Parameters for frameworks and space filling polyhedra

Abstract

Space filling packings of polyhedra are described by 9 summarizing parameters, of which 3 are independent. For structures of “crystal-chemical interest”, presuppositions are formulated and, in addition to equations, an approximation is derived which in principle reduces the degree of freedom to 2. Frameworks of vertices (atoms) and edges (bonds) are also regarded as packings of polyhedra though sometimes of unconventional properties. The approach offers qualitative and topological insights which are hardly achievable in a precise manner; e.g. the average size of the rings in frameworks as a function of coordination number and the various kinds of limitations for packings of polyhedra may be surveyed.