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Spatial bi-stacked central configurations formed by two dual regular polyhedra

Spatial bi-stacked central configurations formed by two dual regular polyhedra
 
Corbera Subirana, Montserrat ; Llibre, Jaume ; Pérez-Chavela, Ernesto
2014

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Enllaç permanent: http://hdl.handle.net/10854/2697
 
Versió de l'editor: http://dx.xoi.org/10.1016/j.jmaa.2013.12.015
 

Resum:

In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, and the other one consisting of twenty masses at the vertices of a regular dodecahedron and twelve masses ...»»»»
In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, and the other one consisting of twenty masses at the vertices of a regular dodecahedron and twelve masses at the vertices of a regular icosahedron. The masses on the two different polyhedra are in general different. We note that the cube and the octahedron, the dodecahedron and the icosahedron are dual regular polyhedra. The tetrahedron is itself dual. There are also spatial stacked central configurations formed by two tetrahedra, one and its dual.^^^^

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(c) 2014 Elsevier. Published article is available at: http://dx.doi.org10.1016/j.jmaa.2013.12.015

Citació Bibliogràfica:

Corbera Subirana, M., Llibre, J., & Pérez-Chavela, E. (2014). Spatial bi-stacked central configurations formed by two dual regular polyhedra. Journal of Mathematical Analysis and Applications, 413(2), 648-659. doi:10.1016/j.jmaa.2013.12.015