On Index 2 Subgroups of Hyperbolic Symmetry Groups
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 . 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.
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.