Primes of the G hexomino

9 × 12, 9 × 20, 9 × 28
12 × 13, 12 × 14, 12 × 17, 12 × 19, 12 × 21, 12 × 24, 12 × 25, 12 × 29
15 × 28, 15 × 32, 15 × 36, 15 × 40, 15 × 44, 15 × 48, 15 × 52
16 × 18, 16 × 27, 16 × 30, 16 × 33, 16 × 39, 16 × 42
20 × 21, 20 × 24
complete

smallest rectangle: 9 × 12

The 9 × 12 rectangle, which has a unique tiling, was given by Klarner [1, Figure 3].

It is proved in [2, Theorem 5.4] that any rectangle tiled by the G hexomino has one side divisible by 4 . The complete set of primes is given in [3, Example 5.8].

Also see Torsten Sillke's G hexomino page.

References

[1] David A. Klarner, Some Results Concerning Polyominoes, Fibonacci Quarterly 3 (1965), no. 1, pp. 9-20.
[2] Michael Reid, Tile Homotopy Groups, L'Enseignement Mathématique 49 (2003), no. 1-2, pp. 123-155.
[3] Michael Reid, Klarner Systems and Tiling Boxes with Polyominoes, Journal of Combinatorial Theory, Series A 111 (2005), no. 1, pp. 89-105.

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Updated August 25, 2011.