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Symmetry groups associated with tilings on a flat torus
Author(s) -
Loyola Mark L.,
De Las Peñas Ma. Louise Antonette N.,
Estrada Grace M.,
Santoso Eko Budi
Publication year - 2015
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s205327331402419x
Subject(s) - torus , substitution tiling , homogeneous space , symmetry (geometry) , hexagonal tiling , tessellation (computer graphics) , euclidean geometry , mathematics , combinatorics , rotational symmetry , planar , space (punctuation) , geometry , euclidean space , group (periodic table) , pure mathematics , physics , computer science , quantum mechanics , computer graphics (images) , grid , operating system
This work investigates symmetry and color symmetry properties of Kepler, Heesch and Laves tilings embedded on a flat torus and their geometric realizations as tilings on a round torus in Euclidean 3‐space. The symmetry group of the tiling on the round torus is determined by analyzing relevant symmetries of the planar tiling that are transformed to axial symmetries of the three‐dimensional tiling. The focus on studying tilings on a round torus is motivated by applications in the geometric modeling of nanotori and the determination of their symmetry groups.