regular polytope

In mathematics, a regular polytope is a certain kind of geometric figure with a high degree of symmetry. Examples in two dimensions include the square, the regular pentagon and hexagon, and other regular polygons, including star polygons. In three dimensions the regular polytopes include the cube, the dodecahedron, and other regular polyhedra. There exist examples in higher dimensions also. Circles and spheres, although highly symmetric, are not considered polytopes because they do not have plane faces. The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.
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