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

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Originally appearing in Volume V08, Page 369 of the 1911 Encyclopedia Britannica.
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DODECAHEDRON (Gr. Melia, twelve, and ESpa, a See also:face or See also:base) , in See also:geometry, a solid enclosed by twelve See also:plane faces. The " See also:ordinary dodecahedron " is one of the Platonic solids (see See also:POLYHEDRON). The Greeks discovered that if a See also:line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a See also:cube and dodecahedron inscriptible in the same See also:sphere. The " small stellated dodecahedron," the " See also:great dodecahedron " and the " great stellated dodecahedron " are See also:Kepler-See also:Poinsot solids; and the " truncated " and " snub dodecahedra " are Archimedean solids (see POLYHEDRON). In See also:crystallography, the See also:regular or ordinary dodecahedron is an impossible See also: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 See also: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.

End of Article: DODECAHEDRON (Gr. Melia, twelve, and ESpa, a face or base)

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