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
This solution was found by Carl Schwenke and Johann Schwenke.
Octiamonds
Enneiamonds
Dekiamonds
The second tiling was found by Dr. Karl Scherer.
Thanks to Carl Schwenke and Johann Schwenke for reporting this.
Carl Schwenke and Johann Schwenke found the third tiling.
Hendekiamonds
Dodekiamonds
The first tiling in the fourth row was found
by Carl Schwenke and Johann Schwenke.
Last revised 2025-11-16.
Back to Polyiamond and Polyming Tiling
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Polyform Curiosities
Col. George Sicherman
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