  We introduce a family of nonnegative integer vectors - primitive vectors -
defining hyperplanes of the real affine cube over $C^n:=\{-1,1\}^n$ and study
their properties with respect to the rectangles of the cube. As a consequence
we give a short proof that, for small dimensions ($n\leq 7$), the real affine
cube can be recovered from its signed rectangles and its signed cocircuits
complementary of its facets and skew-facets.
