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...

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

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

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...

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...

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

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...

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...

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...

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

list of nonprismatic semiregular convex polytopes with regular facets (convex regular 4-polytopes) in his publication On the Regular and Semi-Regular...

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...

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

facets. A uniform 8-polytope is one which is vertex-transitive, and constructed from uniform 7-polytope facets. Regular 8-polytopes can be represented...

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...

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

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...

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...

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

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...

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...

24: 6–10. Coxeter, H. S. M. (1948). Regular Polytopes. Methuen and Co. Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover Publications...

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

icositetragram, with twenty four edges 257-gram, with two hundred and fifty seven edges List of regular polytopes and compounds § Stars Complex polygon...