Coxeter-Dynkin diagram, shown as . Rectified heptapeton (Acronym: ril) (Jonathan Bowers) The vertices of the rectified 6-simplex can be most simply positioned...

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...

semiregular polytope, labeling it as S1 7. Rectified octaexon (Acronym: roc) (Jonathan Bowers) The vertices of the rectified 7-simplex can be most simply positioned...

the 5-cell centers of the 9-simplex. The rectified 9-simplex is the vertex figure of the 10-demicube. Rectified decayotton (reday) (Jonathan Bowers) The...

In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex. There are unique...

5-cell centers of the 10-simplex. The rectified 10-simplex is the vertex figure of the 11-demicube. Rectified hendecaxennon (Acronym ru) (Jonathan Bowers)...

seen as facets of the rectified 6-orthoplex or birectified 6-cube respectively. This configuration matrix represents the rectified 5-simplex. The rows and...

containing all regular polytope facets, containing all simplexes and orthoplexes. The rectified 421 can be seen as a rectification of the 421 polytope...

4-faces (3-simplexes), 4788 5-faces (756 pentacrosses, and 4032 5-simplexes), 632 6-faces (576 6-simplexes and 56 221). Its vertex figure is a 6-demicube...

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...

uniform polytope. It has 56 vertices, and 702 facets: 126 311 and 576 6-simplexes. For visualization this 7-dimensional polytope is often displayed in...

8-orthoplex, . A second construction in 8-space, from the center of a rectified 8-orthoplex is given by coordinate permutations of: (1,-1,0,0,0,0,0,0)...

vertices of {4,3,...,3}. The vertex figures of demihypercubes are rectified n-simplexes. They are represented by Coxeter-Dynkin diagrams of three constructive...

simplexes and orthoplexes. The 221 polytope is fourth in dimensional series 2k2. The 221 polytope is second in dimensional series 22k. The rectified 221...

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...

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...

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...

positive orthant facet of the stericated 6-orthoplex. A second construction in 6-space, from the center of a rectified 6-orthoplex is given by coordinate permutations...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math...

heptellated 9-orthoplex. A second construction in 9-space, from the center of a rectified 9-orthoplex is given by coordinate permutations of: (1,-1,0,0,0,0,0,0...

vertex figure. All facets of these polytopes are regular polytopes, namely simplexes and orthoplexes. The 261 honeycomb is composed of 251 9-honeycomb and...

15 cuboctahedra and 60 triangular prisms), and 27 4-faces (6 cantellated 5-cell, 6 rectified 5-cells, and 15 tetrahedral prisms). Cantellated hexateron...

vertices at infinity.) The family starts uniquely as 6-polytopes. The triangular prism and rectified 5-cell are included at the beginning for completeness...

series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (5-simplices and 5-orthoplexes in the case of the 5-demicube)...

construction as and quasiregular form as . All elements are simplexes. Real {3,4}, or , with 6 vertices, 12 edges, and 8 faces 2{3}2{4}3, or , with 9 vertices...

unless it is all 5 vertices. It is impossible to rotate two concentric 4-simplexes with respect to each other such that some, but not all, of their vertices...

Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1] (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math...