A normal tiling of the plane is a tessellation for which every tile is topologically equivalent to a disk, the intersection of any two tiles is a connected set or the empty set, and all tiles are uniformly bounded. Normality condition disallows tiles that are pathologically long or thin. The automorphism group of a tiling is a bijection of vertices such that each edge and tile is mapped to an edge and tile, respectively. So, the automorphisms extend to homeomorphisms of the plane. I have the following questions:

- Is the automorphism group of a normal tiling finitely generated?
- Is the group acts on the plane properly discontinuously?

Do the answers change if we restrict them to semi-regular tilings? We know that fundamental domain of an infinitely generated automophism group has infinitely many edges. But the domain may be the union of infinitely many tiles. The literatures on tilings concerns themselves usually with the existence of tilings with special properties, but not the automorphism group.