Wikipedia:WikiProject Uniform Polytopes

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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.

Tasks

Create a template navigator:
- Template:Polytopes - started with list of polytopes by dimension

Members

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.
Mateus Zica - i'm here to help!
Double sharp - I will usually stick to the polychora, polytera, and polypeta but may sometimes venture out into higher dimensions.
OfficialURL (talk) – As with WikiProject Polyhedra, I'll translate articles to Spanish.

Articles

Polytope terminology:
- Vertex, Edge, Face, Cell, Hypercell, Peak, Ridge, Facet, Euler characteristic
- Dual polyhedron, Conway polyhedron notation, Chiral polytope

Regular polytope

Uniform polytopes/tessellations by dimension
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: Uniform tiling List of uniform tilings 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

Geometers who have worked on regular and uniform polytopes:
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

Related pages

User:Tomruen/list of uniform polychora
User:Tomruen/Uniform operator conversion - Johnson vs Bower names
User:Tomruen/List of Coxeter groups
User:Tomruen/Uniform polyteron verf
Talk:Vertex_figure/polychoron
User:Tomruen/Gosset-Elte figures
User:Tomruen/Convex_uniform_tetracomb
User:Tomruen/References
User:Double sharp/Polyhedra
User:Double sharp/Polychora
User:Double sharp/Polytera (these three give lists with full names)
List of uniform polyhedra by Schwarz triangle
User:Double sharp/List of uniform tilings by Schwarz triangle
User:Double sharp/List of uniform polychora by Goursat tetrahedron