I have found a new property of the Tetrahedron. In fact, this is a 3D generalization of theorem 1 in my paper "A Note on Reflection", published by Forum Geometricorum. Consider any Tetrahedron ABCD. Take an arbitrary point P on the space. Now, reflect P around the four centroids of the four triangular faces of the Tetrahedron.Then, the line segments joining the vertices with the symmetry image of P corresponding to the opposite faces of the vertices are concurrent.
There has been discussion here :
I wonder whether this property can be generalizes to other polyhedra.