Unusual building blocks based on close-packed spheres

So, take a stack of cannonballs–these are close-packed spheres, and their centers define the so-called “face centered cubic” lattice. Then imagine “inflating” the cannonballs, without moving their centers, until there are no empty spaces left inside the stack. The cannonballs are now rhombic dodecahedra, and their edges define what is known as the Voronoi diagram (Wikipedia) of the face-centered cubic lattice.

Mathematician and artist George Hart (who writes our Math Monday column), created a cool set of six building blocks by slicing up and combining bits of these rhombic dodecahedra. Theoretically, the same set of blocks can be used to build tetrahedra and octahedra of any size. Thingiverse user Lenbok printed a set on a MakerBot. George’s are printed in nylon using selective laser sintering, and, as he points out, look a lot like fancy sugar cubes. I suppose you could print them on a CandyFab and make them actual sugar cubes. Or sugar Voronoi cells, I should say.