Polytopes vibrations within Coxeter group symmetries
- 257 Downloads
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.
KeywordsSolid State and Materials
- 3.B. Wei, in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (SAGE Publishing, 2013), Vol. 2Google Scholar
- 5.M. Szajewska, Polytope contractions within Weyl group symmetries, accepted in Math. Phys. Anal. Geom. (2016)Google Scholar
- 8.L. Chen, R.V. Moody, J. Patera, Fields Institute Monograph Series, in Quasicrystals and Discrete Geometry, edited by J. Patera (Amer. Math. Soc., 1998), Vol. 10, pp. 135–178Google Scholar
- 9.H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd edn. (Addison-Wesley, New York, 2000)Google Scholar
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.