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.