If we represent each of their hexagonal cells by 24 triangles, all 333 heptahexes can be tiled with the heptiamonds. Below is show one solution for each shape. Because 7 and 24 don't have a common divisor, it is impossible to break any of these into two pieces with hexagonal boundaries (say, a trihex and a tetrahex). If this was possible, it would have been easier to prove that some heptahexes are heptiamond tilable.