Regular polytope

polytope whose symmetry group acts transitively on its flags
(Redirected from Regular polyhedron)

In mathematics, a regular polytope is a shape with sides and vertices that are symmetrical. Like other polytopes, regular polytopes are found in any number of dimensions.

A dodecahedron, one of the five Platonic solids

A two-dimensional regular polytope is a regular polygon, and a three-dimensional regular polytope is a regular polyhedron. Even though these groups include different shapes, they are based on the same idea of the shapes having regular symmetry. Regular polytopes have regular facets (faces to speak from the 3D viewpoint), and their vertex figures are regular.

Each number of dimensions has a different set of regular polytopes. However, all of them have a simple shape. The simplest of regular polytopes is the triangle in 2D, the tetrahedron in 3D, and the pentachoron in 4D.