Shortest distance

Point me in the right direction with this problem since I have no idea on how to tackle it.You're given 4 set of coordinates in R^3 that form a tetrahedron, then another 4 set of coordinates in R^3 that form another tetrahedron.
How do I find the smallest distance from the surface of one tetrahedron to the other?

>>1
Each tetrahedron has four points, eight edges, and four surfaces.  That's sixteen parts per tetrahedron.  Write a function to check distance point to point, point to edge, edge to edge, point to surface, and edge to surface.  Surface to surface can be ignored since it won't ever give a smaller result than the other five types of tests.  That gives 240 possible pairs of parts to check.

>>5
No.  This won't work when the shortest path is from one edge to another edge.

>>7
Hell no.