# 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.*

Back to Polyiamond and Polyming Tiling
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Polyform Tiling
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Polyform Curiosities

Col. George Sicherman
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