Consider the following region:
reg = Polyhedron[{{-0.8420454545454543, -1.8784090909090905, 37.99999999999999}, {-1.95, -4.35, 88.}, {-1.95, 4.35, 88.}, {-0.8420454545454545, 1.8784090909090907, 38.}, {1.95, -4.35, 88.}, {1.95, 4.35, 88.}, {0.8420454545454543, -1.8784090909090905, 37.99999999999999}, {0.8420454545454543, 1.8784090909090905, 37.99999999999999}}, {{1, 2, 3, 4}, {5, 6, 3, 2}, {7, 5, 2, 1}, {8, 6, 5, 7}, {4, 3, 6, 8}, {8, 7, 1, 4}}]; Graphics3D[reg] 
I need to define the minimal and maximal polar angles $\theta = \arccos(z/\sqrt{x^{2}+y^{2}+z^{2}})$ for this region. (well, the minimal angle is clearly 0 in this case, but I would like to automatize it)
For this purpose, I want to use the answer to this question. It requires the discretization of (the boundary of) the region, i.e.
DiscretizeRegion[reg] or
BoundaryDiscretizeRegion[reg] However, I get the following message:
A non-degenerate region is expected at position 1 of DiscretizeRegion
Could you please tell me how either to discretize it properly or to evaluate minimal and maximal polar angles automatically?
