(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 crystallographic
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}, {khl}, {h'kl} and {k'hl}; 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)3).