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Clifford Algebra Unveils a Surprising Geometric Significance of Quaternionic Root Systems of Coxeter Groups

- Pierre-Philippe Dechant
- Mathematics, Physics
- 7 May 2012

Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E8, have been used extensively in the literature. The present paper analyses such Coxeter groups in… Expand

The birth of E8 out of the spinors of the icosahedron

- Pierre-Philippe Dechant
- Mathematics, Medicine
- Proceedings of the Royal Society A: Mathematical…
- 18 February 2016

TLDR

Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups

- Pierre-Philippe Dechant, C. Boehm, R. Twarock
- Physics, Mathematics
- 24 October 2011

Motivated by recent results in mathematical virology, we present novel asymmetric -integer-valued affine extensions of the non-crystallographic Coxeter groups H2, H3 and H4 derived in a… Expand

Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction

- Pierre-Philippe Dechant
- Mathematics, Physics
- 31 July 2012

In this paper, we show that via a novel construction every rank-3 root system induces a root system of rank 4. Via the Cartan-Dieudonn\'e theorem, an even number of successive Coxeter reflections… Expand

Viruses and fullerenes--symmetry as a common thread?

- Pierre-Philippe Dechant, J. Wardman, T. Keef, R. Twarock
- Mathematics, Physics
- Acta crystallographica. Section A, Foundations…
- 18 February 2014

TLDR

Affine extensions of non-crystallographic Coxeter groups induced by projection

- Pierre-Philippe Dechant, C. Boehm, R. Twarock
- Physics, Mathematics
- 24 October 2011

In this paper, we show that affine extensions of non-crystallographic Coxeter groups can be derived via Coxeter-Dynkin diagram foldings and projections of affine extended versions of the root systems… Expand

Platonic solids generate their four-dimensional analogues.

- Pierre-Philippe Dechant
- Mathematics, Physics
- Acta crystallographica. Section A, Foundations of…
- 25 July 2013

TLDR

Clifford Algebra is the Natural Framework for Root Systems and Coxeter Groups. Group Theory: Coxeter, Conformal and Modular Groups

- Pierre-Philippe Dechant
- Mathematics, Physics
- 18 February 2016

In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric… Expand

A Clifford Algebraic Framework for Coxeter Group Theoretic Computations

- Pierre-Philippe Dechant
- Physics, Mathematics
- 20 July 2012

Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional (affine) Coxeter… Expand

Models of viral capsid symmetry as a driver of discovery in virology and nanotechnology

- Pierre-Philippe Dechant, R. Twarock
- Physics
- 3 February 2021

Viruses are prominent examples of symmetry in biology. A better understanding of symmetry and symmetry breaking in virus structure via mathematical modelling opens up novel perspectives on how… Expand

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