Xie, Jiale2017-08-282017-08-282017-08-282017-08-23http://hdl.handle.net/10012/12233For a hyperbolic plane tessellation there is a generating function with respect to the distance. This generating function is the same as the growth function of a group of isometries of hyperbolic plane that acts regularly in the tessellation. For most of the tessellation the generating functions have a symmetric form. In this thesis we will show the computation of the generating function for the hyperbolic plane tessellation and find the tessellations that have a symmetric form in the generating functions.enMaster Thesis