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Full-Text Articles in Algebraic Geometry
Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap
Local And Global Color Symmetries Of A Symmetrical Pattern, Ma. Louise Antonette N. De Las Peñas, Agatha Kristel Abila, Eduard C. Taganap
Mathematics Faculty Publications
This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern P consisting of disjoint congruent symmetric motifs. The pattern P has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of P ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of P, a coloring that is perfect and transitive under G, satisfying the condition that the coloring …
Symmetry Groups Associated With Tilings On A Flat Torus, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Grace M. Estrada, Eko Budi Santoso
Symmetry Groups Associated With Tilings On A Flat Torus, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Grace M. Estrada, Eko Budi Santoso
Mathematics Faculty Publications
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.