This is a constrained version of the 'fair partition' ('spicy chicken' - https://arxiv.org/abs/1306.2741) question.
It seems that there are convex polyhedrons that cannot be cut into n convex pieces all with same volume, surface area and total edge length for any value of n. For example, is it true that there are tetrahedrons (say, with all angles between edges irrational fractions of $\pi$) that cannot be cut into n convex pieces (where n could have any integer value) with all 3 quantities equal?
Is this claim valid: "the only convex polyhedrons that allow, for any value of n, partition into n convex polyhedral pieces all of same volume, surface area and edge length are prisms"?
