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) - 08:04, 5 March 2024 |
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... 41 KB (5,251 words) - 03:57, 8 February 2024 |
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... 9 KB (934 words) - 17:02, 17 December 2023 |
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... 86 KB (9,737 words) - 18:21, 23 March 2024 |
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... 29 KB (2,667 words) - 03:43, 2 October 2023 |
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... 20 KB (1,852 words) - 05:44, 31 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... 37 KB (4,287 words) - 22:52, 20 March 2024 |
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... 25 KB (2,581 words) - 21:08, 5 April 2024 |
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 |
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)... 11 KB (1,100 words) - 19:38, 1 December 2023 |
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... 6 KB (621 words) - 21:24, 20 January 2024 |
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... 73 KB (8,797 words) - 11:23, 9 April 2024 |
The Birkhoff polytope Bn (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete... 8 KB (994 words) - 11:59, 13 September 2023 |
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... 9 KB (876 words) - 21:10, 21 November 2022 |
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... 47 KB (5,298 words) - 22:02, 5 April 2024 |
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to... 8 KB (697 words) - 15:16, 18 August 2023 |
mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic... 9 KB (1,415 words) - 09:31, 17 December 2023 |
convex polytopes, a distributive polytope is a convex polytope for which coordinatewise minima and maxima of pairs of points remain within the polytope. For... 1 KB (151 words) - 09:31, 17 December 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... 25 KB (2,081 words) - 19:32, 25 March 2024 |
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... 38 KB (1,927 words) - 01:24, 9 March 2024 |
mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid... 8 KB (1,293 words) - 01:59, 19 June 2022 |