Dodecahedron

A dodecahedron is any polyhedron with twelve flat faces, but the term most often refers to the regular dodecahedron, one of the five Platonic solids, whose twelve faces are regular pentagons meeting three to a vertex. It has twenty vertices and thirty edges, and its symmetry group, icosahedral symmetry, has order 120. Plato listed the five Platonic solids and associated the dodecahedron with the cosmos as a whole, setting it apart from the other four, which he matched to the classical elements. The regular dodecahedron is dual to the regular icosahedron, meaning each can be formed by connecting the face centers of the other, and other dodecahedra with different symmetry, such as the pyritohedron and the rhombic dodecahedron, are studied as distinct shapes with the same face count.