Semi-regular tilings of the hyperbolic plane (Q2225663)

This paper deals with (edge-to-edge) semi-regular tilings of the hyperbolic plane, i.e., tessellations by regular (geodesic) polygons that have the same pattern at each vertex. A semi-regular tiling of the Euclidean plane is an Archimedean tiling. The authors determine criteria for the existence and uniqueness of some kinds of semi-regular tilings of the hyperbolic plane (with a specific vertex type). Concerning this, they prove some positive results and pose some new open questions.