Crystallography and the penrose pattern
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.
- Publication:
-
Physica A Statistical Mechanics and its Applications
- Pub Date:
- August 1982
- DOI:
- 10.1016/0378-4371(82)90359-4
- Bibcode:
- 1982PhyA..114..609M