High Quality Content by WIKIPEDIA articles! A uniform polytope is a vertex-transitive polytope made from uniform polytope facets. A uniform polytope must also have only regular polygon faces. Uniformity is a generalization of the older category semiregular, but also includes the regular polytopes. Further, nonconvex regular faces and vertex figures (star polygons) are allowed, which greatly expand the possible solutions. A strict definition requires uniform polytopes be finite, while a more expansive definition allows uniform tessellations (tilings and honeycombs) of Euclidean and hyperbolic space to be considered polytopes as well.

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