Iron pyrites, or pyrite, belongs crystallographically to the parallelfaced hemihedral class of the cubic system.
Quartz crystallizes in the trapezohedral-hemihedral class of the rhombohedral division of the hexagonal system.
A polyhedron is said to be the hemihedral form of another polyhedron when its faces correspond to the alternate faces of the latter or holohedral form; consequently a hemihedral form has half the number of faces of the holohedral form.
Hemihedral forms are of special importance in crystallography, to which article the reader is referred for a fuller explanation of these and other modifications of polyhedra (tetartohedral, enantiotropic, &c.).
Since the tetrahedron is the hemihedral form of the octahedron, and the octahedron and cube are reciprocal, we may term these two latter solids " reciprocal holohedra " of the tetrahedron.