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 the only polyiamond I know of whose convex tiling with the fewest tiles uses tiles of different sizes. So far as I know, this polyiamond (the C heptiamond) cannot tile any convex polyiamond at uniform scale.
If you find another such polyiamond, or a tiling with fewer tiles than shown, please write.
See also Similar Polyaboloes Forming a Convex Shape.
Last revised 2022-04-25.