Spongy Diamond

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 rodlike polymer derived from hexahydroxycyclohexane was imagined. Further, the idea of linear polymer synthesized from dehydroadamantane was extended in the design of a threedimensional crystal network, named dia(s), of which tile is a hyperadamantane (an adamantane of which vertices are just adamantanes). It was suggested that this network could be synthesized starting from the real molecule tetrabromoadamantane, by dehydrogenation and polymerization. The crystal structures herein proposed were characterized by connectivity and ring surrounding sequences and also by the Omega polynomial.