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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Bipyramid (section 4-polytopes with bipyramidal cells)
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
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
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
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
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
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
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
90 (number) (section Witting polytope)
( 9 2 + 3 2 ) , ( 8 2 + 5 2 + 1 2 ) , ( 7 2 + 5 2 + 4 2 ) , ( 8 2 + 4 2 + 3 2 + 1 2 ) , ( 7 2 + 6 2 + 2 2 + 1 2 ) , ( 6 2 + 5 2 + 4 2 + 3 2 + 2 2 ) {\displaystyle...
15 KB (2,028 words) - 18:26, 11 April 2025