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Unbalanced Anisohedral Tiling

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Description: Joseph Myers and John Berglund found a polyhex that must be placed in two different ways in a tiling of a plane, such that one placement occurs twice as often as the other.
A tile that is unbalanced - with different sized transitivity classes There are many tiles that are 2-anisohedral. The two transitivity classes required for these tiles will usually be the same size. (OK, OK, that's not precise. Look at ratios of classes in ever expanding disks or take the ratio in a block that tiles isohedrally.) But a tile has been discovered that requires one transitivity class to be twice the size of the other.
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