title: Symmetry groups associated with tilings on a flat torus.
abstract: 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.
authors.affiliation: Mathematics Department, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City, Metro Manila 1108, Philippines.
authors.forename: Mark L
authors.initials: ML
authors.lastname: Loyola
authors.affiliation: Mathematics Department, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City, Metro Manila 1108, Philippines.
authors.forename: Ma Louise Antonette N
authors.initials: ML
authors.lastname: De Las Peñas
authors.affiliation: Mathematics Department, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City, Metro Manila 1108, Philippines.
authors.forename: Grace M
authors.initials: GM
authors.lastname: Estrada
authors.affiliation: Mathematics Department, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City, Metro Manila 1108, Philippines.
authors.forename: Eko Budi
authors.initials: EB
authors.lastname: Santoso
keywords: color symmetry; flat torus; nanotori; symmetry groups