  We obtain an important generalization of the inverse weighted
Fermat-Torricelli problem for tetrahedra in R^3 by assigning at the
corresponding weighted Fermat-Torricelli point a remaining positive number
(residual weight). As a consequence, we derive a new plasticity principle of
weighted Fermat-Torricellitrees of degree five for boundary closed hexahedra in
R^3 by applying a geometric plasticity principle which lead to the plasticity
of mass transportation networks of degree five in R^3. We also derive a
complete solution for an important generalization of the inverse weighted
Fermat-Torricelli problem for three non-collinear points and a new plasticity
principle of mass networks of degree four for boundary convex quadrilaterals in
R^2. The plasticity of mass transportation networks provides some first
evidence in a creation of a new field that we may call in the future
Mathematical Botany.
