Coincidences of a Shifted Hexagonal Lattice and the Hexagonal Packing |
| J.C.H. Arias, E.D. Gabinete and M.J.C. Loquias
Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia St., UP Campus Diliman, 1101 Quezon City, Philippines |
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| A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices and coincidence site modules, 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. |
DOI: 10.12693/APhysPolA.126.516 PACS numbers: 61.50.Ah, 61.44.Br |