Primes of the octomino

22 × 80, 22 × 88, 22 × 96, 22 × 104, 22 × 112, 22 × 120, 22 × 128, 22 × 136, 22 × 144, 22 × 152
26 × 64, 26 × 72, 26 × 80, 26 × 88, 26 × 96, 26 × 104, 26 × 112, 26 × 120
28 × 60, 28 × 64, 28 × 72, 28 × 80, 28 × 84, 28 × 88, 28 × 92, 28 × 96, 28 × 100, 28 × 104, 28 × 108, 28 × 112, 28 × 116
30 × 56, 30 × 64, 30 × 72, 30 × 80, 30 × 88, 30 × 96, 30 × 104
32 × 48, 32 × 52, 32 × 54, 32 × 56, 32 × 58, 32 × 60, 32 × 62, 32 × 64, 32 × 66, 32 × 68, 32 × 70, 32 × 72, 32 × 74, 32 × 76, 32 × 78, 32 × 80, 32 × 82, 32 × 84, 32 × 86, 32 × 88, 32 × 90, 32 × 92, 32 × 94, 32 × 98
34 × 48, 34 × 56, 34 × 64, 34 × 72, 34 × 80, ...
36 × 40, 36 × 44, 36 × 48, 36 × 56, 36 × 64, 36 × 72, ...
38 × 48, 38 × 64, 38 × 80, ...
40 × 40, 40 × 42, 40 × 44, 40 × 46, 40 × 48, 40 × 50, 40 × 52, 40 × 54, 40 × 56, 40 × 58, 40 × 60, 40 × 62, 40 × 64, 40 × 66, 40 × 68, 40 × 70, 40 × 74
42 × 48, 42 × 64, ...
44 × 48, 44 × 56, 44 × 64, ...
46 × 48, 46 × 64, ...
48 × 48, 48 × 50, 48 × 52, 48 × 54, 48 × 56, 48 × 58, 48 × 60, 48 × 62
50 × 64, ...
56 × 56, ...
...

smallest rectangle: 36 × 40

Marshall [1, Figure 2] gives a 32 × 48 rectangle tiled by this octomino. The minimal rectangle is 36 × 40 , as shown above; it has a unique tiling, and this tiling is not symmetric.

Reference

[1] William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192.

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Updated March 23, 2008.