1911 Encyclopædia Britannica/Dodecahedron

DODECAHEDRON (Gr. δώδεκα, twelve, and ἕδρα, 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.