Primes of the L pentomino

2 × 5 (smallest rectangle)
7 × 15 (smallest odd rectangle)
complete

smallest rectangle: 2 × 5




smallest odd rectangle: 7 × 15

Klarner [2, Figure 12] gave a 9 × 15 rectangle, which was thought to be the smallest odd rectangle. However, it was later discovered (see [1, Figure 164], [3, Figure 11], [4, Figure 9]) that 7 × 15 is the smallest odd rectangle.

Also see Torsten Sillke's L pentomino page.

References

[1] Solomon W. Golomb, Polyominoes, Second edition, Second printing (paperback version), Princeton University Press, 1996.
[2] David A. Klarner, Packing a Rectangle with Congruent N-ominoes, Journal of Combinatorial Theory 7 (1969) pp. 107-115.
[3] William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192.
[4] Michael Reid, Tiling Rectangles and Half Strips with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 80 (1997), no. 1, pp. 106-123.

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Updated August 25, 2011.