Tiling a Triangle with a Scaled Polyiamond

When can a polyiamond at various scales tile a triangle? Here I show some minimal tilings of triangles by scaled copies of a polyiamond. Please write if you know of other such tilings.

Every triangular polyiamond has an imbalance of cells pointing up and cells pointing down. Thus any polyiamond whose cell parity balances cannot tile a triangle.

Here I show the solution with the fewest known tiles for each polyiamond. In the figures below, the numbers are the side of the triangle and the number of tiles used.

See also Tiling a Triangle with a Polyiamond.

Moniamond

Triamond

Tetriamonds

Pentiamonds

Hexiamonds

Heptiamonds

Octiamonds

Enneiamonds

Dekiamonds

Dodekiamonds

Last revised 2023-05-10.


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Col. George Sicherman [ HOME | MAIL ]