Affine coxeter group Wa(A4), quaternions, and decagonal quasicrystals

DOI10.1142/S0219887814500315zbMath1293.11080arXiv1209.1878OpenAlexW3106342372MaRDI QIDQ5420252

Nazife Ozdes Koca, Mehmet Koca, Ramazan Koç

Publication date: 11 June 2014

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.1878

zbMATH Keywords

quaternionsquasicrystalaffine Coxeter groups\(A_4\) lattice

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Automorphism groups of lattices (11H56) Division algebras and Jordan algebras (17C60) Affine algebraic groups, hyperalgebra constructions (14L17)

Related Items (3)

SU(5) grand unified theory, its polytopes and 5-fold symmetric aperiodic tiling ⋮ M-theory cosmology, octonions, error correcting codes ⋮ Group-theoretical analysis of aperiodic tilings from projections of higher-dimensional latticesB_n

Cites Work

• Similar sublattices of the root lattice \(A_4\)
• Maximal subgroups of the Coxeter group \(W(H_4)\) and quaternions.
• Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture
• Polyhedra obtained from Coxeter groups and quaternions
• Wavefronts and reflection groups
• Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
• Quaternionic roots of SO(8), SO(9), F4 and the related Weyl groups
• Catalan solids derived from three-dimensional-root systems and quaternions
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