PYRITOHEDRAL CLASS (Parallel-faced hemihedral ; dodecahedral.) Crystals of this class possess three cubic planes of symmetry but no dodecahedral planes. There are only three dyad axes of symmetry, which coincide with the crystal lographic axes; in addition there are three triad axes and a centre of symmetry.
Here the cube, octahedron, rhombic dodecahedron, triakis-octa hedron and icositetrahedron are geometrically the same as in the first class. The characters of the faces will, however, be different; thus the cube faces will be striated parallel to one edge only (fig. 89), and triangular markings on the octahedron faces will be placed obliquely to the edges. The remaining simple forms are "hemihedral with parallel faces," and from the corresponding holohedral forms two hemihedral forms, a positive and a negative, may be derived.
Pentagonal dodecahedron (fig. 34).—This is bounded by twelve pentagonal faces, but these are not regular pentagons, and the angles over the three sets of different edges are different. The regular dodecahedron of geometry, con tained by twelve regular pentagons, is not a possible form in crystals. The indices are {hko } : as a simple form { 21O } is of very common occurrence in pyrites, and it is known as the "pyritohedron." Dyakis-dodecahedron (fig. 35).—This is the hemihedral form of the hexakis-octa hedron and has the indices { hkl } ; it is bounded by twenty-four faces. As a sim ple form {32I 1 is met with in pyrites.
Combinations (figs. 36--39) of these forms with the cube and the octahedron are common in pyrites. Fig. 37 resembles in general appearance the regular icosahedron of geometry, but only eight of the faces are equilateral triangles. Cobaltite, smaltite and other sulphides and sulpharsenides of the pyrites group of minerals crystallize in these forms. The alums also belong to this class; from an aqueous solution they crystallize as simple octahedra, sometimes with subordinate faces of the cube and rhombic dodecahedron, but from an acid solution as octahedra combined with the pentagonal dodecahedron