On 2-skeleta of hypercubes

Abstract

It is shown that the 2-skeleton of the odd-d-dimensional hypercube can be decomposed into s_d spheres and τ_d tori, where s_d = (d − 1)2^d − 4 and τ_d is asymptotically in the range (64/9)2^d − 7 to (d − 1)(d − 3)2^d − 7.