ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex. These polytopes are...

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...

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

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...

semiregular polytope, labeling it as S1 5. Rectified hexateron (Acronym: rix) (Jonathan Bowers) The vertices of the rectified 5-simplex can be more simply positioned...

(tetrahedra), 16128 4-faces (4-simplexes), 4788 5-faces (756 pentacrosses, and 4032 5-simplexes), 632 6-faces (576 6-simplexes and 56 221). Its vertex figure...

that are facets of 7-simplexes. Since every 7-orthoplex has 128 (27) 6-simplex facets, half of which are not incident to 7-simplexes, the 421 polytope has...

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...

3-sphere tiling, a tetrahedral hosohedron.) Rectified hecatonicosihexa-pentacosiheptacontahexa-exon as a rectified 126-576 facetted polyexon (acronym: ranq)...

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...

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...

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...

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

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)...

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

stericated 6-orthoplex. A second construction in 6-space, from the center of a rectified 6-orthoplex is given by coordinate permutations of: (1,-1,0,0,0,0) The...

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...

8-simplex Truncated 8-simplex Rectified 8-simplex Quadritruncated 8-simplex Tritruncated 8-simplex Bitruncated 8-simplex Orthogonal projections in A8...

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

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...

632 4788 16128 20160 10080 2016 126 2 Rectified 231 (rolaq) 758 10332 47880 100800 90720 30240 2016 3 Rectified 132 (rolin) 758 12348 72072 191520 241920...

truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10 cells: 5 tetrahedra, and 5 truncated tetrahedra. Each vertex is surrounded...

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 {3,3,3,4}, , with 10 vertices, 40 edges, 80 faces, 80 cells, and 32 4-faces 2{3}2{3}2{3}2{4}3...

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...