Lord
A substitution tiling with inflation factor sqrt(3), using a single prototile, namely a 60ยบ rhomb. The substitution sends one rhomb to seven rhombs (instead of three, as one would expect from the inflation factor), thus the tiles in higher iterations do overlap. But the substitution is chosen in a way such that tiles do either overlap completely, or not at all. So overlapping tiles can be identified, and the substitution yields a proper tiling.

Finite Rotations
P Adic Windowed Tiling
Polytopal Tiles
Parallelogram Tiles
Rhomb Tiles