Primes of the P hexomino

2 × 6
3 × 4
5 × 18
6 × 11
9 × 10
complete

smallest rectangles: 2 × 6, 3 × 4




smallest odd rectangle: 6 × 11

The smallest odd rectangle was given by Klarner [1, Figure 10], who remarked that it is unusual for an odd order to be prime. Also, this is the only known shape with odd order less than 15, other than rectangles.

Also see Torsten Sillke's P hexomino page.

Reference

[1] David A. Klarner, Packing a Rectangle with Congruent N-ominoes, Journal of Combinatorial Theory 7 (1969) pp. 107-115.

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Updated August 23, 2011.