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...

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

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...

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...

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...

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...

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...

pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of...

Its vertex figure is a rectified 5-cell pyramid. Truncated icosihepta-heptacontadi-peton as a truncated 27-72 facetted polypeton (Acronym: tojak) Vertices...

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

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

face-to-face) with the two opposite vertices centered. In the case of simplexes such as the 5-cell, certain irregular forms are in some sense more fundamental...

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...

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...

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

(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)...

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

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified...

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

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

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

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...

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

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...

order truncations (runcination) of the regular 8-simplex. There are eleven unique runcinations of the 8-simplex, including permutations of truncation and...

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

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

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