A dodecahedron is a
Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. Its
dual is the
icosahedron. Canonical coordinates for the vertices of a dodecahedron centered at the origin are (0,±1/τ,±τ), (±1/τ,±τ,0), (±τ,0,±1/τ), (±1,±1,±1), where τ = (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 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.
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