there are 60 edge pieces, consisting of 12 central, 24 intermediate, and 24 outer edges. the central edges can be flipped but the rest cannot (because the internal shape of the pieces is asymmetrical), nor can an edge from one set exchange places with one from another set. the five edges in each matching quintet are distinguishable, since corresponding non-central edges are mirror images of each other. there are 12!/2 ways to arrange the central edges, since an odd permutation of the corners implies an odd permutation of these pieces as well. there are 2 ways that they can be flipped, since the orientation of the twelfth edge depends on the preceding eleven. any permutation of the intermediate and outer edges is possible, including odd permutations, giving 24! arrangements for each set or 24! total, regardless of the position or orientation of any other pieces.