I recently asked on mathoverflow and also asked several people I know to prove the following:

How do I prove that the average caliper diameter of the polyhedron across all possible rotations is given by this formula: $$\sum_{e\in E} L_e(\pi - \delta_e)/(4\pi)$$

(see here for more information). Several people gave me proofs for which I'm grateful but there seemed to be some conflict on whether or not this equation is true for both convex and concave polyhedra.

I thought I'd start a new question for this as I don't want to confuse the purpose of the old thread... is anyone able to tell me is this equation true for concave polyhedra?/provide a counterexample if not? (Thank you in advance!)

I recently asked on MathOverflow and also asked several people I know to prove the following:

How do I prove that the average caliper diameter of the polyhedron across all possible rotations is given by this formula: $$\sum_{e\in E} L_e(\pi - \delta_e)/(4\pi)$$

(see here for more information). Several people gave me proofs for which I'm grateful but there seemed to be some conflict on whether or not this equation is true for both convex and concave polyhedra.

I thought I'd start a new question for this as I don't want to confuse the purpose of the old thread... is anyone able to tell me is this equation true for concave polyhedra?/provide a counterexample if not?

I recently asked on mathoverflow and also asked several people I know to prove the following:

How do I prove that the average caliper diameter of the polyhedron across all possible rotations is given by this formula: $$\sum_{e\in E} L_e(\pi - \delta_e)/(4\pi)$$

(see here for more information). Several people gave me proofs for which I'm grateful but there seemed to be some conflict on whether or not this equation is true for concave polyhedra.

I thought I'd start a new question for this as I don't want to confuse the purpose of the old thread... is anyone able to tell me is this equation true for concave polyhedra?/provide a counterexample if not? (Thank you in advance!)

I recently asked on mathoverflow and also asked several people I know to prove the following:

How do I prove that the average caliper diameter of the polyhedron across all possible rotations is given by this formula: $$\sum_{e\in E} L_e(\pi - \delta_e)/(4\pi)$$

(see here for more information). Several people gave me proofs for which I'm grateful but there seemed to be some conflict on whether or not this equation is true for both convex and concave polyhedra.

I thought I'd start a new question for this as I don't want to confuse the purpose of the old thread... is anyone able to tell me is this equation true for concave polyhedra?/provide a counterexample if not? (Thank you in advance!)