# Prime Rectangle Tilings of the Y Pentomino

## Introduction

A *pentomino* is a figure made of five squares joined
edge to edge.
There are 12 pentominoes, not distinguishing reflections and rotations.
They were first enumerated and studied by Solomon Golomb,
who named them after letters of the alphabet.
Four pentominoes can tile rectangles: I, L, P, and Y.
A rectangle tiled by a polyomino is said to be *prime*
if it cannot be composed of smaller tilable rectangles.
Michael Reid's
Rectifiable
Polyomino Page catalogues prime rectangles for small polyominoes.
It shows some examples, including the smallest rectangle for each polyomino.

Erich Friedman's page
Polyominoes in
Rectangles shows prime rectangles for many polyominoes, including
the Y pentomino.

Here are tilings of all 40 prime rectangles for the Y pentomino.
The tilings are not unique.
They are sorted by their shorter dimension.

Last revised 2017-04-22.

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Col. George Sicherman
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