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The Fermat-Torricelli point and isosceles tetrahedra. (English) Zbl 0795.51006

The Fermat-Torricelli point of a triangle \(ABC\) is the point \(P\) such that \(AP+BP+CP\) is as small as possible. The corresponding point for a tetrahedron has been considered by several authors. In the present paper the authors summarize the known facts about this point, and prove some new results. In particular, they consider isosceles tetrahedra, that is, those in which the lengths of opposite edges are equal.

MSC:

51M04 Elementary problems in Euclidean geometries
51M20 Polyhedra and polytopes; regular figures, division of spaces
51M16 Inequalities and extremum problems in real or complex geometry
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