# Wikipedia:WikiProject Uniform Polytopes

The uniform 421 polytope, shown inside its Petrie polygon as an orthogonal projection, defined by its Coxeter–Dynkin diagram:
Uniform operators on the regular cube and octahedron

Welcome to WikiProject Uniform Polytopes, the WikiProject which aims to improve Wikipedia's coverage of uniform polytopes! A uniform polytope is an extension to the regular polytopes, including regular and semiregular polytopes, being vertex transitive, and having regular polygon faces.

Regular polytopes are identified by Schläfli symbols. Uniform polytopes are (nearly all) identified by Coxeter–Dynkin diagrams, existing in Coxeter group symmetry families. These are called Wythoffian, being generated by reflection symmetry called a Wythoff construction. Most of the remaining nonwythoffian forms are generated by operational modifications on the reflective forms.

## News

• All links to Richard Klitzing's site have to be updated as the address moved from ogre.nu to bendwavy.org in January 2011.

## Contents

• Create a template navigator:

## Members

1. Tom Ruen (talk) - I referenced all the wiki articles I know related to this topic, still quite unsure what the immediate goals for this project should be.
2. Mateus Zica - i'm here to help!
3. Double sharp - I will usually stick to the polychora, polytera, and polypeta but may sometimes venture out into higher dimensions.

## Articles

 2-polytopes: Regular polygon Star polyhedron Tessellations: Apeirogon 3-polytopes/2-tilings: Regular polyhedra: Platonic_solid (regular, convex) Kepler–Poinsot_polyhedron (regular, nonconvex) Hosohedron and Dihedron (regular, degenerate) List of spherical symmetry groups Uniform polyhedron Archimedean solid (uniform, convex) Semiregular polyhedron Catalan solid (Uniform duals, convex) Uniform star polyhedron (uniform, nonconvex) Prismatic uniform polyhedron, Prism (geometry) and Antiprism (prismatic) Duals Bipyramid, Trapezohedron Tessellations: Hyperbolic tessellations: Uniform tilings in hyperbolic plane 4-polytopes/3-honeycombs: Regular 4-polytope (regular, convex and star) Uniform 4-polytope (uniform, convex) Duoprism (uniform, prismatic, convex) Tessellations: Convex uniform honeycombs (infinite, uniform, convex) Hyperbolic tessellations: Convex uniform honeycombs in hyperbolic_space (hyperbolic, infinite, uniform, convex) Paracompact uniform honeycombs 5-polytopes: Uniform 5-polytope (uniform, convex) 6-polytopes: Uniform 6-polytope (uniform, convex) Uniform 7-polytopes (convex) Uniform 8-polytopes (convex) Uniform 9-polytopes (convex) Uniform 10-polytopes (convex)

### Geometers

 Plato (428–348 BC) Archimedes (287–212 BC) Johannes Kepler (1571–1630) Leonhard Euler (1707–1783) Louis Poinsot (1777–1859) Ludwig Schläfli (1814–1895) Eugène Charles Catalan (1814–1894) Arthur Cayley (1821–1895) Joseph Bertrand (1822–1900) Edmund Hess (1843–1903) Pieter Hendrik Schoute (1846–1923) Alicia Boole Stott (1860–1940) W. A. Wythoff (1865–1939) Thorold Gosset (1869–1962) Alfredo Andreini (1870–1943) D. M. Y. Sommerville (1879–1934) M. C. Escher (1898–1972) H. S. M. Coxeter (1907–2003) J. C. P. Miller (1906–1981) Magnus Wenninger (1919–) Michael S. Longuet-Higgins (1925–) Branko Grünbaum (1929–) Norman Johnson (1930–) John Horton Conway (1937–) Keith Critchlow George Olshevsky (1946–) George W. Hart (1955–) Jeffrey Weeks