Dodecahedron
| Dodecahedron
|
Click on picture for large version.
Click for spinning version.
|
| Type
| Platonic
|
| Face polygon
| pentagon
|
| Faces
| 12
|
| Edges
| 30
|
| Vertices
| 20
|
| Faces per vertex
| 3
|
| Vertices per face
| 5
|
| Symmetry group
| icosahedral (Ih)
|
| Dual polyhedron
| icosahedron
|
| Properties
| regular, convex
|
A
dodecahedron is a
Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. It has twenty vertices and thirty edges. Its
dual polyhedron is the
icosahedron. Canonical coordinates for the vertices of a dodecahedron centered at the origin are {(0,±1/φ,±φ), (±1/φ,±φ,0), (±φ,0,±1/φ), (±1,±1,±1)}, where φ = (1+√5)/2 is the
golden mean. Five cubes can be made from these, with their edges as diagonals of the dodecahedron's faces, and together these comprise the regular
polyhedral compound of five cubes. The stellations of the dodecahedron make up three of the four Kepler-Poinsot solids.
The area A and the volume V of a regular dodecahedron of edge length a are:
-
The term dodecahedron is also used for other
polyhedra with twelve faces, most notably the
rhombic dodecahedron which is dual to the
cuboctahedron and occurs in nature as a crystal form. The normal dodecahedron is sometimes called the pentagonal dodecahedron to distinguish it.
The 20 vertices and 30 edges of a dodecahedron form the basic map for a computer game called Hunt The Wumpus.
Especially in roleplaying, this solid is known as a d12, one of the more common Polyhedral dice.
See also
External links
