geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex. There are unique 3 degrees of truncation. Vertices...

constructed from 14 snub 5-simplexes, 42 snub 5-cell antiprisms, 70 3-s{3,4} duoantiprisms, and 2520 irregular 5-simplexes filling the gaps at the deleted...

due to symmetrically-ringed Coxeter-Dynkin diagram. The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all...

based on facets of the bicantitruncated 7-orthoplex. The truncated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all...

geometry, a truncated 7-simplex is a convex uniform 7-polytope, being a truncation of the regular 7-simplex. There are unique 3 degrees of truncation. Vertices...

6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex. There are 8 unique sterications for the 6-simplex...

geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices...

4-faces (6 5-cell and 6 truncated 5-cells). Truncated hexateron (Acronym: tix) (Jonathan Bowers) The vertices of the truncated 5-simplex can be most simply...

64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the...

6th-order truncations (hexication) from the regular 7-simplex. There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations...

duoantiprisms, and 23040 irregular 5-simplexes filling the gaps at the deleted vertices. These polytopes are from a set of 63 uniform 6-polytopes generated from the...

4th order truncations (sterication) of the regular 7-simplex. There are 14 unique sterication for the 7-simplex with permutations of truncations, cantellations...

order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation...

truncations (heptellation) from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of truncations...

order truncations (pentellation) of the regular 7-simplex. There are 16 unique pentellations of the 7-simplex with permutations of truncations, cantellations...

8-orthoplex. The trirectified 7-simplex is the intersection of two regular 7-simplexes in dual configuration. E. L. Elte identified it in 1912 as a semiregular...

There are unique 4 degrees of cantellation for the 5-simplex, including truncations. The cantellated 5-simplex has 60 vertices, 240 edges, 290 faces (200...

some of the Johnson solids, the truncated right triangular prism, and Schönhardt polyhedron. A triangular prism has 6 vertices, 9 edges, and 5 faces....

tetrahedral cells meet at each edge. The 5-cell is self-dual (as are all simplexes), and its vertex figure is the tetrahedron. Its maximal intersection with...

of the regular 7-simplex. There are unique 6 degrees of cantellation for the 7-simplex, including truncations. Small rhombated octaexon (acronym: saro)...

Cube. The birectified 5-simplex is the intersection of two regular 5-simplexes in dual configuration. The vertices of a birectification exist at the...

3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations of the 7-simplex with permutations of truncations, and cantellations...

Dih6 or simple rotation group [6,2]+, order 12. The compound of two 5-simplexes in dual configurations can be seen in this A6 Coxeter plane projection...

six unique cantellations for the 8-simplex, including permutations of truncation. Small rhombated enneazetton (acronym: srene) (Jonathan Bowers) The Cartesian...

(360 truncated octahedra, 90 cubes, and 90 hexagonal prisms), and 62 4-faces (12 omnitruncated 5-cells, 30 truncated octahedral prisms, and 20 6-6 duoprisms)...

hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex. The Cartesian coordinates of the vertices of...

3rd order truncations (Runcination) of the regular 5-simplex. There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations...

8-polytope with 5th order truncations of the regular 8-simplex. There are two unique pentellations of the 8-simplex. Including truncations, cantellations, runcinations...

{\displaystyle \mathbb {E} _{8}} lattice. The 621 honeycomb is made of 9-simplexes and 9-orthoplexes, with 1023 total polytope elements making up each 9-simplex...

There are two degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10...