Local and global color symmetries of a symmetrical pattern

• Main Authors: Abila, Agatha Kristel, De Las Peñas, Ma. Louise Antonette N, Taganap, Eduard C
• Format: text
• Published: Archīum Ateneo 2019
• Subjects: color symmetry; local symmetry; global symmetry; perfect colorings; transitive perfect colorings; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/47; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1046&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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 of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of P, the symmetry of P that is both a global and local symmetry, effects the same permutation of the colors used to color P and the corresponding motif, respectively.