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Polytopes vibrations within Coxeter group symmetries

Author

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  • Goce Chadzitaskos

    (Faculty of nuclear sciences and physical engineering, Czech Technical University in Prague)

  • Jiří Patera

    (Centre de recherches mathématiques, Université de Montréal)

  • Marzena Szajewska

    (Institute of Mathematics, University of Bialystok)

Abstract

We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean space R3. By changing one simple element of the polytope (position of one vertex or length of an edge), one can retain the exact symmetry of the polytope by simultaneously changing other corresponding elements of the polytope. A simple method of using the symmetry of polytopes in order to determine several resonant frequencies is presented. Knowledge of these frequencies, or at least their ratios can be used for control of some principal changes of the polytopes.

Suggested Citation

  • Goce Chadzitaskos & Jiří Patera & Marzena Szajewska, 2016. "Polytopes vibrations within Coxeter group symmetries," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(5), pages 1-7, May.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:5:d:10.1140_epjb_e2016-60891-2
    DOI: 10.1140/epjb/e2016-60891-2
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    Keywords

    Solid State and Materials;

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