How few similar (scaled) copies of a given polyiamond can form a convex shape? For most polyiamonds, the convex tilings with the fewest tiles use equal tiles, as with this tetriamond:
Here I show three polyiamonds whose convex tiling with the fewest tiles uses tiles of different sizes. So far as I know, these polyiamonds cannot tile any convex polyiamond at uniform scale. Andrew Bayly discovered the second and third tilings.
See also Similar Polyaboloes Forming a Convex Shape.
Last revised 2025-04-20.