The snub dodecahedron is a 92-faced solid having 4 triangles and a pentagon at each corner.

Rhombic dodecahedron (Iio), and f the four-faced cube (310).

Crystals of blende belong to that subclass of the cubic system in which there are six planes of symmetry parallel to the faces of the rhombic dodecahedron and none parallel to the cubic faces; in other words, the crystals are cubic with inclined hemihedrism, and have no centre of symmetry.

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The rhombic faces of the dodecahedron are often striated parallel to the longer diagonal.

The first three were certainly known to the Egyptians; and it is probable that the icosahedron and dodecahedron were added by the Greeks.

Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe (see Plut.

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.

It is self-reciprocal; the cube and octahedron, the dodecahedron and icosahedron, the small stellated dodecahedron and great dodecahedron, and the great stellated dodecahedron and great icosahedron are examples of reciprocals.

Other examples of reciprocal holohedra are: the rhombic dodecahedron and cuboctahedron, with regard to the cube and octahedron; and the semiregular triacontahedron and icosidodecahedron, with regard to the dodecahedron and icosahedron.

The great stellated dodecahedron is formed by stellating the faces of a great dodecahedron.