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.
Last revised 2014-12-04.