  Las Vergnas Cube Conjecture states that the cube matroid has exactly one
class of orientations. We prove that this conjecture is equivalent to saying
that the oriented matroid of the affine dependencies of the n-cube can be
reconstructed from the underlying matroid and one of the following partial
lists of signed circuits or cocircuits: A) the signed circuits of rank 3, or B)
the positive signed cocircuits.
