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.
at Andrew Clarke's Poly
I found this tiling in April 2023 after Patrick Hamlyn and Edo Timmermans
raised some questions about tiling trapezoids and triangles with the
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.
According to Erich Friedman, Brendan Owen tiled
this triangle with this hexiamond around 2003.
page at Erich's Math Magic.
So far as I know, Karl Scherer first tiled a triangle
with this octiamond.
The triangle had side 32.
Last revised 2023-05-02.
Back to Polyiamond and Polyming Tiling
Col. George Sicherman