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Coincidences of a shifted hexagonal lattice and the hexagonal packing

Research paper by Jeanine Concepcion H. Arias, Evelyn D. Gabinete, Manuel Joseph C. Loquias

Indexed on: 04 Dec '13Published on: 04 Dec '13Published in: Mathematics - Metric Geometry



Abstract

A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices (CSLs) and coincidence site modules (CSMs), respectively. Recently, coincidences of shifted lattices and multilattices (i.e. finite unions of shifted copies of a lattice) have been investigated. Here, we solve the coincidence problem for a shifted hexagonal lattice. This result allows us to analyze the coincidence isometries of the hexagonal packing by viewing the hexagonal packing as a multilattice.