Warren Smith wrote:

Brilliantly simple! Lovable!

Thank you!

Recently a new phase of matter was discovered. It supposedly appears amorphous to Xray crystallography, but nevertheless exact chemical-composition ratios and "nucleation+growth" behavior are seen. I suppose your sort of lego is one possible explanation of that.

X-ray crystallography would probably detect the `layered' aspect of the tiling from certain angles, but appear amorphous from other angles. Doesn't glass have an exact chemical composition (SiO2, empirically) coupled with an amorphous structure (the crystalline phase being quartz)? Aperiodic tilings are observed in quasicrystals. I seem to recall that certain alloys have local icosahedral symmetry, and generalise the Penrose tiling to three dimensions.

(PS. How'd you make the cool graphics?)

Wolfram Mathematica 8. I actually cheated by not including the indentations on the bottom (since they wouldn't be visible from that aspect): Module[{block = {Cuboid[{-5, -5, 0}, {5, 5, 3}],    GeometricTransformation[     Table[If[Abs[i] + Abs[j] <= 3,       Cylinder[{{2 i, 2 j, 3}, {2 i, 2 j, 3.5}}, 0.6], {}], {i, -3,       3}, {j, -3, 3}], {{4/5, 3/5, 0}, {-3/5, 4/5, 0}, {0, 0, 1}}]}},  Graphics3D[{Red, block, Green, Translate[block, {10, 0, 0}], Purple,    Translate[block, {10, 10, 0}], Yellow,   GeometricTransformation[{block, Orange,     GeometricTransformation[      block, {{{4/5, 3/5, 0}, {-3/5, 4/5, 0}, {0, 0, 1}}, {0, 0,        3}}]}, {{{4/5, 3/5, 0}, {-3/5, 4/5, 0}, {0, 0, 1}}, {10, 0,      3}}]}, Boxed -> False]] I think that Mathematica might be able to export 3D models, although it would be far preferable to rebuild the block in a dedicated CAD package. Sincerely, Adam P. Goucher