BUFFON-LEM.pdf (1.42 MB)
In search for a perfect shape of polyhedra: Buffon transformation
journal contribution
posted on 2016-09-23, 13:14 authored by Veronika Schreiber, Alexander VeselovAlexander Veselov, Joseph P. WardFor an arbitrary polygon generate a new one by joining the centres of consecutive edges. Iteration of this procedure leads to a shape which is affine equivalent to a regular polygon. This regularisation effect is usually ascribed to Count Buff on (1707–1788). We discuss a natural analogue of this procedure for 3-dimensional polyhedra, which leads to a new notion of affine
B
-regular polyhedra. The main result is the proof of existence of star-shaped affine $$-regular polyhedra with prescribed combinatorial structure, under partial symmetry and simpliciality assumptions. The proof is based on deep results from spectral graph theory due to Colin de Verdière and Lovász.
History
School
- Science
Department
- Mathematical Sciences
Published in
L’Enseignement MathématiqueVolume
61Issue
3Pages
261 - 284Citation
SCHREIBER, V., VESELOV, A.P. and WARD, J.P., 2015. In search for a perfect shape of polyhedra: Buffon transformation. L’Enseignement Mathématique, 61 (3/4), pp. 261 - 284.Publisher
© European Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
This article was published in the journal, L’Enseignement Mathématique [© © European Mathematical Society] and the definitive version is available at: http://dx.doi.org/10.4171/LEM/61-3/4-1ISSN
0013-8584Publisher version
Language
- en