DODECAHEDRON (Gr. Melia, twelve, and ESpa, a

See also:

• FACE (from Lat. fades, derived either from facere, to make, or from a root fa-, meaning " appear "; cf. Gr. cbatvstv)

face or

See also:

• BASE

base)  , in geometry, a solid enclosed by twelve plane faces . The " ordinary dodecahedron " is one of the Platonic solids (see POLYHEDRON) . The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere . The " small stellated dodecahedron," the " great dodecahedron " and the " great stellated dodecahedron " are Kepler-Poinsot solids; and the " truncated " and " snub dodecahedra " are Archimedean solids (see POLYHEDRON) . In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the " pentagonal dodecahedron " of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones . The " rhombic dodecahedron," one of the geometrical semiregular solids, is an important crystal form . Many other dodecahedra exist as crystal forms, for which see CRYSTALLOGRAPHY .