On the 2-sphere, a pair of geodesics defines two antipodal points (separated by 180[sup]o[/sup]), so there are 4 geodesic sections, or paths, from one point to its antipode. So an Euler circuit (visiting each section exactly once) would visit the two points twice, and have 4! possible permutations. What happens on the 3-sphere? Geodesics on the 2-sphere are lines traced out by points, on the 3-sphere these would be surfaces traced out by lines, so would that mean visiting four 'places' in sequence, and only one permutation for an Euler circuit?