Wikipedia:WikiProject Uniform Polytopes

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The uniform 421 polytope, shown inside its Petrie polygon as an orthogonal projection, defined by its Coxeter–Dynkin diagram:
CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel branch.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
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.


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


  • Create a template navigator:


  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.


Uniform polytopes/tessellations by dimension


Geometers who have worked on regular and uniform polytopes:

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