• Thumbnail for Rectified 10-simplexes
    ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex. These polytopes are...
    9 KB (446 words) - 04:33, 4 April 2023
  • Thumbnail for Rectified 7-simplexes
    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...
    9 KB (525 words) - 00:54, 14 June 2025
  • Thumbnail for Rectified 8-simplexes
    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...
    8 KB (456 words) - 04:41, 4 April 2023
  • Thumbnail for Rectified 6-simplexes
    Coxeter-Dynkin diagram, shown as . Rectified heptapeton (Acronym: ril) (Jonathan Bowers) The vertices of the rectified 6-simplex can be most simply positioned...
    5 KB (394 words) - 14:15, 3 June 2025
  • Thumbnail for Rectified 9-simplexes
    In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-simplex. These polytopes are...
    9 KB (461 words) - 04:36, 4 April 2023
  • Thumbnail for Rectified 5-simplexes
    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...
    14 KB (978 words) - 16:06, 9 January 2024
  • Thumbnail for 2 31 polytope
    (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...
    14 KB (589 words) - 00:48, 6 June 2025
  • Thumbnail for 4 21 polytope
    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...
    38 KB (2,559 words) - 22:53, 4 July 2025
  • Thumbnail for 3 21 polytope
    3-sphere tiling, a tetrahedral hosohedron.) Rectified hecatonicosihexa-pentacosiheptacontahexa-exon as a rectified 126-576 facetted polyexon (acronym: ranq)...
    18 KB (1,026 words) - 18:37, 5 June 2025
  • Thumbnail for Pentellated 6-simplexes
    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...
    55 KB (1,127 words) - 14:20, 3 June 2025
  • Thumbnail for Demihypercube
    vertices of {4,3,...,3}. The vertex figures of demihypercubes are rectified n-simplexes. They are represented by Coxeter-Dynkin diagrams of three constructive...
    12 KB (702 words) - 14:46, 22 May 2025
  • Thumbnail for 2 21 polytope
    simplexes and orthoplexes. The 221 polytope is fourth in dimensional series 2k2. The 221 polytope is second in dimensional series 22k. The rectified 221...
    18 KB (1,256 words) - 17:48, 5 June 2025
  • Thumbnail for Rectified 5-cell
    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...
    12 KB (901 words) - 02:31, 25 April 2025
  • 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...
    5 KB (378 words) - 12:31, 18 August 2024
  • Thumbnail for 5-cell
    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...
    38 KB (3,699 words) - 19:35, 25 March 2025
  • ) The family starts uniquely as 6-polytopes. The triangular prism and rectified 5-cell are included at the beginning for completeness. The demipenteract...
    10 KB (717 words) - 17:54, 23 March 2025
  • Thumbnail for Hexicated 7-simplexes
    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)...
    38 KB (1,287 words) - 18:51, 7 June 2025
  • 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...
    10 KB (1,090 words) - 18:02, 29 June 2025
  • Thumbnail for Truncated 8-simplexes
    8-simplex Truncated 8-simplex Rectified 8-simplex Quadritruncated 8-simplex Tritruncated 8-simplex Bitruncated 8-simplex Orthogonal projections in A8...
    9 KB (422 words) - 04:42, 4 April 2023
  • Thumbnail for Stericated 5-simplexes
    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...
    19 KB (1,045 words) - 18:14, 9 June 2025
  • Thumbnail for Cantellated 5-simplexes
    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...
    11 KB (455 words) - 00:57, 29 January 2025
  • E9 honeycomb (category 10-polytopes)
    vertex figure. All facets of these polytopes are regular polytopes, namely simplexes and orthoplexes. The 261 honeycomb is composed of 251 9-honeycomb and...
    13 KB (804 words) - 21:57, 12 December 2023
  • Thumbnail for Heptellated 8-simplexes
    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...
    8 KB (599 words) - 21:30, 8 July 2025
  • Thumbnail for Uniform 7-polytope
    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...
    107 KB (1,008 words) - 19:56, 6 June 2025
  • Thumbnail for Truncated 5-cell
    Truncated 5-cell (redirect from 10-cell)
    truncated 5-cell, truncated pentachoron or truncated 4-simplex is bounded by 10 cells: 5 tetrahedra, and 5 truncated tetrahedra. Each vertex is surrounded...
    21 KB (1,345 words) - 18:24, 9 June 2025
  • Thumbnail for 5-demicube
    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)...
    9 KB (670 words) - 16:53, 9 April 2024
  • 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...
    154 KB (6,983 words) - 07:42, 7 April 2025
  • Thumbnail for 120-cell
    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...
    131 KB (14,824 words) - 19:21, 6 April 2025