Non-flat tilings with flat tiles

In general, a tiling is considered to be a set of tiles placed next to each other in a flat plane. The tiles are placed in the plane in such a way that there are no gaps and no overlaps. But what if we leave out the condition that the plane has to be flat? For when there are no gaps and no overlaps between the tiles we still can call it a tiling. The consequences for the possible shapes of the tiles in non-flat tilings as well as the possible symmetrical structures that can be used are discussed in this paper.status: publishe