A new characteristic of Möbius transformations by use of polygons having type A

In the hyperbolic plane Möbius transformations can be characterized by Lambert quadrilaterals, i.e., a continuous bijection which maps Lambert quadrilaterals to Lambert quadrilaterals must be Möbius. In this paper we generalize this result to the case of polygons with n sides having type A, that is, having exactly two non-right interior angle.