If I have blocks of size $1\times 1\times 2$ cubes, how many ways there are to stack them isohedrally in 3D space? I now have pretty robust system for solving this kind of problem in 2D, but 3D escapes me.
I presume that it could be solved by simply enumerating various kinds of planar layers composed of $1\times 2$ rectangles and/or $1\times 1$ squares and stacking them on top of each other, but that seems like it would have a lot of false solutions and couldn't be easily generalized for other shapes/geometries.