TETARTOHEDRAL  CLASS (

Tetrahedral pentagonal dodecahedral) . Here, in addition to four polar triad axes, the only other elements of symmetry are three dyad axes, which coincide with the crystallo- i From a)6ycos, placed sideways, referring to the absence of planes and centre of symmetry . 2 From yipos, a ring or spiral, and tlSos, form.graphic axes . Six of the simple forms, the cube, tetrahedron, rhombic dodecahedron, deltoid dodecahedron, triakis-tetrahedron and pentagonal dodecahedron, are geometrically the same in this class as in either the tetrahedral or pyritohedral classes . The general form is the Tetrahedral pentagonal dodecahedron (fig . 41) . This is bounded by twelve irregular pentagons, and is a tetartohedral or quarter-faced form of the hexakis-octahedron . Four such forms may be derived, the indices of which are {hkl), {khll, 1hkl) and (khl); the first pair are enantiomorphous with respect to one another, and so are the last pair . Barium nitrate, lead nitrate, sodium chlorate and sodium bromate crystallize in this class, as also do the minerals ullmannite (NiSbS) and langbeinite (K2Mg2(SO4)2) . 2 . TETRAGONAL SYSTEl1 (Pyramidal; Quadratic; Dimetric) . In this system the three crystallographic axes are all at right angles, but while two are equal in length and interchangeable the third is of a different length .

The unequal

axis is spoken of as the principal axis or morphological axis of the crystal, and it is always placed in a vertical position ; in five of the seven classes of this system it coincides with the single tetrad axis of symmetry . The parameters are a: a: c, where a refers to the two equal hori- zontal axes, and c to the vertical axis; c may be either shorter (as in fig . 42) or longer (fig . 43) than a . The ratio a: c is spoken of as the axial ratio of a crystal, and it is dependent on the angles between the faces . In all crystals of the same substance this ratio is constant, and is characteristic of the substance; for other substances crystallizing in the tetragonal system it will be different . For example, in cassiterite it is given as a : c =I: 0.67232 or simply as c =0.67232, a being unity; and in anatase as c =1.7771 .