Abstract: This paper provides an overview of methods for creating symmetric patterns based on tessellations and applications of isometries to basic objects of hyperbolic plane. Algorithm for creating and drawing different types of planar edge-to-edge tessellations of Euclidean, elliptic and hyperbolic plane with regular polygons as tiles (not all congruent) and vertices of the same type, including regular, uniform, non-uniform and coloured tessellations is implemented in “Mathematica 4.0”® package “Tess”. Using tools provided in the package we focus on discovering the intrinsic abstract beauty of mathematics by creating more intricate tessellations. Automatically generated coloured tessellations of the hyperbolic plane presented in a Poincare disk model, together with additional data provided, are combined with an arbitrary additional motif in order to obtain a new design. Based upon a choice of the subpattern/motif the same tessellation will become more/less symmetrical and can appear totally different.