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...

Polytopes" (PDF). Weisstein, Eric W. "Regular polychoron". MathWorld. Jonathan Bowers, 16 regular 4-polytopes Regular 4D Polytope Foldouts Catalog of...

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...

a chapter on cross-sections and projections of polytopes, and a chapter on star polytopes and polytope compounds. The second edition was published in...

The list has not been proven complete. Regular 4-polytopes are a subset of the uniform 4-polytopes, which satisfy additional requirements. Regular 4-polytopes...

4-dimensional cross-polytope also goes by the name hexadecachoron or 16-cell. It is one of the six convex regular 4-polytopes. These 4-polytopes were first described...

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

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...

coefficients. Like all polytopes, 4-polytopes may be classified based on properties like "convexity" and "symmetry". A 4-polytope is convex if its boundary...

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...

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...

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 vertices...

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...

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

Ziegler, Günter M. (1995). "Chapter 4: Steinitz' Theorem for 3-Polytopes". Lectures on Polytopes. Graduate Texts in Mathematics. Vol. 152. Springer-Verlag...

a regular star 4-polytope with Schläfli symbol {5/2,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is also one of two such polytopes that...

starts as 1-polytopes and ends with n = 5 as infinite tessellations of 4-dimensional hyperbolic space. There are two types of pentagonal polytopes; they may...

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...

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...

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...

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...

Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math...

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...

Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math...

6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of...

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...