Three-dimensional analogs of the planar Penrose tilings and quasicrystals

DOI10.1016/0012-365X(89)90282-3zbMath0681.52007OpenAlexW1975100787WikidataQ127633634 ScholiaQ127633634MaRDI QIDQ1823471

Yanyan Li

Publication date: 1989

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(89)90282-3

zbMATH Keywords

quasicrystalsPenrose tiling

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (15)

The countability of a tiling family and the periodicity of a tiling ⋮ Polytopes that fill \(\mathbb{R}^ n\) and scissors congruence ⋮ Canonical substitutions tilings of Ammann-Beenker type ⋮ Quasiperiodic canonical-cell tiling with pseudo icosahedral symmetry ⋮ Binary tiling quasicrystals and matching rules ⋮ Undecidable translational tilings with only two tiles, or one nonabelian tile ⋮ Integral cohomology of rational projection method patterns ⋮ Quasicrystals: The view from Les Houches ⋮ Packing, covering and tiling in two-dimensional spaces ⋮ Ammann bars and quasicrystals ⋮ DIFFRACTION ON ICOSAHEDRAL DANZER TILINGS ⋮ Aperiodic tiles ⋮ Local rules for quasiperiodic tilings of quadratic 2-planes in \({\mathbb{R}{}}^ 4\) ⋮ On the index of Siegel grids and its application to the tomography of quasicrystals ⋮ Local rules for multi-dimensional quasicrystals

Cites Work

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• Theory of matching rules for the 3-dimensional Penrose tilings
• Some generalized Penrose patterns from projections ofn-dimensional lattices
• On periodic and non-periodic space fillings ofE^mobtained by projection
• Space-group theory for a nonperiodic icosahedral quasilattice

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