==> geometry/ham.sandwich.s <==
Yes.  There is a theorem in topology called the Ham Sandwich Theorem,
which says: Given 3 (finite) volumes (each may be of any shape, and in
several pieces), there is a plane that cuts each volume in half.  You
would learn about it typically in a first course in algebraic topology,
or maybe in a course on introductory topology (if you studied the
fundamental group).