  We determine a positive real number (weight), which corresponds to a vertex
of a tetrahedron and it depends on the three weights which correspond to the
other three vertices and an infinitesimal number $\epsilon.$ As a limiting
case, for $\epsilon\to 0,$ the quad of the corresponding weights yields a
degenerate weighted Fermat-Torricelli tree which coincides with the three
neighbouring edges of the tetrahedron and intersect at this vertex.
