66 × 84, ...

...

smallest rectangle: 66 × 84

It was asked in [1] (see question 4 at the end) if this shape can tile any rectangle. The 66 × 84 rectangle above is the smallest rectangle tiled by this shape, and also the first rectangle found. It is unknown if this shape is odd, i.e. tiles any rectangle using an odd number of tiles.

**Reference**

[1] Michael Reid,
Tiling Rectangles and
Half Strips with Congruent Polyominoes,
*Journal of Combinatorial Theory, Series A* **80** (1997),
no. 1, pp. 106-123.

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Updated May 18, 2005.