Orthorhombic and Tetragonal Lattices

Abstract

In the previous chapters we discussed isometric lattices and their space-filling Dirichlet Domains. When these lattices are distorted by stretching the translation vectors differently in different directions, the Domains could be proportionately distorted, and still be space fillers. The Domains of the lattices would still be mutually congruent. However, the Domains of the lattice complexes would be stretched or compressed differently if originally they had been differently oriented. For instance, the space-filling octahedron has to be oriented in three different directions to fill space. If the spacing of the points of the J-complex, being at the centers of the octahedra, is altered differently in different directions, then some octahedra will be squashed or stretched along their polar axis, while others have their equators deformed instead.