Asimov also asks for the smallest triangle that will always cover at least one point of the integer lattice, or equivalently a triangle such that no matter at what angle you place copies of it on an integer lattice, they always cover the plane; my guess is that the worst angle is parallel and 30 degrees to the lattice, giving a triangle with 2-unit sides and contradicting an earlier answer to Asimov's question.
Quasicrystals and aperiodic tilings, A. Zerhusen, U. Kentucky. Includes a nice description of how to make 3d aperiodic tiles from zometool pieces.
From the Geometry Junkyard,
and recreational geometry pointers.
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David Eppstein, Theory Group, ICS, UC Irvine.
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