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.

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Col. George Sicherman [ HOME | MAIL ]