In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0?≤?j?≤?n, where n is the dimension of the polytope) ? cells, faces and so on ? are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤?n.
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