A regular polyhedron is a polyhedron whose faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive - i.e. it is transitive on its flags. This last alone is a sufficient definition.
A regular polyhedron is identified by its Schläfli symbol of the form {n, m}, where n is the number of sides of each face and m the number of faces meeting at each vertex. There are 5 finite regular polyhedra, which are called the Platonic solids, the self-dual tetrahedron {3,3}, dual-pair cube/octahedron {4,3}, and dual pair dodecahedron/icosahedron {5,3}.
Read more about Regular Polyhedron: The Regular Polyhedra, Duality of The Regular Polyhedra, Regular Polyhedra in Nature, Further Generalisations
Famous quotes containing the word regular:
“He hung out of the window a long while looking up and down the street. The world’s second metropolis. In the brick houses and the dingy lamplight and the voices of a group of boys kidding and quarreling on the steps of a house opposite, in the regular firm tread of a policeman, he felt a marching like soldiers, like a sidewheeler going up the Hudson under the Palisades, like an election parade, through long streets towards something tall white full of colonnades and stately. Metropolis.”
—John Dos Passos (1896–1970)