TETRAHEDRAL CLASS (Tetrahedral-hemihedral ; Hexakis-tetrahedral In this class there is no centre of symmetry nor cubic planes of symmetry; the three tetrad axes become dyad axes of symmetry, and the four triad axes are polar, i.e., they are associated with different faces at their two ends. The six dodecahedral planes are the same as in the last class.
Of the seven simple forms, the cube, rhombic dodecahedron and tetrakis-hexa hedron are geometrically the same as be fore, though on actual crystals the faces will have different surface characters. For instance, the cube faces will be striated parallel to only one of the diagonal (fig. 90), and etched figures on this face will be symmetrical with respect to two lines, in stead of four as in the last class. The re maining simple forms have, however, only half the number of faces as the corre sponding form in the last class, and are spoken of as "hemihedral with inclined faces." Tetrahedron (fig. 26).—This is bounded by four equilateral triangles and is identical with the regular tetrahedron of geome try. The angles between the normals to the faces are 109° 28'. It may be derived from the octahedron by suppressing the alternate faces.
Deltoid 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 1 of the icositetrahedron; it is bounded by twelve isosceles triangles arranged in threes over the tetrahedron faces.
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.
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 in dices {III } and {III } , which may be dis tinguished as positive and negative respec tively. Fig. 3o 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 illus trate other tetrahedral combinations.
Tetrahedrite, blende, diamond, boracite and pharmacosiderite are substances which crystallize in this class.