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Runcinated 8-simplexes
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<table><tbody><tr><td><a href="/facts/8-simplex/QUhcnmk2">8-simplex</a></td><td>Runcinated 8-simplex</td><td>Biruncinated 8-simplex</td><td>Triruncinated 8-simplex</td></tr><tr><td>Runcitruncated 8-simplex</td><td>Biruncitruncated 8-simplex</td><td>Triruncitruncated 8-simplex</td><td>Runcicantellated 8-simplex</td></tr><tr><td>Biruncicantellated 8-simplex</td><td>Runcicantitruncated 8-simplex</td><td>Biruncicantitruncated 8-simplex</td><td>Triruncicantitruncated 8-simplex</td></tr><tr><th colspan="4"><a href="/facts/Orthogonal_projection/sElXGkxD">Orthogonal projections</a> in A8 <a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th></tr></tbody></table> <p>In eight-dimensional <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a runcinated 8-simplex is a convex <a href="/facts/Uniform_8-polytope/M93v3h3c">uniform 8-polytope</a> with 3rd order <a href="/facts/Truncation_(geometry)/DYb589Je">truncations</a> (<a href="/facts/Runcination/nwUxfUIX">runcination</a>) of the regular <a href="/facts/8-simplex/QUhcnmk2">8-simplex</a>. </p><p>There are eleven unique runcinations of the 8-simplex, including permutations of truncation and cantellation. The <i>triruncinated 8-simplex</i> and <i>triruncicantitruncated 8-simplex</i> have a doubled symmetry, showing [18] order reflectional symmetry in the A8 <a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a>. </p>