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.
Mitscherlich, who also observed the similarity of the crystallographic characters of selenates and sulphates, which afforded valuable corroboration of his doctrine of isomorphism.
The term allotropy has also been applied to inorganic compounds, identical in composition, but assuming different crystallographic forms. Mercuric oxide, sulphide and iodide; arsenic trioxide; titanium dioxide and silicon dioxide may be cited as examples.
A crystal may be regarded as built up of primitive parallelepipeda, the edges of which are in the ratio of the crystallographic axes, and the angles the axial angles of the crystals.
To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters' (x, ?i, w), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules.
These cracks coincide with planes of easy separation or of gliding in the crystal; they are especially useful in helping to determine the crystallographic orientation of a cleavage flake of mica when crystal faces are absent.
He also devoted much attention to the pyroelectric phenomena of crystals, which served as the theme of one of the two memoirs he presented for the degree of D.Sc. in 1869, and to the determination of crystallographic constants.
The cleavage of slates must be distinguished from cleavage of minerals, the latter being due to different degrees of cohesion along definite crystallographic planes.