Local and global color symmetries of a symmetrical pattern
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...
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| Main Authors: | , , |
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| Format: | text |
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Archīum Ateneo
2019
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| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/47 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1046&context=mathematics-faculty-pubs |
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| Institution: | Ateneo De Manila University |
| Summary: | 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. |
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