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:
“This is the frost coming out of the ground; this is Spring. It precedes the green and flowery spring, as mythology precedes regular poetry. I know of nothing more purgative of winter fumes and indigestions. It convinces me that Earth is still in her swaddling-clothes, and stretches forth baby fingers on every side.”
—Henry David Thoreau (1817–1862)