Rhombellane-related crystal networks

Abstract

Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane, HHCH, was imagined. Further, the idea of linear polymer synthesized from dehydro-adamantane, DHAda, was extended in the design of a three-dimensional crystal network, called here Ada-Ada, of which tile is a hyper-adamantane (an adamantane of which vertices are just adamantanes). It was suggested that Ada-Ada would be synthesized starting from the real molecule tetrabromo-adamantane, by dehydrogenation and polymerization. The crystal structures herein proposed were characterized by connectivity and ring sequences and also by the Omega polynomial.