https://doi.org/10.1140/epjb/e2016-60891-2
Regular Article
Polytopes vibrations within Coxeter group symmetries
1
Department of physics, Faculty of nuclear sciences and physical
engineering, Czech Technical University in Prague, Břehová 7, 115 19 Prague 1, Czech
Republic
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
a
e-mail: m.szajewska@math.uwb.edu.pl
Received:
16
November
2015
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
© The Author(s) 2016. This article is published with open access at Springerlink.com
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