• 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...
    154 KB (6,983 words) - 07:42, 7 April 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 (3,119 words) - 14:57, 6 June 2025
  • Thumbnail for Cross-polytope
    In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean...
    20 KB (1,113 words) - 02:05, 10 June 2025
  • Thumbnail for Regular polytope
    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...
    43 KB (5,346 words) - 16:28, 4 June 2025
  • general complex polytope in any number of complex dimensions. In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon...
    3 KB (393 words) - 21:13, 12 May 2024
  • 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 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 (2,557 words) - 11:32, 7 June 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) - 02:40, 5 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 Abstract polytope
    mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...
    34 KB (4,552 words) - 18:59, 9 May 2025
  • 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) - 19:49, 9 June 2025
  • Thumbnail for Convex polytope
    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 (3,262 words) - 01:53, 22 May 2025
  • Thumbnail for Polyhedron
    Polyhedron (redirect from 3-polytope)
    a two-dimensional polygon and a three-dimensional specialization of a polytope, a more general concept in any number of dimensions. Polyhedra have several...
    97 KB (10,633 words) - 18:39, 9 June 2025
  • and B Complex analytic space Complex Lie group Complex polytope Complex projective space Cousin problems Deformation Theory#Deformations of complex manifolds...
    26 KB (3,677 words) - 14:31, 7 September 2023
  • 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
  • A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes...
    30 KB (2,692 words) - 15:23, 9 February 2025
  • Thumbnail for List of regular polytopes
    regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...
    100 KB (5,446 words) - 18:33, 2 May 2025
  • Thumbnail for Hypercube
    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...
    27 KB (2,223 words) - 20:00, 17 March 2025
  • Thumbnail for Simplicial complex
    the CW complexes. Infinite complexes are a technical tool basic in algebraic topology. See also the discussion at Polytope of simplicial complexes as subspaces...
    14 KB (1,992 words) - 00:21, 18 May 2025
  • Polygon (redirect from 2-polytope)
    image, Coxeter, H.S.M.; Regular Polytopes, 3rd Edn, Dover (pbk), 1973, p. 114 Shephard, G.C.; "Regular complex polytopes", Proc. London Math. Soc. Series...
    37 KB (4,236 words) - 14:28, 13 January 2025
  • the 4 21 {\displaystyle 4_{21}} polytope, which shares 240 vertices with the Witting polytope in four-dimensional complex space. By Coxeter, the incidence...
    15 KB (2,028 words) - 18:26, 11 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) - 19:27, 11 May 2025
  • Thumbnail for 2 21 polytope
    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 (1,256 words) - 17:48, 5 June 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 Witting polytope
    In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices...
    9 KB (623 words) - 08:52, 28 November 2024
  • 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 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
  • Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial...
    4 KB (311 words) - 12:17, 30 October 2023
  • Thumbnail for Stellation
    in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure...
    18 KB (2,189 words) - 08:24, 31 December 2024
  • Thumbnail for Simplicial polytope
    alternated cubic honeycomb Simplicial higher polytope families: simplex cross-polytope (Orthoplex) Simplicial complex Delaunay triangulation Polyhedra, Peter...
    2 KB (183 words) - 06:44, 27 August 2024