  If all tiles in a tiling are congruent, the tiling is called monohedral.
Tiling by convex polygons is called edge-to-edge if any two convex polygons are
either disjoint or share one vertex or one entire edge in common. In this
paper, we prove that a convex polygon that can generate an edge-to-edge
monohedral tiling must be able to generate a periodic tiling.

Metric Geometry