On Index 2 Subgroups of Hyperbolic Symmetry Groups

Authors

Ma. Louise Antonette N. De Las Peñas, Ateneo de Manila UniversityFollow
Rene P. Felix, University of the Philippines Diliman
Eden Delight Miro, Ateneo de Manila UniversityFollow

Document Type

Article

Publication Date

2007

Abstract

Subgroups of crystallographic groups play an important role in many branches of mathematics, physics and crystallography such as representation theory, the theories of phase transitions, manifolds and in the comparative study of crystal structures [14]. In this work, the index 2 subgroups of a huge family of crystallographic groups called triangle groups are derived using black and white tilings. The focus of the work will be in determining the index 2 subgroups of triangle groups in the hyperbolic plane.

Recommended Citation

De Las, M. L. A. N., Felix, R. P., & Provido, E. D. B. (2007). On index 2 subgroups of hyperbolic symmetry groups. Zeitschrift für Kristallographie, 222(9), 443-448.