The Isometric Tetrahedral Class

Another suboerdinate divisionof the Isometric System is known as the Tetrahedral Class, deriving its name from its chief form, the tetrahedrom.

Symmetry and Forms. The symmetry of this class is as follows: The there crystallographic axes are axes of binary symmetry; the four diagonal axes are axes of trigonal symmetry; there are six diagonal planes of symmetry.

The characteristic forms of the Tetragonal class are as follows:

1. Tetrahedron.
The tetrahedron is a form composed of four equilateral triangular faces, each of which intersects all of the crystallographic axes at equal lengths. It can be considered as derived from the octahedron of the Normal Class by the omission of the alternate faces and the extension of the others, is known as the positive tetrahedron and has for its symbol (111). If the other four faces of the octahedron resulting would have had a different orientation. This is known as the negative tetrahedron and has for its symbol (111). The positive and negative tetrahedrons when occurring alone are geometrically identical, and the only reason for recognizing the possibility of the existence of two different orientations lies in the fact that at times they may occur truncating each other, if a positive and negative tetrahedron occurred together with equal development, the resulting crystal could not be distinguished from an octahedrom, unless, as is usually the case, the faces of the two forms, showed different lusters, etchings or striations that would serve to differentiate them.

Other possible but rare tetrahedral forms are the following: The tristetrahedron, the faces of which correspond to one half the faces of a trapezohedron; the deltoid dodecahedron, the of which correspond to one-half those of the trisoctahedron; the hexakistetrahedron, the faces of which correspond to one-half the faces of the hexoctahedron.

The cube and dodecahedron are also found on minerals of the Tetrahedral Class. Tetrahedrite and the related tennantite are the only common minerals that ordinarily show distinct tetrahedral forms. Sphalerite occasionally exhibits them, but commonly its crystals are quite complex and distorted.

Characteristic of Isometric Crystals
The striking characteristics of isometric crystals which would aid in their recognition may be summarized as follows:

The crystals are equidimensional in three directions at right angles to each other. These three directions in crystals of the Normal class are axes of tetragonal symmetry. The crystals commonly show faces that are squares or equilateral triangles or these figures with truncated corners. They are characterized by the large number of similar faces, the smallest number on any form of the Normal Class being six. Every form by itself would make a solid.

Important Isometric Angles. Below are given various interfacial angles which may assist in the recognition of the commoner isometric forms:

• Cube (100) ^cube (010) = 90° 0’ 00’’
• Octahedron (111) ^ octahedron (111) = 70° 31’ 44’’
• Dodecahedron (110) ^dodecahedron (101) = 60° 0’ 00’’
• Cube (100) ^ octahedron (111) 54° 44’ 8’’
• Cube (100) ^ dodecahedron (110) = 45° 0’ 00’’
• Octahedron (111) ^ dodecahedron (110) = 35° 15’ 52’’