and 12 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...

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

geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex. There are six unique...

appearance to Metatron's Cube. The birectified 5-simplex is the intersection of two regular 5-simplexes in dual configuration. The vertices of a birectification...

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...

truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10 cells: 5 tetrahedra, and 5...

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...

5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex. There are 4 unique runcinations of the 5-simplex...

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...

Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively...

regular 5-cell is that of a triangular bipyramid (two tetrahedra joined face-to-face) with the two opposite vertices centered. In the case of simplexes such...

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

containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified 5-cell). The Coxeter symbol for the rectified 5-cell is 021...

of the pyramid are made of 5-cell cells. These are seen as vertex figures of truncated regular 6-polytopes, like a truncated 6-cube. Another form is {3...

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...

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes. The 221 polytope is fourth in dimensional series 2k2...

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

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

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

3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations of the 7-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...

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...

snub 5-demicubes, 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...

graphs with even k 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...

construction is 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...

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

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

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...

orthoschemes. Coxeter identifies various orthoschemes as the characteristic simplexes of the polytopes they generate by reflections. The characteristic simplex...

with one or more rings. All 71 are enumerated below. Norman Johnson's truncation names are given. Bowers names and acronym are also given for cross-referencing...