Rhombellanic Crystals and Quasicrystals

Abstract

Received 1 April 2018 Accepted 24 April 2018 Published online 1 June 2018 Academic Editor: Ali Reza Ashrafi Design of some crystal and quasicrystal networks, based on rhombellane tiling, is presented. [1,1,1]Propellane, is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane, may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, connectivity sequence, ring sequence and map operations relating structures to their seeds. It is shown, by alternating sum of ranked substructures, that radial structures represent complex constructions of higher rank. Basic properties of rhombellanes, coloring included, are outlined.