Deltoid[1] dodecahedron (fig. 27). This is the hemihedral form of the triakis-octahedron; it has the indices {hhk} and is bounded by twelve trapezoidal faces.
Triakis-tetrahedron (fig. 28). The hemihedral form {hkk} of the icositetrahedron; it is bounded by twelve isosceles triangles arranged in threes over the tetrahedron faces.
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| Fig. 30.—Combination of twoTetrahedra. | Fig. 31.—Combination of Tetrahedronand Cube. |
Hexakis-tetrahedron (fig. 29). The hemihedral form {hkl} of the hexakis-octahedron; it is bounded by twenty-four scalene triangles and is the general form of the class.
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| Fig. 32.—Combination of Tetrahedron, Cube and Rhombic Dodecahedron. | Fig. 33.—Combination of Tetrahedron and Rhombic Dodecahedron. |
Corresponding to each of these hemihedral forms there is another geometrically similar form, differing, however, not only in orientation, but also in actual crystals in the characters of the faces. Thus from the octahedron there may be derived two tetrahedra with the indices {111} and {111}, which may be distinguished as positive and negative respectively. Fig. 30 shows a combination of these two tetrahedra, and represents a crystal of blende, in which the four larger faces are dull and striated, whilst the four smaller are bright and smooth. Figs. 31-33 illustrate other tetrahedral combinations.
Tetrahedrite, blende, diamond, boracite and pharmacosiderite are substances which crystallize in this class.
Pyritohedral[2] Class
(Parallel-faced hemihedral; Dyakis-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 crystallographic axes; in addition there are three triad axes and a centre of symmetry.