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The rhombic dodecahedron is a polyhedron which has similar
symmetry to a cube and can be tiled to fill space like a cube,
but is much less boring than a cube. One could conceivably
bake rhombic dodecahedral lumps of clay into bricks -
even without a mold, it wouldn't be all that hard to cut the
shape, given a clay knife or wire that could be guided along a
Walls built with rhombic dodecahedra would be a bit lumpy, but
sometimes that's desirable (for example, for baffling sound).
The walls could merge seamlessly at various nontraditional angles
without breaking the tiling. (You could do right angles too, depending
on how they're oriented.) You could even continue the tiling into a
There are some other possible space-filling solids, but none
that combine regularity and oddness in quite so pleasing a
Mark Newbold's Rhombic Dodecahedron Page
A page about the rhombic dodecahedron with a focus on its stranger properties. [baf, May 13 2000, last modified Oct 04 2004]
Are there space-filling versions other than trivial prismatic extensions? [rmutt, May 13 2000, last modified Oct 04 2004]
Yes, there are. [egnor, May 13 2000, last modified Oct 04 2004]
||Two words, man. "Rhombic Lego." I'd buy 'em.
||OK, which side(s) of Lego Rhombrix do you put the bumps and dimples on? Actually might be better to make them like Bristle Blocks, which have unisex interlocking "fingers". Or flat magnets which have alternating north/south polar stripes/regions (although alignment might be a problem). Or Velcro stripes.
||didn't buckminster fuller do this already?