Polytopes vibrations within Coxeter group symmetries
Department of physics, Faculty of nuclear sciences and physical
engineering, Czech Technical University in Prague, Břehová 7, 115 19 Prague 1, Czech
2 Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, H3C 3J7, Canada
3 Institute of Mathematics, University of Bialystok, 1M Ciolkowskiego, 15-245 Bialystok, Poland
Received in final form: 11 April 2016
Published online: 23 May 2016
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.
Key words: Solid State and Materials
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