Local rules for quasiperiodic tilings of quadratic 2-planes in \({\mathbb{R}{}}^ 4\)

DOI10.1007/BF02096563zbMath0769.52016MaRDI QIDQ1207984

Sergej Piunikhin, Vladimir Sadov, Le Ty Kuok Tkhang

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

quasicrystalslocal rulepoint groupquasiperiodic tilings

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Other geometric groups, including crystallographic groups (20H15) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (9)

Local rules for pentagonal quasi-crystals ⋮ On diffraction by aperiodic structures ⋮ Weak local rules for planar octagonal tilings ⋮ Canonical projection tilings defined by patterns ⋮ No weak local rules for the \(4_p\)-fold tilings ⋮ Atlas of quasicrystalline tilings. ⋮ Weak colored local rules for planar tilings ⋮ Local rules for multi-dimensional quasicrystals ⋮ When periodicities enforce aperiodicity

Cites Work

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• Several new results on quasicrystallographic groups in Novikov's sense
• Theory of matching rules for the 3-dimensional Penrose tilings
• Absence of weak local rules for the planar quasicrystalline tiling with the 8-fold rotational symmetry
• Three-dimensional analogs of the planar Penrose tilings and quasicrystals
• Some generalized Penrose patterns from projections ofn-dimensional lattices
• On periodic and non-periodic space fillings ofE^mobtained by projection
• Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings
• Quasiperiodic patterns and icosahedral symmetry

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