Polytopes vibrations within Coxeter group symmetries

  • Goce Chadzitaskos
  • Jiří Patera
  • Marzena Szajewska
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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.

Keywords

Solid State and Materials 

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Copyright information

© The Author(s) 2016

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Goce Chadzitaskos
    • 1
  • Jiří Patera
    • 2
  • Marzena Szajewska
    • 3
  1. 1.Department of physicsFaculty of nuclear sciences and physical engineering, Czech Technical University in PraguePragueCzech Republic
  2. 2.Centre de recherches mathématiques, Université de MontréalMontréalCanada
  3. 3.Institute of Mathematics, University of BialystokBialystokPoland

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