In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any...
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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...
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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) - 01:38, 10 April 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...
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In geometry, a cross-polytope, hyperoctahedron, orthoplex, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space. A 2-dimensional...
21 KB (1,016 words) - 18:47, 19 February 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...
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mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...
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Vertex (geometry) (redirect from Polytope vertex)
generally, a vertex of a polyhedron or polytope is convex, if the intersection of the polyhedron or polytope with a sufficiently small sphere centered...
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Prism (geometry) (redirect from Prismatic polytope)
polytope is a higher-dimensional generalization of a prism. An n-dimensional prismatic polytope is constructed from two (n − 1)-dimensional polytopes...
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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...
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Face (geometry) (redirect from Polytope face)
polyhedra and higher-dimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions)...
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Tesseract (category 4-polytopes)
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...
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The Birkhoff polytope Bn (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete...
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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 a 3-ball in the Manhattan (ℓ1) metric. If the...
26 KB (2,748 words) - 01:59, 14 March 2024
Polygon (redirect from 2-polytope)
polytopes. (In other conventions, the words polyhedron and polytope are used in any dimension, with the distinction between the two that a polytope is...
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combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex...
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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...
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Edge (geometry) (redirect from Polytope edge)
polyhedron, like this cube. Every edge is shared by three or more faces in a 4-polytope, as seen in this projection of a tesseract. In geometry, an edge is a particular...
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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...
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Polyhedron (redirect from 3-polytope)
examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Convex polyhedra are...
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regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...
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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...
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Tetrahedron (redirect from 1 10 polytope)
triangle faces. For a regular k-polytope, the Coxeter-Dynkin diagram of the characteristic k-orthoscheme is the k-polytope's diagram without the generating...
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mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid...
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In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only...
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In geometry, a five-dimensional polytope (or 5-polytope) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which share a...
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Schläfli symbol (category Polytopes)
, q , r , . . . } {\displaystyle \{p,q,r,...\}} that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century...
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In geometry, a monostatic polytope (or unistable polyhedron) is a d-polytope which "can stand on only one face". They were described in 1969 by J. H. Conway...
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List of mathematical shapes (section Regular polytopes)
needed] 142 polytope, 241 polytope, 421 polytope, Truncated 421 polytope, Truncated 241 polytope, Truncated 142 polytope, Cantellated 421 polytope, Cantellated...
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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) - 22:14, 5 April 2024