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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.