• Thumbnail for Cantellated 120-cell
    meeting at each vertex. Cantellated 120-cell Norman Johnson Cantellated hecatonicosachoron / Cantellated dodecacontachoron / Cantellated polydodecahedron Small...
    15 KB (758 words) - 02:15, 24 December 2024
  • Thumbnail for Runcinated 120-cells
    runcinated 120-cell (or runcinated 600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 120-cell. There are...
    15 KB (707 words) - 07:27, 3 May 2025
  • Thumbnail for 120-cell
    In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called...
    131 KB (14,824 words) - 19:21, 6 April 2025
  • tesseract, Cantellated tesseract, Runcinated tesseract Rectified 16-cell, Truncated 16-cell Rectified 24-cell, Truncated 24-cell, Cantellated 24-cell, Runcinated...
    30 KB (2,692 words) - 15:23, 9 February 2025
  • Thumbnail for Rectified 120-cell
    In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell. E. L. Elte identified it in 1912 as a semiregular...
    6 KB (328 words) - 03:18, 24 July 2024
  • Thumbnail for Truncated 120-cells
    In geometry, a truncated 120-cell is a uniform 4-polytope formed as the truncation of the regular 120-cell. There are three truncations, including a bitruncation...
    12 KB (535 words) - 03:18, 24 July 2024
  • tesseract, Cantellated tesseract, Runcinated tesseract Rectified 16-cell, Truncated 16-cell Rectified 24-cell, Truncated 24-cell, Cantellated 24-cell, Runcinated...
    46 KB (3,547 words) - 00:42, 27 May 2025
  • Thumbnail for Rectified 600-cell
    rectified 600-cell or rectified hexacosichoron is a convex uniform 4-polytope composed of 600 regular octahedra and 120 icosahedra cells. Each edge has...
    7 KB (493 words) - 18:29, 9 June 2025
  • Thumbnail for Cantellated 5-cell
    of the cantellated 5-orthoplex. The convex hull of two cantellated 5-cells in opposite positions is a nonuniform polychoron composed of 100 cells: three...
    20 KB (646 words) - 18:11, 9 June 2025
  • Thumbnail for 600-cell
    five triangles meeting at every vertex. Its dual polytope is the 120-cell. The 600-cell is the fifth in the sequence of 6 convex regular 4-polytopes (in...
    217 KB (28,920 words) - 13:47, 28 April 2025
  • Thumbnail for Triangular prism
    triangular prisms. There are 9 uniform honeycombs that include triangular prism cells: Gyroelongated alternated cubic honeycomb, elongated alternated cubic honeycomb...
    19 KB (1,629 words) - 04:40, 8 July 2025
  • Thumbnail for Uniform 4-polytope
    cells, faces, edges, and vertices are congruent: 6 regular convex 4-polytopes: 5-cell {3,3,3}, 8-cell {4,3,3}, 16-cell {3,3,4}, 24-cell {3,4,3}, 120-cell...
    134 KB (4,315 words) - 11:59, 20 April 2025
  • Thumbnail for Uniform 5-polytope
    Snub 24-cell honeycomb, with symbols s{3,4,3,3}, and constructed by four snub 24-cell, one 16-cell, and five 5-cells at each vertex. 16-cell honeycomb...
    92 KB (2,241 words) - 02:24, 28 October 2024
  • Thumbnail for Cantellated tesseract
    truncations. Two are also derived from the 24-cell family. The cantellated tesseract, bicantellated 16-cell, or small rhombated tesseract is a convex uniform...
    14 KB (1,339 words) - 20:56, 15 June 2025
  • Thumbnail for Rectified 24-cell
    be considered a cantellated 16-cell with the lower symmetries B4 = [3,3,4]. B4 would lead to a bicoloring of the cuboctahedral cells into 8 and 16 each...
    7 KB (529 words) - 03:18, 24 July 2024
  • Thumbnail for Runcinated 24-cells
    second set of coordinates coincide with the vertices of an inscribed cantellated tesseract. The regular skew polyhedron, {4,8|3}, exists in 4-space with...
    17 KB (1,115 words) - 18:57, 25 March 2025
  • Thumbnail for Cantellated 24-cells
    four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell. There are 2 unique...
    10 KB (766 words) - 18:29, 7 June 2025
  • Thumbnail for 24-cell
    figures: the great 120-cell and grand stellated 120-cell. With itself, it can form a polytope compound: the compound of two 24-cells. The 24-cell can also be...
    234 KB (30,655 words) - 13:52, 5 July 2025
  • Thumbnail for Runcinated 5-cell
    bitruncated 5-cell. The runcitruncated 5-cell or prismatorhombated pentachoron is composed of 60 vertices, 150 edges, 120 faces, and 30 cells. The cells are: 5...
    40 KB (1,759 words) - 19:20, 9 June 2025
  • Thumbnail for Order-5 dodecahedral honeycomb
    vertex figure. The cantellated order-5 dodecahedral honeycomb, , has rhombicosidodecahedron, icosidodecahedron, and pentagonal prism cells, with a wedge vertex...
    16 KB (663 words) - 16:48, 3 August 2024
  • Thumbnail for Icosahedral honeycomb
    figure. The cantellated icosahedral honeycomb, t0,2{3,5,3}, , has rhombicosidodecahedron, icosidodecahedron, and triangular prism cells, with a wedge...
    19 KB (716 words) - 23:01, 17 April 2025
  • tesseract which is bounded by 24 cells: 8 regular octahedra, and 16 truncated tetrahedra. It has half the vertices of a cantellated tesseract with construction...
    17 KB (1,289 words) - 03:18, 24 July 2024
  • Thumbnail for Uniform polytope
    [3,4,3]: the 24-cell {3,4,3}, self-dual; group [3,3,5]: 600-cell {3,3,5}, its dual 120-cell {5,3,3}, and their ten regular stellations. group [31,1,1]:...
    53 KB (2,930 words) - 15:27, 14 May 2025
  • Thumbnail for 4 21 polytope
    vertices birectified 8-cube - (0,0,±1,±1,±1,±1,±1,±1) - 1792 vertices cantellated 8-orthoplex - (0,0,0,0,0,0,±1,±1,±2) - 1344 vertices These graphs represent...
    38 KB (2,559 words) - 22:53, 4 July 2025
  • Thumbnail for Cantellated 7-simplexes
    In seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex. There are unique...
    12 KB (436 words) - 19:43, 4 June 2025
  • Thumbnail for Rhombicuboctahedron
    conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the rhombic dodecahedral honeycomb, and it cannot be surpassed, since...
    23 KB (2,325 words) - 00:32, 1 July 2025
  • Thumbnail for Hexagonal tiling honeycomb
    truncated tetrahedron and hexagonal tiling cells, with a digonal disphenoid vertex figure. The cantellated hexagonal tiling honeycomb, t0,2{6,3,3}, has...
    21 KB (843 words) - 09:49, 9 January 2025
  • Thumbnail for H4 polytope
    there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular. Each can be visualized as symmetric orthographic projections...
    15 KB (501 words) - 03:21, 24 July 2024
  • cells and edges, while the truncated 5-orthoplex and cantellated 5-orthoplex respectively have 240 cells and vertices. The uniform prismatic family A 1 ×...
    6 KB (868 words) - 15:02, 29 June 2025
  • Thumbnail for Runcinated tesseracts
    prisms. The runcitruncated 16-cell may be constructed by contracting the small rhombicuboctahedral cells of the cantellated tesseract radially, and filling...
    29 KB (2,218 words) - 19:28, 9 June 2025