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.