This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the **hemihedral** form of the regular octahedron and consequently a form of the cubic system.

The bisphenoids (the **hemihedral** forms of the tetragonal and rhombic bipyramids)., and the trigonal pyramid of the hexagonal system, are examples of non-regular tetrahedra (see Crystallography).

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.

In this way a mixture of the two asparagines was obtained, which were separated by picking out the **hemihedral** crystals.