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...

article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only...

mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra...

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

Polyhedra? Branko Grünbaum (2003), Fig. 3 Regular polytopes, p.95 Coxeter, The Densities of the Regular Polytopes II, 1932, p.53 Lee, Hwa Young; "Origami-Constructible...

X: The Regular Polytopes. Coxeter, H.S.M.; Regular Polytopes (third edition). Dover Publications Inc. ISBN 0-486-61480-8 'there are 48 regular polyhedra'...

convex 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...

mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...

In geometry, a cross-polytope, hyperoctahedron, orthoplex, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space. A 2-dimensional...

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...

tetrahedral sides. The regular 5-cell is bounded by five regular tetrahedra, and is one of the six regular convex 4-polytopes (the four-dimensional analogues...

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 two...

{ p , q , r , . . . } {\displaystyle \{p,q,r,...\}} that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century...

obtuse 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...

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...

4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons...

general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric. If the edge length of a regular octahedron is a, the radius...

of regular compounds of regular polytopes. Coxeter lists a few of these in his book Regular Polytopes. McMullen added six in his paper New Regular Compounds...

Cylinder". Coxeter 1973, p. 12, §1.8 Configurations. Park, Poo-Sung. "Regular polytope distances", Forum Geometricorum 16, 2016, 227-232. http://forumgeom...

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

the image, Coxeter, H.S.M.; Regular Polytopes, 3rd Edn, Dover (pbk), 1973, p. 114 Shephard, G.C.; "Regular complex polytopes", Proc. London Math. Soc. Series...

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...

four-dimensional 120-cell, a regular 4-dimensional polytope, constructed from 120 dodecahedra, projecting it down to 3-dimensions. The regular dodecahedron can also...

Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter. It was originally published by Methuen in 1947 and...

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...

for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections: A principal diagonal of a...

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...

tetrahedra)", Regular Polytopes, pp. 71–72 Coxeter, H. S. M. (1973), "§7.6 The symmetry group of the general regular polytope", Regular Polytopes Vinberg,...

7-2c". Regular Polytopes (3rd ed.). Dover. pp. 122-123. ISBN 0-486-61480-8. p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n dimensions...

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one...