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Pentellated 6-simplexes
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<table><tbody><tr><td><a href="/facts/6-simplex/mInfSIeH">6-simplex</a></td><td>Pentellated 6-simplex</td><td>Pentitruncated 6-simplex</td><td>Penticantellated 6-simplex</td></tr><tr><td>Penticantitruncated 6-simplex</td><td>Pentiruncitruncated 6-simplex</td><td>Pentiruncicantellated 6-simplex</td><td>Pentiruncicantitruncated 6-simplex</td></tr><tr><td>Pentisteritruncated 6-simplex</td><td>Pentistericantitruncated 6-simplex</td><td colspan="2">Pentisteriruncicantitruncated 6-simplex(Omnitruncated 6-simplex)</td></tr><tr><th colspan="4"><a href="/facts/Orthogonal_projection/sElXGkxD">Orthogonal projections</a> in A6 <a href="/facts/Coxeter_plane/4B80wH8V">Coxeter plane</a></th></tr></tbody></table> <p>In six-dimensional <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a pentellated 6-simplex is a convex <a href="/facts/Uniform_6-polytope/pxqFTw2F">uniform 6-polytope</a> with 5th order <a href="/facts/Truncation_(geometry)/DYb589Je">truncations</a> of the regular <a href="/facts/6-simplex/mInfSIeH">6-simplex</a>. </p><p>There are unique 10 degrees of pentellations of the 6-simplex with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-simplex is also called an expanded 6-simplex, constructed by an <a href="/facts/Expansion_(geometry)/eMpoRlnm">expansion</a> operation applied to the regular <a href="/facts/6-simplex/mInfSIeH">6-simplex</a>. The highest form, the <i>pentisteriruncicantitruncated 6-simplex</i>, is called an <i>omnitruncated 6-simplex</i> with all of the nodes ringed. </p>