Upper bound for the geodesic complexity of the icosahedron

Let the geodesic complexity of a convex polyhedron mean the minimum number of sets needed to cover its geodesic motion-planning problem, so that a complexity of at most four means that at most five sets are needed. Icosahedron upper-bound conjecture. The geodesic complexity of an icosahedron is at most four, requiring at most five sets. Together with the corresponding lower-bound conjecture, this would determine the icosahedron's geodesic complexity; the paper presents the claim as an expected result, and no resolution is supplied here.