Unable to compute tip coordinates

[git-hub-jc]

advanced_fetch_polytopes() and sample_polytopes() often give no solution for cy.toric_kahler_cone().tip_of_stretched_cone(c=1). This problem remains even after reducing to c=10^(-6) or using the backend=“mosek” optimizer. This might be related to whether or not to use points in facets.

[natemacfadden]

The following code shows this behavior

`from cytools import Polytope

pts = [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [-23, -13, -9, -2], [-2, -1, -1, 1], [-2, -1, 0, 1], [-1, 0, 0, 1], [-25, -14, -10, -2], [-12, -7, -4, -1], [-11, -6, -4, -1], [-10, -5, -4, 1], [-5, -2, -2, 1], [-3, -2, 0, 0], [-20, -11, -8, -1], [-15, -8, -6, 0], [-12, -7, -5, -1], [-8, -4, -3, 1], [-6, -3, -2, 1], [-4, -2, -1, 1], [-3, -1, -1, 1], [-1, -1, 0, 0], [-18, -10, -7, -1], [-16, -9, -6, -1], [-15, -8, -6, -1], [-14, -8, -5, -1], [-13, -7, -5, 0], [-11, -6, -4, 0], [-10, -5, -4, 0], [-9, -5, -3, 0], [-7, -4, -3, 0], [-7, -4, -2, 0], [-5, -3, -1, 0], [-5, -2, -2, 0], [-13, -7, -5, -1], [-8, -4, -3, 0], [-6, -3, -2, 0], [-5, -3, -2, 0], [-4, -2, -1, 0], [-3, -2, -1, 0], [-3, -1, -1, 0], [-2, -1, -1, 0], [-2, -1, 0, 0], [-1, 0, 0, 0]]
h = [0, 91667174, 91678643, 91703661, 91696261, 169143230, 92272730, 92151788, 91756306, 183244240, 112375911, 108833952, 105648718, 94932256, 92857350, 149644712, 123800224, 113260971, 100486163, 96498661, 93689930, 92762399, 91775486, 138523161, 128671948, 123840889, 119906258, 115639947, 108736399, 105563649, 102960757, 98901707, 98381067, 94989691, 94823839, 115745866, 100405235, 96440315, 95318604, 93635433, 92926877, 92622187, 92120967, 92094347, 91649140]

p = Polytope(pts)

for use_pts_in_facets in [False,True]:
t = p.triangulate(heights=h,include_points_interior_to_facets=use_pts_in_facets)
cy = t.get_cy()
kc = cy.toric_kahler_cone()
tip = kc.tip_of_stretched_cone(c=1,verbose=0)
print(tip)
print()`