What is "regular polyhedron"

Regular \Reg"u*lar\ (-l?r), a. [L. regularis, fr. regula a rule, fr. regere to guide, to rule: cf. F. r['e]gulier. See Rule.]

1. Conformed to a rule; agreeable to an established rule, law, principle, or type, or to established customary forms; normal; symmetrical; as, a regular verse in poetry; a regular piece of music; a regular verb; regular practice of law or medicine; a regular building.

2. Governed by rule or rules; steady or uniform in course, practice, or occurence; not subject to unexplained or irrational variation; returning at stated intervals; steadily pursued; orderlly; methodical; as, the regular succession of day and night; regular habits.

3. Constituted, selected, or conducted in conformity with established usages, rules, or discipline; duly authorized; permanently organized; as, a regular meeting; a regular physican; a regular nomination; regular troops.

4. Belonging to a monastic order or community; as, regular clergy, in distinction dfrom the secular clergy.

5. Thorough; complete; unmitigated; as, a regular humbug.

6. (Bot. & Zo["o]l.) Having all the parts of the same kind alike in size and shape; as, a regular flower; a regular sea urchin.

7. (Crystallog.) Same as Isometric.

   Regular polygon (Geom.), a plane polygon which is both equilateral and equiangular.

   Regular polyhedron (Geom.), a polyhedron whose faces are equal regular polygons. There are five regular polyhedrons, -- the tetrahedron, the hexahedron, or cube, the octahedron, the dodecahedron, and the icosahedron.

   Regular sales (Stock Exchange), sales of stock deliverable on the day after the transaction.

   Regular troops, troops of a standing or permanent army; -- opposed to militia.

   Syn: Normal; orderly; methodical. See Normal.

n. any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent [syn: regular convex solid, regular convex polyhedron, Platonic body, Platonic solid, ideal solid]

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that faces are congruent regular polygons which are assembled in the same way around each vertex.

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 convex regular polyhedra, known as the Platonic solids. These are the: tetrahedron {3, 3}, cube {4, 3}, octahedron {3, 4}, dodecahedron {5, 3} and icosahedron {3, 5}. There are also four regular star polyhedra, making nine regular polyhedra in all.