# 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.

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

The complete set was
first identified in 1992 by Torsten Sillke, and first published
in 2001, in the *Mathematics and Informatics Quarterly,* by
Julian Fogel, Mark Goldenberg, and Andy Liu, who identified it
independently of Sillke.

Last revised 2018-09-28.

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Polyform Tiling
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Polyform Curiosities

Col. George Sicherman
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