All Outputs (9)

Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction (2015)
Journal Article
Dechant, P. (2015). Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction. Journal of Physics: Conference Series, 597(1), Article 012027. https://doi.org/10.1088/1742-6596/597/1/012027

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-Dieudonné theorem, an even number of successive Coxeter reflections yields rotations that in a Clifford algebra framework ar... Read More about Rank-3 root systems induce root systems of rank 4 via a new Clifford spinor construction.

Viruses and fullerenes - symmetry as a common thread? (2014)
Journal Article
Dechant, P., Wardman, J., Keef, T., & Twarock, R. (2014). Viruses and fullerenes - symmetry as a common thread?. Acta Crystallographica Section A: Foundations and Advances, 70(2), 162-167. https://doi.org/10.1107/s2053273313034220

The principle of affine symmetry is applied here to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organizational principle in v... Read More about Viruses and fullerenes - symmetry as a common thread?.

A Clifford algebraic framework for Coxeter group theoretic computations (2014)
Journal Article
Dechant, P. (2014). A Clifford algebraic framework for Coxeter group theoretic computations. Advances in Applied Clifford Algebras, 24(1), 89-108. https://doi.org/10.1007/s00006-013-0422-4

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 groups. Motivated by this progress, we explore here t... Read More about A Clifford algebraic framework for Coxeter group theoretic computations.

Platonic solids generate their four-dimensional analogues (2013)
Journal Article
Dechant, P. (2013). Platonic solids generate their four-dimensional analogues. Acta Crystallographica Section A: Foundations and Advances, 69(6), 592-602. https://doi.org/10.1107/s0108767313021442

This paper shows how regular convex 4-polytopes – the analogues of the Platonic solids in four dimensions – can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan–Dieudonne´ theorem, the reflecti... Read More about Platonic solids generate their four-dimensional analogues.

Affine extensions of non-crystallographic Coxeter groups induced by projection (2013)
Journal Article
Dechant, P., Boehm, C., & Twarock, R. (2013). Affine extensions of non-crystallographic Coxeter groups induced by projection. Journal of Mathematical Physics, 54(9), Article 093508. https://doi.org/10.1063/1.4820441

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 E 8, D 6, and A 4. We show that the induced affine... Read More about Affine extensions of non-crystallographic Coxeter groups induced by projection.

Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups (2013)
Journal Article
Dechant, P. (2013). Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups. Advances in Applied Clifford Algebras, 23(2), 301-321. https://doi.org/10.1007/s00006-012-0371-3

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 the Clifford Geometric Algebra framework, which affo... Read More about Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups.

Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups (2012)
Journal Article
Dechant, P., Boehm, C., & Twarock, R. (2012). Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups. Journal of Physics A: Mathematical and Theoretical, 45(28), Article 285202. https://doi.org/10.1088/1751-8113/45/28/285202

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 Kac–Moody-type formalism. In particular, we show that the affine... Read More about Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups.

Cracking the Taub-NUT (2010)
Journal Article
Dechant, P., Lasenby, A., & Hobson, M. (2010). Cracking the Taub-NUT. Classical and Quantum Gravity, 27(18), Article 185010. https://doi.org/10.1088/0264-9381/27/18/185010

We present further analysis of an anisotropic, non-singular early universe model that leads to the viable cosmology presented in Dechant et al (2009 Phys. Rev. D 79, 043524). Although this model (the Dechant–Lasenby–Hobson (DLH) model) contains scala... Read More about Cracking the Taub-NUT.

Anisotropic, nonsingular early universe model leading to a realistic cosmology (2009)
Journal Article
Dechant, P., Lasenby, A., & Hobson, M. (2009). Anisotropic, nonsingular early universe model leading to a realistic cosmology. Physical Review D, 79(4), Article 043524. https://doi.org/10.1103/physrevd.79.043524

We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular “pancaking” solution: the hypersurface volume goes to zero instantaneously at the “big bang”, but all physical quantities, such... Read More about Anisotropic, nonsingular early universe model leading to a realistic cosmology.