30 degrees
The (provably) unique and trivial tessellation with this prototile.
1
1
1
1
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1
Slice each in half and coloreach orientation uniquely.
Begin tiling:
It seems rather promising, in thatfree-will, nondeterministic sort of way.
But, alas, things don't alwaysfit so snugly as one might hope.
Ick!
So let's be a bit more systematic, in our tiling.
All of these configurations clearly tile. They appear to tessellate hexagonally, but, really, they're just variants of unidirectional nondeterministic replication.
In each of the smallest rectangles, above, we have a choice:
or
Such tessellations consist employ either two or four orientations.
24 orientations. Rotational and axial (reflectional) symmetry.
12 orientations. Rotational and axial (reflectional) symmetry.
24 orientations. Rotational but no axial symmetry.
12 orientations. Rotational but no axial symmetry.
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B
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D
E
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G
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I
J
K
L