Theory of matching rules for the 3-dimensional Penrose tilings

DOI10.1007/BF01218580zbMath0651.52015OpenAlexW2019907608MaRDI QIDQ1106475

A. Katz

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf01218580

zbMATH Keywords

Penrose tilingtiling by rhombohedra

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Polytopes and polyhedra (52Bxx)

Related Items

Nested triacontahedral shells or how to grow a quasi-crystal ⋮ Polytopes that fill \(\mathbb{R}^ n\) and scissors congruence ⋮ Local rules for pentagonal quasi-crystals ⋮ Quasiperiodic canonical-cell tiling with pseudo icosahedral symmetry ⋮ Meyer's concept of quasicrystal and quasiregular sets ⋮ Binary tiling quasicrystals and matching rules ⋮ Weak local rules for planar octagonal tilings ⋮ Canonical projection tilings defined by patterns ⋮ Weak matching rules for quasicrystals ⋮ Quasicrystals: The view from Les Houches ⋮ Aperiodic tiles ⋮ Local rules for quasiperiodic tilings of quadratic 2-planes in \({\mathbb{R}{}}^ 4\) ⋮ Symmetry revisited ⋮ Three-dimensional analogs of the planar Penrose tilings and quasicrystals ⋮ Weak colored local rules for planar tilings ⋮ Local rules for multi-dimensional quasicrystals

Cites Work

• Unnamed Item
• A geometrical approach of quasiperiodic tilings
• Pentaplexity. A class of non-periodic tilings of the plane
• On periodic and non-periodic space fillings ofE^mobtained by projection