List of regular polytopes information

Only counting polytopes of full rank. There are more regular polytopes of each rank > 1 in higher dimensions. There are no Euclidean regular star tessellations...

There are no exceptional regular polytopes in these dimensions. See also the list of regular polytopes. Regular polytopes can be further classified according...

geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions...

called a deltahedron. Euclidean tilings by convex regular polygons Platonic solid List of regular polytopes and compounds Equilateral polygon Carlyle circle...

[1948]. "§1.8 Configurations". Regular Polytopes (3rd ed.). New York: Dover. Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed.). Cambridge: Cambridge...

List of surfaces List of polygons, polyhedra and polytopes List of regular polytopes and compounds Solid geometry, including table of major three-dimensional...

comparison mensuration. It also has many relations with other polytopes. The appearance of regular icosahedron can be found in nature, such as the virus with...

Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591] (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math...

lists 32 regular compounds of regular 4-polytopes in his book Regular Polytopes. McMullen adds six in his paper New Regular Compounds of 4-Polytopes, in which...

of space. This and the regular tessellation of cubes are the only such uniform honeycombs in 3-dimensional space. Like all regular convex polytopes,...

(1973). Regular Polytopes (3rd ed.). New York: Dover. pp. 122–123. Weisstein, Eric W. "Cube". MathWorld. Cube: Interactive Polyhedron Model* Volume of a cube...

Glossary". Stella. Retrieved 2023-03-09. H. S. M. Coxeter (1948). Regular Polytopes (1 ed.). London: Methuen & Co. LTD. pp. 120–121. OCLC 4766401. Zbl 0031...

10-polytope 10-cube 10-demicube 10-orthoplex 10-simplex Regular polytope and List of regular polytopes Simplex Hypercube Cross-polytope Uniform polytope...

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...

the emblem of Azerbaijan. An eleven pointed star called the hendecagram was used on the tomb of Shah Nematollah Vali. List of regular polytopes and compounds#Stars...

polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these...

Coxeter: Regular and Semi-Regular Polytopes, Part I, Mathematische Zeitschrift, Springer, Berlin, 1940 N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs...

tetrahedral centers of the 421. These polytopes are part of a family of 255 = 28 − 1 convex uniform 8-polytopes, made of uniform 7-polytope facets and vertex...

of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon). The square is in two families of polytopes in...

5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or...

lists a few of these in his book Regular Polytopes. McMullen added six in his paper New Regular Compounds of 4-Polytopes. Self-duals: Dual pairs: Uniform...