Symmetry Groups Associated With Tilings on a Flat Torus

• Main Authors: De Las Peñas, Ma. Louise Antonette N, Loyola, Mark L, Estrada, Grace M, Santoso, Eko Budi
• Format: text
• Published: Archīum Ateneo 2015
• Subjects: nanotori; flat torus; symmetry groups; color symmetry; Algebraic Geometry; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/8; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1007&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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.