The local extremality criterion from [3] for the volume of hypercube sections at sub-diagonals of order less than the dimension misses a term. The results regarding the main diagonal of the hypercube do not change but the results about its sub-diagonals of lower order have to be corrected by taking this additional term into account which is the purpose of this corrigendum. The only significant change to the main results of [3] is that the volume of the sections of the hypercube [0, 1]d by a hyperplane H orthogonal to a sub-diagonal of order at least 4 and less than d is never locally extremal when H is close to the center of [0, 1]d.
