# Polytope contractions within icosahedral symmetry

@article{Bodner2014PolytopeCW, title={Polytope contractions within icosahedral symmetry}, author={M. Bodner and J. Patera and M. Szajewska}, journal={Canadian Journal of Physics}, year={2014}, volume={92}, pages={1446-1452} }

Icosahedral symmetry is ubiquitous in nature, and understanding possible deformations of structures exhibiting it can be critical in determining fundamental properties. In this work we present a framework for generating and representing deformations of such structures while the icosahedral symmetry is preserved. This is done by viewing the points of an orbit of the icosahedral group as vertices of an icosahedral polytope. Contraction of the orbit is defined as a continuous variation of the… Expand

#### 4 Citations

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Abstract
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In this paper the root polytopes of all finite reflection groups W with a connected Coxeter-Dynkin diagram in {\bb R}^n are identified, their faces of dimensions 0 ≤ d ≤ n - 1 are counted, and the… Expand

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A reduction of orbits of finite reflection groups to their reflection subgroups is produced by means of projection matrices, which transform points of the orbit of any group into points of the orbits… Expand

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