Tiling a Triangle with a Polyiamond

When can a polyiamond tile a triangle? Here I show some minimal tilings of triangles by 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.

See also Rectifiable Polyiamonds at Andrew Clarke's Poly Pages.

Moniamond

Triamond

Tetriamonds

Pentiamonds

I found this tiling in April 2023 after Patrick Hamlyn and Edo Timmermans raised some questions about tiling trapezoids and triangles with the straight pentiamond. Edo had used one of my trapezium (N. Amer. trapezoid) tilings to tile a triangle with side 45.

So far as I know, Mike Reid was the first to tile this triangle with the straight pentiamond.

Hexiamonds

According to Erich Friedman, Brendan Owen tiled this triangle with this hexiamond around 2003. See this page at Erich's Math Magic.

Octiamonds

So far as I know, Karl Scherer first tiled a triangle with this octiamond. The triangle had side 32.

Enneiamonds

Dodekiamonds

Last revised 2023-05-02.

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Col. George Sicherman [ HOME | MAIL ]