Lars Luthman wrote:

> You could probably use rhombidodecahedrons (phew!). They look like hexagons
> from one angle and squares from another angle. I'm pretty sure they would
> fit into each other nicely, but I haven't really tried.

Of all regular polyhedra, only cubes tesselate, I believe...
Try saying small rhombic triacontahedron three times fast! (Or small
hexagrammic hexecontahedron...)

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