Tiling a Holey Badge with a Polyiamond

A polyiamond badge is a convex polyiamond whose side lengths have the pattern a b a b a b.

If one of a, b is zero, the badge reduces to a triangle. (If both a, b are zero, the badge vanishes.)

Given a polyiamond, how few copies of it can be joined to form a badge with optional isolated moniamond holes that do not touch the perimeter of the badge?

Here I show minimal known holey badge tilings for polyiamonds with up through 7 cells. If you find a smaller solution or solve an unsolved case, please write.

[ Moniamond [ Diamond | Triamond | Tetriamonds | Pentiamonds | Hexiamonds | Heptiamonds ]

Moniamond

Diamond

Triamond

Tetriamonds

Pentiamonds

Impossible

Hexiamonds

Impossible

Heptiamonds

Unsolved

Solutions with Holes Touching the Perimeter

Last revised 2026-08-13.


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Col. George Sicherman [ HOME | MAIL ]