Finding a cutting plane that splits a polyhedron evenly
I can't remember the analytic way to do this!

But this a classical problem for Genetic Programming! If you are familiar with it you can use a normalized vectors in the center of the polyhedron that describes the cutting plane.

So your population is a set of [x,y,z,...] normalized vectors and as fitting function you use the difference between the 2 split volumes!

So, if the difference tends to zero more "fit" is your vector/plane!