Geodesic
Central Configurations of the 5-body problem with equal masses in three-dimensional space
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 292-317

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We enumerate central configurations with axial symmetry in the 5-body problem with equal masses in three-dimensional space. It is thus shown, that only two of these configurations, have a unique symmetry axis. The use of Symbolic Computation techniques is necessary because of the very tedious computations involved in the proof. 
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     title = {Central {Configurations} of the 5-body problem with equal masses in three-dimensional space},
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I. Kotsireas; D. Lazard. Central Configurations of the 5-body problem with equal masses in three-dimensional space. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 292-317. http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a15/