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Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 473–483 | Cite as

Rhombellane space filling

  • Mircea V. DiudeaEmail author
  • Csaba L. Nagy
Original Paper
  • 30 Downloads

Abstract

A space-filling polyhedron is a polyhedron that can tessellate the 3D space. The complete bipartite graph K2.3 is the graph representation of [1,1,1]-propellane, a synthesized molecule, or rather of its reduced form, appearing in the polymer called staffane, with all rings being rhombs/squares. Further, the complete bipartite graphs K2.n represent generalized [1,..,1n]-propellanes, in the following named rhombellanes; they are involved in the space-filling within rhombic arrays. This paper presents construction of some crystals and quasicrystals consisting of rhombellanes, and their characterization in crystallographic terms (by connectivity and ring signature) and in topological terms (by Omega polynomial).

Keywords

Rhombellane Ring signature sequence Hamiltonian circuit 

Notes

Acknowledgements

This work was supported by a Grant of the Romanian National Authority for Scientific Research and Innovation, CCCDI—UEFISCDI, Project Number 8/2015, acronym GEMNS).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabeș-Bolyai UniversityCluj-NapocaRomania

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