Primes of the heptomino

[heptomino]

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

smallest rectangle: 2 × 7

[2 x 7 rectangle]

smallest odd rectangle: 11 × 21

[11 x 21 rectangle]

The smallest odd rectangle is given in [1, Figure 13] and [2, Figure 11]. All three prime rectangles were also found independently 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.

Updated August 25, 2011.