TY - JOUR
T1 - Spatial bi-stacked central configurations formed by two dual regular polyhedra
AU - Corbera, Montserrat
AU - Llibre, Jaume
AU - Pérez-Chavela, Ernesto
PY - 2014/5/15
Y1 - 2014/5/15
N2 - 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.
AB - 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.
KW - Dual regular polyhedra
KW - N-Body problem
KW - Spatial central configurations
U2 - https://doi.org/10.1016/j.jmaa.2013.12.015
DO - https://doi.org/10.1016/j.jmaa.2013.12.015
M3 - Article
VL - 413
SP - 648
EP - 659
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -