Crystals as point structures

Within the context of an orbit-by-orbit analysis of structure, it is attractive to consider the growth of extended structures by decoration of a point following the restrictions imposed by particular choices of overall symmetry. 

As a first example, consider the growth of a cubic lattice about the origin. For the simple primitive lattice , most familiar as the structure of the model crystal cubium , the cubic array 

The Qf-phase of polonium is the only known real example of a simple cubic structure. 

These observations provide a convenient method to classify the electronic densities of states in finite clusters for metals exhibiting cubic crystal structures. Each m, n, p set determining 

Kovalev, Irreducible Representations of the Space Groups [Gordon and Breach, New York, 1965] O. V. Kovalev, Representations of the Crystallographic Space Groups Edition 2 [Gordon and Breach Science Publishers, Switzerland, 1993]. 

---