n-Dimensional array languages and description of crystal Symmetry—II

In this paper the array models are generalized ton-dimensions and these are seen to preserve a natural hierarchy among different families corresponding to a partial ordering induced inn-tuples of integers. Then-dimensional array models are closed under union, concatenation (in all directions), Kleene closure (in all directions) and ε-free general homo-morphlsm. Symmetry operations such as translation, reflection about co-ordinate planes, rotation through angles π/2 and π about the co-ordinate axes, inversion about the origin and conjugation are examined. Three-dimensional matrix models are used to generate space groups of three-dimensional crystallography. Certain regular solids such as the cube, the tetrahedron, the octohedron, prisms and pyramids are generated using the array models to describe the growth of crystals.