Sphere decompositions of hypercubes
Richard H. Hammack, Paul C. Kainen · The Art of Discrete and Applied Mathematics · 2020
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 = 5n, then such a decomposition can be achieved, but with non-isomorphic spheres.