splitting the tetrahedron into convex bricks

dear sirs

i would like that somebody help me to solve the next question:

i would like to have proof, that when splitting the tetrahedron in the manner that is depicted on this picture:

Imageshack - tetra

the four 8-nodal elements (usually brick like elements) that are produced must be convex, no matter of how much differs the starting tetrahedron.

i have empirical proof already because i developed software for that purpose, the only thing i need is mathematical proof

thank you for your interest, and sorry on not-so-good english