Primes of the L hexomino

2 × 6
7 × 12
8 × 15
9 × 14, 9 × 16, 9 × 34
10 × 15
11 × 18
complete

smallest rectangle: 2 × 6



smallest odd rectangle: 9 × 14

The smallest odd rectangle was given in [2, Figure 13] and [3, Figure 11]. Several primes were found by Fletcher [1]. The complete set of primes was given in [4, Example 5.13].

References

[1] Raymond R. Fletcher III, Tiling Rectangles with Symmetric Hexagonal Polyominoes, Proceedings of the Twenty-seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, LA, 1996, Congressus Numerantium 122 (1996), pp. 3-29.
[2] William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192.
[3] Michael Reid, Tiling Rectangles and Half Strips with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 80 (1997), no. 1, pp. 106-123.
[4] 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.