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...

pentellated 8-simplex is a convex uniform 8-polytope with 5th order truncations of the regular 8-simplex. There are two unique pentellations of the 8-simplex...

geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex. There are 35...

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...

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...

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...

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

permutations of truncation. Small rhombated enneazetton (acronym: srene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the cantellated 8-simplex...

eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique...

eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex. There are eleven...

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the...

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

5-cell cells. These are seen as vertex figures of truncated regular 6-polytopes, like a truncated 6-cube. Another form is {3,3}∨{ }, with [3,3,2,1] symmetry...

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

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...

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...

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...

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

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...

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

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...

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

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...

squares), 540 cells (360 truncated octahedra, 90 cubes, and 90 hexagonal prisms), and 62 4-faces (12 omnitruncated 5-cells, 30 truncated octahedral prisms,...

4th order truncations (sterication) of the regular 6-simplex. There are 8 unique sterications for the 6-simplex with permutations of truncations, cantellations...

contained in an n-simplex and n−1 simplex is contained in exactly two n-simplexes, then the underlying space of X is a topological pseudomanifold. If X...

runcination (3rd order truncations) of the regular 6-simplex. There are 8 unique runcinations of the 6-simplex with permutations of truncations, and cantellations...

truncations. Small rhombated octaexon (acronym: saro) (Jonathan Bowers) The vertices of the cantellated 7-simplex can be most simply positioned in 8-space...