Lower bound for the geodesic complexity of the dodecahedron

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 least four means that at least five sets are needed. Dodecahedron lower-bound conjecture. The geodesic complexity of a dodecahedron is at least four, requiring at least five sets. These conjectures concern the number of continuous motion-planning rules needed on convex polyhedra; the paper presents them as expected future results, and no resolution is supplied here.