• 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 (2,938 words) - 22:13, 13 July 2025
  • 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 (1,017 words) - 21:56, 20 July 2025
  • Thumbnail for Uniform 4-polytope
    geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and...
    135 KB (4,386 words) - 00:41, 14 July 2025
  • Thumbnail for Uniform 6-polytope
    geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete...
    69 KB (1,500 words) - 22:43, 13 July 2025
  • Thumbnail for Uniform 5-polytope
    a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope...
    92 KB (2,250 words) - 22:47, 13 July 2025
  • Thumbnail for Uniform 8-polytope
    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 uniform 8-polytope...
    149 KB (1,015 words) - 02:22, 18 July 2025
  • Thumbnail for 4-polytope
    three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate...
    16 KB (1,774 words) - 21:18, 20 July 2025
  • In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any...
    26 KB (3,125 words) - 20:08, 14 July 2025
  • Thumbnail for Uniform 9-polytope
    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 uniform 9-polytope...
    82 KB (892 words) - 22:12, 13 July 2025
  • Thumbnail for 5-polytope
    geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which...
    10 KB (887 words) - 22:11, 13 July 2025
  • Thumbnail for Uniform 10-polytope
    8-polytope ridge. A uniform 10-polytope is one which is vertex-transitive, and constructed from uniform facets. Regular 10-polytopes can be represented...
    23 KB (831 words) - 22:12, 13 July 2025
  • geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the En Coxeter group, and having only regular polytope facets. The...
    10 KB (703 words) - 13:02, 18 July 2025
  • In geometry, 1k2 polytope is a uniform polytope in n dimensions (n = k + 4) constructed from the En Coxeter group. The family was named by their Coxeter...
    8 KB (395 words) - 12:37, 18 July 2025
  • Thumbnail for 6-polytope
    six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional figure...
    10 KB (887 words) - 22:11, 13 July 2025
  • Thumbnail for 1 22 polytope
    122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named...
    27 KB (866 words) - 04:45, 21 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...
    8 KB (395 words) - 14:48, 18 July 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...
    37 KB (3,706 words) - 23:27, 16 July 2025
  • Thumbnail for E6 polytope
    6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry. The two simplest forms are the 221 and 122 polytopes, composed of 27 and 72 vertices...
    6 KB (247 words) - 03:02, 5 June 2025
  • 10-polytope 10-simplex 10-demicube 10-cube 10-orthoplex Regular polytope and List of regular polytopes Simplex Hypercube Cross-polytope Uniform polytope...
    30 KB (2,692 words) - 15:23, 9 February 2025
  • 5-cube (category 5-polytopes)
    operation, deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called...
    10 KB (828 words) - 09:34, 22 July 2025
  • higher-dimensional polytopes and tessellations. All uniform polytopes are isogonal, for example, the uniform 4-polytopes and convex uniform honeycombs. The...
    9 KB (694 words) - 13:43, 11 July 2025
  • Thumbnail for Tesseract
    Tesseract (category Regular 4-polytopes)
    2307/2369565. JSTOR 2369565. Norman Johnson Uniform Polytopes, Manuscript (1991) N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966) Victor...
    26 KB (2,666 words) - 11:51, 4 June 2025
  • Thumbnail for 4 21 polytope
    In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset...
    38 KB (2,559 words) - 17:05, 22 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 (7,134 words) - 18:53, 14 July 2025
  • Thumbnail for Truncated 24-cells
    Truncated 24-cells (category Uniform 4-polytopes)
    In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell. There are two...
    24 KB (1,744 words) - 03:18, 24 July 2024
  • Polyhedra? Branko Grünbaum (2003), Fig. 3 Regular polytopes, p.95 Coxeter, The Densities of the Regular Polytopes II, 1932, p.53 Lee, Hwa Young; "Origami-Constructible...
    31 KB (3,060 words) - 00:29, 13 July 2025
  • Regular polytope Regular polyhedron List of uniform tilings Uniform tilings in hyperbolic plane List of uniform polyhedra List of uniform polyhedra...
    54 KB (752 words) - 01:11, 22 July 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 List of F4 polytopes
    In 4-dimensional geometry, there are 9 uniform 4-polytopes with F4 symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular...
    12 KB (413 words) - 03:21, 24 July 2024
  • Thumbnail for Coxeter–Dynkin diagram
    Coxeter–Dynkin diagram (category Polytope notation systems)
    (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group. A class of closely related...
    57 KB (3,233 words) - 15:31, 14 May 2025