Sphere decompositions of hypercubes

Abstract

For d ≡ 1 or 3 (mod 6), the 2-skeleton of the d-dimensional hypercube is decomposed into the union of pairwise face-disjoint isomorphic 2-complexes, each a topological sphere. If d = 5, then such a decomposition can be achieved, but with non-isomorphic spheres.