts/Uniform_5-honeycomb/pxqFTw2F">Uniform 5-honeycomb</a></th><td><a href="/facts/5-simplex_honeycomb/XSLrRsLz">0[6]</a></td><td><a href="/facts/5-cubic_honeycomb/bqAJvIBI">δ6</a></td><td><a href="/facts/5-demicubic_honeycomb/eYp2lMB8">hδ6</a></td><td><a href="/facts/Quarter_5-cubic_honeycomb/r3AAQHbg">qδ6</a></td><td></td></tr><tr><th>E6</th><th><a href="/facts/Uniform_6-honeycomb/suCJSvTN">Uniform 6-honeycomb</a></th><td><a href="/facts/6-simplex_honeycomb/H7LWND7E">0[7]</a></td><td><a href="/facts/6-cubic_honeycomb/2FdezLvD">δ7</a></td><td><a href="/facts/6-demicubic_honeycomb/oxttB0n0">hδ7</a></td><td><a href="/facts/Quarter_6-cubic_honeycomb/vDRQk9kS">qδ7</a></td><td><a href="/facts/2_22_honeycomb/cvXxbk6L">222</a></td></tr><tr><th>E7</th><th><a href="/facts/Uniform_7-honeycomb/M93v3h3c">Uniform 7-honeycomb</a></th><td><a href="/facts/7-simplex_honeycomb/dq8hy2lI">0[8]</a></td><td>δ8</td><td><a href="/facts/7-demicubic_honeycomb/QYm4RCGK">hδ8</a></td><td><a href="/facts/Quarter_7-cubic_honeycomb/GjVHMBLq">qδ8</a></td><td><a href="/facts/1_33_honeycomb/tYL93yF1">133</a> • <a href="/facts/3_31_honeycomb/VlInrcea">331</a></td></tr><tr><th>E8</th><th><a href="/facts/Uniform_8-honeycomb/UdFL9ns2">Uniform 8-honeycomb</a></th><td><a href="/facts/8-simplex_honeycomb/eoAGHg7J">0[9]</a></td><td><a href="/facts/8-cubic_honeycomb/fx3hM5DD">δ9</a></td><td><a href="/facts/8-demicubic_honeycomb/baWsKzQc">hδ9</a></td><td>qδ9</td><td><a href="/facts/1_52_honeycomb/LAJXFvnV">152</a> • <a href="/facts/2_51_honeycomb/XthKHy0m">251</a> • <a href="/facts/5_21_honeycomb/f971VRma">521</a></td></tr><tr><th>E9</th><th><a href="/facts/Uniform_9-honeycomb/Qc5NglV8">Uniform 9-honeycomb</a></th><td>0[10]</td><td>δ10</td><td>hδ10</td><td>qδ10</td><td></td></tr><tr><th>E10</th><th>Uniform 10-honeycomb</th><td>0[11]</td><td>δ11</td><td>hδ11</td><td>qδ11</td><td></td></tr><tr><th>E<i>n</i>-1</th><th>Uniform (<i>n</i>-1)-<a href="/facts/Honeycomb_(geometry)/seyRBcel">honeycomb</a></th><td><a href="/facts/Simplectic_honeycomb/hCmbARWt">0[<i>n</i>]</a></td><td><a href="/facts/Hypercubic_honeycomb/MQxLbDeB">δ<i>n</i></a></td><td><a href="/facts/Alternated_hypercubic_honeycomb/zrU9sG2e">hδ<i>n</i></a></td><td><a href="/facts/Quarter_hypercubic_honeycomb/7Je1f2st">qδ<i>n</i></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></tr></tbody></table>