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Encyclopedia Britannica - Main :: DIO-DRO |
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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
dodecahedron inscriptible in the same sphere. The " small stellated dodecahedron," the " great
great
Kepler
Poinsot
POLYHEDRON ). In crystallography, the regular
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
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