Wikipedia:WikiProject Uniform Polytopes

The uniform4₂₁polytope,shown inside itsPetrie polygonas anorthogonal projection,defined by itsCoxeter–Dynkin diagram:

Uniform operators on the regularcubeandoctahedron

Welcome toWikiProject Uniform Polytopes,the WikiProject which aims to improve Wikipedia's coverage ofuniform polytopes!A uniform polytope is an extension to theregular polytopes,includingregularandsemiregularpolytopes, beingvertex transitive,and havingregular polygonfaces.

Regular polytopes are identified bySchläfli symbols.Uniform polytopes are (nearly all) identified byCoxeter–Dynkin diagrams,existing inCoxeter groupsymmetry families. These are called Wythoffian, being generated by reflection symmetry called aWythoff 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

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.
4. OfficialURL(talk) – As withWikiProject Polyhedra,I'll translate articles to Spanish.

Articles

• Polytopeterminology:
  • Vertex,Edge,Face,Cell,Hypercell,Peak,Ridge,Facet,Euler characteristic
  • Dual polyhedron,Conway polyhedron notation,Chiral polytope

• Regular polytope
  • List of regular polytopes
  • Schläfli symbol
  • Simplex,Hypercube,Orthoplex,Hypercubic honeycomb

• Uniform polyhedronterminology:
  • Coxeter–Dynkin diagram,Wythoff symbol,Vertex figure
  • Schwarz triangle,Goursat tetrahedron,density (polytope)
  • Vertex-transitive,Edge-transitive,Face-transitive,Cell-transitive,Wythoff construction
  • Petrie polygon,Schlegel diagram,Polyhedral net,Uniform coloring
  • Vertex configuration,Face configuration
  • Rectification,Truncation,Bitruncation,Cantellation,Runcination,Sterication,Pentellation,Expansion,Snub
  • demihypercube,Semiregular k 21 polytope,Uniform_2_k1_polytope,Uniform_1_k2_polytope
  • Alternated hypercubic honeycomb

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) HosohedronandDihedron(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)andAntiprism(prismatic) DualsBipyramid,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

Geometerswho 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

Related WikiProjects

• Wikipedia:WikiProject Mathematics
• Wikipedia:WikiProject Polyhedra