This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces.The Schläfli symbol notation describes every regular polytope, and is used widely below as a compact reference name for each.The regular polytopes are grouped by dimension and subgrouped by convex, nonconvex and infinite forms. Nonconvex forms use the same vertices as the convex forms, but have intersecting facets. Infinite forms tessellate a one lower dimensional Euclidean space.
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