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

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...

Full description

Bibliographic Details
Authors: Corbera Subirana, Montserrat|||0000-0002-0367-9667, Llibre, Jaume|||0000-0002-9511-5999, Pérez-Chavela, Ernesto
Format: article
Publication Date:2014
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:150695
Online Access:https://ddd.uab.cat/record/150695
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2013.12.015
Access Level:Open access
Keyword:N-body problem
Spatial central configurations
Dual regular polyhedra
Description
Summary: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.