Communications in Information and Systems

Volume 15 (2015)

Number 3

Combinatorial representation of tetrahedral chains

Pages: 331 – 359

DOI: https://dx.doi.org/10.4310/CIS.2015.v15.n3.a2

Authors

Hassan Babiker (Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Poland)

Stanisław Janeczko (Instytut Matematyczny PAN, Warszawa, Poland; and Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Poland)

Abstract

Tetrahedral chains consisting of face-sharing regular tetrahedra in Euclidean three space are investigated. A parametrization of the chains by sequences of ordered reflections in barycentric coordinates is constructed and periodicity in their combinatorial structure is found. Periodicity along a chain is based on the structure of sequences of admissible triplets of integers and their cycling properties. The corresponding numerical invariants and an indexing role of a binary tetrahedral group are established.

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Published 30 March 2016