Half a croissant, on a plate, with a sign in front of it saying '50c'
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Bricks shaped like rhombic dodecahedra
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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 clay into shape, given a clay knife or wire that could be guided along a 45-degree angle.

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 sloped roof.

There are some other possible space-filling solids, but none that combine regularity and oddness in quite so pleasing a manner.

baf, May 13 2000

Mark Newbold's Rhombic Dodecahedron Page http://dogfeathers.com/mark/rhdodec.html
A page about the rhombic dodecahedron with a focus on its stranger properties. [baf, May 13 2000, last modified Oct 04 2004]

Penrose Tilings http://www.cs.uidah...enrose/penrose.html
Are there space-filling versions other than trivial prismatic extensions? [rmutt, May 13 2000, last modified Oct 04 2004]

Quasicrystals http://www.nirim.go.jp/~weber/qc.html
Yes, there are. [egnor, May 13 2000, last modified Oct 04 2004]


       Two words, man. "Rhombic Lego." I'd buy 'em.
Uncle Nutsy, Jul 12 2000

       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.
lee, Jan 24 2001

       didn't buckminster fuller do this already?
clarence, Sep 08 2002


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