4D-POLYTOPES AND THEIR DUAL POLYTOPES OF THE COXETER GROUP W(A4) REPRESENTED BY QUATERNIONS

DOI10.1142/S0219887812500351zbMath1257.52006arXiv1102.1132WikidataQ126003328 ScholiaQ126003328MaRDI QIDQ4902536

Mehmet Koca, Nazife Ozdes Koca, Mudhahir Al-Ajmi

Publication date: 16 January 2013

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

Full work available at URL: https://arxiv.org/abs/1102.1132

zbMATH Keywords

Coxeter groupsquaternionsdual polytopes\(W(A_4)\)4D-polytopes

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (4)

Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups ⋮ SU(5) grand unified theory, its polytopes and 5-fold symmetric aperiodic tiling ⋮ QUATERNIONIC CONSTRUCTION OF THE W(F₄) POLYTOPES WITH THEIR DUAL POLYTOPES AND BRANCHING UNDER THE SUBGROUPS W(B₄) AND W(B₃) × W(A₁) ⋮ Stereographic visualization of 5-dimensional regular polytopes

Cites Work

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• Quaternionic representation of snub 24-cell and its dual polytope derived from \(E_8\) root system.
• Maximal subgroups of the Coxeter group \(W(H_4)\) and quaternions.
• Quaternionic root systems and subgroups of the Aut(F4)
• Polyhedra obtained from Coxeter groups and quaternions
• Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions
• A highly symmetric four-dimensional quasicrystal
• 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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