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

Montserrat Corbera, Jaume Llibre, Ernesto Pérez-Chavela

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

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. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)648-659
JournalJournal of Mathematical Analysis and Applications
Volume413
Issue number2
DOIs
Publication statusPublished - 15 May 2014

Keywords

  • Dual regular polyhedra
  • N-Body problem
  • Spatial central configurations

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