Primes of the heptomino

2 × 7 (smallest rectangle)
9 × 63
11 × 21 (smallest odd rectangle)
complete

smallest rectangle: 2 × 7




smallest odd rectangle: 11 × 21

The smallest odd rectangle is given in [1, Figure 13] and [2, Figure 11]. In fact, all three prime rectangles were found long ago, but never published, by Andrew Clarke.

Also see Torsten Sillke's page for this heptomino.

References

[1] William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192.
[2] 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 October 23, 2005.