Crystallography and the Penrose pattern
AL Mackay - Physica A: Statistical Mechanics and its Applications, 1982 - Elsevier
Physica A: Statistical Mechanics and its Applications, 1982•Elsevier
The Penrose pattern is a tiling of two-dimensional and of three-dimensional space by
identical tiles of two kinds (acute and obtuse rhombi with α= 72° and 144° in two dimensions
and acute and obtuse rhombohedra with α= 63.43° and 116.57° in three dimensions). The
two-dimensional pattern is a section through that in three dimensions. When joining (or
recursion) rules are prescribed, the pattern is unique and non-periodic. It has local five-fold
axes and thus represents a structure outside the formalism of classical crystallography and …
identical tiles of two kinds (acute and obtuse rhombi with α= 72° and 144° in two dimensions
and acute and obtuse rhombohedra with α= 63.43° and 116.57° in three dimensions). The
two-dimensional pattern is a section through that in three dimensions. When joining (or
recursion) rules are prescribed, the pattern is unique and non-periodic. It has local five-fold
axes and thus represents a structure outside the formalism of classical crystallography and …
Abstract
The Penrose pattern is a tiling of two-dimensional and of three-dimensional space by identical tiles of two kinds (acute and obtuse rhombi with α = 72° and 144° in two dimensions and acute and obtuse rhombohedra with α = 63.43° and 116.57° in three dimensions). The two-dimensional pattern is a section through that in three dimensions. When joining (or recursion) rules are prescribed, the pattern is unique and non-periodic. It has local five-fold axes and thus represents a structure outside the formalism of classical crystallography and might be designated a quasi-lattice.
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