Symmetry of gems
Equilateral five-, seven- or eight-sided tiles would not do. In the same way, five-, seven- or eightfold symmetry is unknown in crystallography, but may be found among certain animals such as radiolaria, corals, molluscs, sea-urchins and starfish, and also among many flowering plants. The degree of symmetry of the crystal depends upon the number of axes and planes of symmetry which it contains. The least symmetrical crystals are those belonging to the triclinic system which have no elements of symmetry; and the most symmetrical is the cube, which possesses nine planes of symmetry, thirteen axes of symmetry—of which three are of four-fold, four of three-fold and six of two-fold symmetry—as well as a centre of symmetry. Another aspect of crystal symmetry is that corresponding faces have certain properties in common. Thus, in many crystals, dull or rough faces may alternate with smooth, gleaming faces, while striated faces may lie next to smooth ones. If striated or grooved faces are present in a crystal the orientation of the lines is governed by the symmetry pattern (Plate 12); and if foreign particles are included within the crystal their alignment is controlled by the same factor)