Investigation of regular and semi-regular tilings ofeuclidean and hyperbolic plane

In this thesis, it is investigated the tilings of the same vertex type (the case of the same polygons in the same order at every vertex) among which can be made by the regular polygons in Euclidean and in hyperbolic plane. These type of tilings are called regular and semi-regular tilings. It is proven that there are 11 type of regular or semi-regular Euclidean tilings. In a similar way with Euclidean case, the hyperbolic case is studied and it is proven that there are infinitely many regular tilings in hyperbolic plane. Well known semi-regular tilings which are obtained from the regular ones are also examined. Furthermore, it is studied possible cases of the vertex-types of hyperbolic semi-regular tilings according to the number of polygons adjoined at a vertex. Finally a proramme is written for hyperbolic regular tilings.