Platonic solids generate their four-dimensional analogues

DOI10.1107/S0108767313021442zbMath1284.52016arXiv1307.6768WikidataQ51150738 ScholiaQ51150738MaRDI QIDQ5406859

Pierre-Philippe Dechant

Publication date: 4 April 2014

Published in: Acta Crystallographica Section A Foundations of Crystallography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.6768

zbMATH Keywords

Coxeter groupspolytopesrepresentationssymmetriesspinorsClifford algebrasquaternionsroot systemsMcKay correspondencefour-dimensional geometryplatonic solidstrinities

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Three-dimensional polytopes (52B10) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Clifford algebras, spinors (15A66) Other geometric groups, including crystallographic groups (20H15) Symmetry properties of polytopes (52B15)

Related Items (5)

Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups ⋮ The \(E_8\) geometry from a Clifford perspective ⋮ Affine extensions of non-crystallographic Coxeter groups induced by projection ⋮ A Clifford algebraic framework for Coxeter group theoretic computations. ⋮ Clifford spinors and root system induction: \(H_4\) and the grand antiprism

Cites Work

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• Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• New foundations for classical mechanics.
• Spacelike singularities and hidden symmetries of gravity
• Quaternionic root systems and subgroups of the Aut(F4)
• Topological Solitons

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