Quadrilateral and hexagonal maps corresponding to the subgroups Γ0(N) of the modular group

Abstract

Let N = 2(alpha)3(beta). The normalizer Gamma(B)(N) of Gamma(0)(N) in PSL(2, R) is the triangle group (2, 4, infinity) for alpha = 1, 3, 5, 7; beta = 0, 2 and the triangle group (2, 6, infinity) for alpha = 0, 2, 4, 6; (beta) = 1, 3. In this paper we examine relationship between the normalizer and the regular maps. We define a family of subgroups of the normalizer and then we study maps with quadrilateral and hexagonal faces using these subgroups and calculating the associated arithmetic structure.