Ideal and defective vertex configurations in the planar octagonal quasilattice

The well-known two-dimensional octagonal quasilattice is realized by means of dualization and Klotz construction. We discuss the geometric properties and the extended symmetry of the pattern. The concept of geometric defects is introduced, and an elastic energy measure {Δ}E is presented that allows a simple sequencing of the forbidden vertices. After a sketchy comparison with Lennard-Jones calculations, some thermodynamic consequences of {Δ}E are discussed. It turns out that the specific heat should show a significant increase in comparison with the crystallographic case.