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:
“While you’re playing cards with a regular guy or having a bite to eat with him, he seems a peaceable, good-humoured and not entirely dense person. But just begin a conversation with him about something inedible, politics or science, for instance, and he ends up in a deadend or starts in on such an obtuse and base philosophy that you can only wave your hand and leave.”
—Anton Pavlovich Chekhov (1860–1904)