Communications in Information and Systems
Volume 15 (2015)
Combinatorial representation of tetrahedral chains
Pages: 331 – 359
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.