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][1] 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!)


  [1]: https://mathoverflow.net/questions/306318/average-caliper-diameter-of-a-polyhedron