The Geometry Junkyard


One way to define a tiling is a partition of an infinite space (usually Euclidean) into pieces having a finite number of distinct shapes. Tilings can be divided into two types, periodic and aperiodic, depending on whether they have any translational symmetries. If these symmetries exist, they form a lattice. However there has been much recent research and excitement on aperiodic tilings (which lack such symmetries) and their possible realization in certain crystal structures. Tilings also have connections to much of pure mathematics including operator K-theory, dynamical systems, and non-commutative geometry.

From the Geometry Junkyard, computational and recreational geometry pointers.
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David Eppstein, Theory Group, ICS, UC Irvine.
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