Hexiamonds + heptiamonds and side 2 decahexes

Since all trihexes can be tiled with the hexiamonds and all heptahexes can be tiled with the heptiamonds, could all decahexes be tiled when joining the sets of hexiamonds and heptiamonds? The question would be solved if every decahex could be cut into three parts: a monohex, a dihex and a heptahex. An example is shown below:

It seems to me that this is indeed possible. Cutting off the monohex is not a problem. It should be the case that any endecahex can be cut into a dihex and a heptahex: the dihex has simply to lie somewhere on the edge and not inside the endecahex, which could lead to splitting the shape into unconnected parts.

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