Combinatorial representation of tetrahedral chains
Hassan Babiker, Stanislaw Tadeusz Janeczko · Communications in Information and Systems · 2015
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.