Bi-tilability

Hexiamonds + heptiamonds and one sided tetrahexes

This case is the natural sum of the following two: since hexiamonds make it up for 12 hexagons and heptiamonds -- for 28, this means that when both sets are combined we can have 40 hexagons. This is precisely the total area of the one sided tetrahexes, since only three (out of seven) tetrahexes lack symmetry. One sided pieces cannot be turned over when puzzles are solved -- assymmetrical pieces come in two varieties.

There are many shapes that can be formed with the one sided tetrahexes. However, the examples below are only highly symmetrical ones. In addition, I've kept the hexiamonds and heptiamonds groupes together and fitting in the hexagonal grid.

Beautiful solutions are obtained when the tetrahexes, covered by the hexiamonds, are all assymmetrical and their mirror images are covered by the heptiamonds. In this case the part covered by the heptiamonds corresponds to the set of seven regular tetrahexes, as below:

In this case the heptiamond part is bi-tilable, which was not true in the preceding two examples with ternary symmetry.

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