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?

One way to do it would be with math.
You write an equation which contains all the points in a tetrahedron, then apply that general equation to 2 hypothetical tetrahedrons (so you have 2 functions). The distance in 3D space is given by another simple formula. Afterwards, you just need to minimize this distance and this can be done using calculus. At least, that's the general idea. Once you have the formula, writing a program is easy enough.