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.