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 (2,556 words) - 04:13, 24 July 2024
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 (3,117 words) - 07:21, 6 August 2024
geometry, there are 255 uniform polytopes with E8 symmetry. The three simplest forms are the 421, 241, and 142 polytopes, composed of 240, 2160 and 17280...
9 KB (283 words) - 06:36, 8 September 2020
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 (822 words) - 04:13, 24 July 2024
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 (4,310 words) - 03:16, 24 July 2024
2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets...
21 KB (1,017 words) - 21:38, 19 August 2024
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 family...
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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...
60 KB (7,175 words) - 03:39, 24 July 2024
Tesseract (redirect from 4-4 duoprism)
regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken...
25 KB (2,644 words) - 21:19, 2 September 2024
90 (number) (section Witting polytope)
the vertex arrangement of the 4 21 {\displaystyle 4_{21}} polytope, which shares 240 vertices with the Witting polytope in four-dimensional complex space...
15 KB (2,025 words) - 17:30, 30 July 2024
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset...
18 KB (1,025 words) - 19:06, 3 September 2023
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional...
23 KB (3,266 words) - 17:46, 21 May 2024
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In...
42 KB (5,265 words) - 06:21, 31 August 2024
regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...
98 KB (5,291 words) - 09:50, 1 September 2024
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 respectively...
6 KB (254 words) - 09:54, 23 April 2023
mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...
34 KB (4,530 words) - 22:20, 16 September 2023
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset...
18 KB (1,230 words) - 22:44, 16 February 2024
5-demicube (redirect from Gosset 1 21 polytope)
five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed...
9 KB (670 words) - 16:53, 9 April 2024
Rectified 5-cell (redirect from 0 21 polytope)
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge...
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Octahedron (redirect from 3-cross-polytope)
octahedron is the three-dimensional case of the more general concept of a cross-polytope. A regular octahedron is an octahedron that is a regular polyhedron. All...
36 KB (3,630 words) - 05:40, 5 September 2024
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...
26 KB (874 words) - 05:06, 4 April 2023
Hypercube (redirect from Measure polytope)
measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The...
26 KB (2,146 words) - 18:34, 30 August 2024
A 0/1-polytope is a convex polytope generated by the convex hull of a subset of d coordinates value 0 or 1, {0,1}d. The full domain is the unit hypercube...
2 KB (165 words) - 05:24, 20 May 2024
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension...
154 KB (6,979 words) - 07:25, 17 May 2024
8-orthoplex (redirect from 8-cross polytope)
8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces...
9 KB (620 words) - 00:28, 17 November 2022
Polyhedron (redirect from 3-polytope)
generalization of a 2-dimensional polygon and a 3-dimensional specialization of a polytope, a more general concept in any number of dimensions. Convex polyhedra are...
87 KB (9,892 words) - 02:13, 5 September 2024
List of mathematical shapes (section Polytope elements)
needed] 142 polytope, 241 polytope, 421 polytope, Truncated 421 polytope, Truncated 241 polytope, Truncated 142 polytope, Cantellated 421 polytope, Cantellated...
47 KB (3,580 words) - 17:01, 29 June 2024
8-cube (category 8-polytopes)
(the 4-cube) and oct for eight (dimensions) in Greek. It can also be called a regular hexdeca-8-tope or hexadecazetton, being an 8-dimensional polytope constructed...
9 KB (640 words) - 00:28, 17 November 2022
24-cell (redirect from Order-4-3 triangular honeycomb)
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}...
237 KB (31,089 words) - 18:33, 2 September 2024
7-simplex (redirect from 0 60 polytope)
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell...
8 KB (655 words) - 16:17, 9 April 2024