A lattice is a regular arrangement of an infinite set of points in space. A Bravais lattice is one where every point looks the same as every other point. You can build any lattice from a Bravais lattice by "decorating" it, in which case we call it a lattice with a basis. We show how to construct the Wigner-Seitz cell, a particular type of unit cell. Roger Penrose, mathematician, came up with a way to tile space that has (in a manner of speaking) five fold symmetry, and never repeats. The patterns are beautiful. Be sure and google Penrose tiles. Audio

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