Wulff-shape and density deviation (Q1971729)

The shape of ideal crystals and quasicrystals, called the Wulff-Shape, is usually explained via minimum energy principles. Another approach which leads to surprisingly good models of crystals and quasicrystals is via dense sphere packings and an appropriate density measure (parametrie density and density deviation). In this paper the author investigates the basic mathematical properties of these tools. For some other concepts of dense sphere packings he shows that they are less appropriate models for crystallography, which underlines the quality of parametric density and density deviation.