The twist angle of weighted Steiner minimal trees in the three dimensional Euclidean Space

Abstract

We find the equations that allow us to compute the position of the two interior nodes (weighted Fermat-Torricelli points) w.r. to the weighted Steiner problem for four points determining a tetrahedron in R^3. Furthermore, by applying the solution w.r. to the weighted Steiner problem for a boundary tetrahedron, we calculate the twist angle between the two weighted Steiner planes formed by one edge and the line defined by the two weighted Fermat- Torricelli points and a non-neighbouring edge and the line defined by the two weighted Fermat-Torricelli points.

12 Pages, 3 Figures