Some minimum networks for four points in the three dimensional Euclidean Space
Abstract
We construct a minimum tree for some boundary symmetric tetrahedra R3, which has two nodes (interior points) with equal weights (positive numbers) having the property that the common perpendicular of some two opposite edges passes through their midpoints. We prove that the length of this minimum tree may have length less than the length of the full Steiner tree for the same boundary symmetric tetrahedra.
0