• Thumbnail for 2 41 polytope
    In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its...
    18 KB (748 words) - 11:08, 7 June 2025
  • Thumbnail for 1 42 polytope
    In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its...
    33 KB (814 words) - 22:02, 2 October 2024
  • Thumbnail for 4-polytope
    In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure...
    16 KB (1,774 words) - 16:36, 3 July 2025
  • In geometry, 2k1 polytope is a uniform polytope in n dimensions (n = k+4) constructed from the En Coxeter group. The family was named by their Coxeter...
    7 KB (410 words) - 13:08, 2 June 2025
  • Thumbnail for Regular 4-polytope
    In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular...
    27 KB (1,648 words) - 08:01, 15 October 2024
  • Thumbnail for Uniform 7-polytope
    7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is...
    107 KB (1,008 words) - 19:56, 6 June 2025
  • Thumbnail for Tesseract
    Tesseract (category Regular 4-polytopes)
    labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The Oxford English...
    26 KB (2,666 words) - 11:51, 4 June 2025
  • Thumbnail for Uniform 4-polytope
    In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra...
    134 KB (4,315 words) - 11:59, 20 April 2025
  • Thumbnail for 120-cell
    120-cell (category Regular 4-polytopes)
    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
  • Thumbnail for 24-cell
    24-cell (category Regular 4-polytopes)
    In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}...
    234 KB (30,655 words) - 13:52, 5 July 2025
  • Thumbnail for 16-cell
    16-cell (redirect from 4-cross polytope)
    convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described...
    61 KB (7,127 words) - 15:37, 20 May 2025
  • Thumbnail for 5-cell
    5-cell (redirect from 0 30 polytope)
    In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells...
    38 KB (3,699 words) - 19:35, 25 March 2025
  • Thumbnail for Uniform 6-polytope
    uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete...
    68 KB (1,491 words) - 15:46, 2 June 2025
  • Thumbnail for 600-cell
    600-cell (category Regular 4-polytopes)
    In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known...
    217 KB (28,920 words) - 13:47, 28 April 2025
  • Thumbnail for Uniform polytope
    In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. Here, "vertex-transitive" means...
    53 KB (2,930 words) - 15:27, 14 May 2025
  • Thumbnail for Uniform 9-polytope
    nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets. A...
    82 KB (883 words) - 15:06, 6 July 2025
  • Thumbnail for 7-demicube
    7-demicube (redirect from 1 41 polytope)
    In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is...
    9 KB (449 words) - 16:49, 9 April 2024
  • geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after...
    11 KB (1,371 words) - 06:17, 13 November 2024
  • Thumbnail for Uniform 5-polytope
    5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets...
    92 KB (2,241 words) - 02:24, 28 October 2024
  • Thumbnail for Uniform 8-polytope
    eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets. A...
    148 KB (1,000 words) - 00:12, 11 July 2025
  • Thumbnail for Hyperpyramid
    Hyperpyramid (category Polytopes)
    construction gets generalised to n dimensions. The base becomes a (n – 1)-polytope in a (n – 1)-dimensional hyperplane. A point called apex is located outside...
    4 KB (514 words) - 12:20, 20 June 2025
  • neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function...
    42 KB (6,261 words) - 14:30, 16 June 2025
  • Thumbnail for Truncated 120-cells
    Truncated 120-cells (category Uniform 4-polytopes)
    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
  • C_{\overline {AE}}&\leq 2\pi .\end{aligned}}} A generalized n-dimensional "bipyramid" is any n-polytope constructed from an (n − 1)-polytope base lying in a hyperplane...
    33 KB (3,655 words) - 12:10, 24 June 2025
  • Thumbnail for D8 polytope
    In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, 64 are unique, and 127 are shared with the B8 symmetry. There are two regular...
    34 KB (136 words) - 18:34, 6 May 2025
  • 6-simplex (redirect from 0 50 polytope)
    is cos−1(1/6), or approximately 80.41°. It can also be called a heptapeton, or hepta-6-tope, as a 7-facetted polytope in 6-dimensions. The name heptapeton...
    6 KB (690 words) - 23:48, 26 May 2025
  • convex polytopes. Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics of polytopes; for...
    19 KB (2,304 words) - 19:59, 1 August 2024
  • Thumbnail for B6 polytope
    In 6-dimensional geometry, there are 64 uniform polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices...
    31 KB (252 words) - 00:20, 28 May 2017
  • Kleetope (category Polytopes)
    Kleetope of a polyhedron or higher-dimensional convex polytope P is another polyhedron or polytope PK formed by replacing each facet of P with a pyramid...
    10 KB (1,100 words) - 17:06, 23 June 2025
  • vertices of any convex polytope into a set of vectors or points in a space of a different dimension, the Gale diagram of the polytope. It can be used to describe...
    13 KB (1,912 words) - 09:37, 31 December 2023