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Back to article: DODECAHEDRON (Gr. Melia, twelve, and ESpa, a face or base)

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