Colorings of Hyperbolic Plane Crystallographic Patterns

• Main Authors: De Las Peñas, Ma. Louise Antonette N, Felix, Rene P, Laigo, Glenn R
• Format: text
• Published: Archīum Ateneo 2006
• Subjects: Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/110; https://www.degruyter.com/view/journals/zkri/zkri_zkri.2006.221.issue-10_2015-11-06--12-59-11/zkri.2006.221.issue-10/zkri.2006.221.10.665/zkri.2006.221.10.665.xml
• Institution: Ateneo De Manila University

In color symmetry the basic problem has always been to classify symmetrically colored symmetrical patterns [13]. An important step in the study of color symmetry in the hyperbolic plane is the determination of a systematic approach in arriving at colored symmetrical hyperbolic patterns. For a given uncolored semi-regular tiling with symmetry group G a hyperbolic plane crystallographic group, this question can be addressed by applying a general framework for coloring symmetrical patterns and using right coset colorings as a tool to study the subgroup structure of G. In this paper, we present colored patterns that emerge from the hyperbolic 3 (.) 4 (.) 3 (.) 4 (.) 3 (.) 3 tiling where all the symmetries of the uncolored tiling permute the colors of the patterns.