Can you find a tetrahedron T contained inside a tetrahedron W such that the sum of the lengths of the edges of T is bigger than the sum of the lengths of the edges of W?
I don't see how this is possible for tetrahedra, it certainly is not possible for triangles:
A triangle T contained in triangle W can be enlarged/rotated so that its 3 vertices lie on the sides of W. The triangle inequality assures that the perimeter if T is smaller than that of W.
Posted by Jer
on 2013-07-27 14:36:39