A class of explicit solutions for the Fermat problem for tetrahedra

We present a class of explicit solutions for the problem of minimization of the function f(x,y,z)=∑ᵢ₌₁⁴√(x-xᵢ)²+(y-yᵢ)²+(z-zᵢ)², which gives the location of the unique stationary (Fermat-Torricelli) point for four non-collinear and non-coplanar points Aᵢ=(xᵢ,yᵢ,zᵢ), determining tetrahedra, which are derived by a proper class of isosceles tetrahedra having four equal edges and two equal opposite edges. This class of explicit solutions contains Mehlhos and Glastier's explicit solutions (theoretical constructions) obtained in {Mehlhos:00} and {Glastier:93}, respectively.