  It is folklore that the cycle space of graphs of polytopes is generated by
the cycles bounding the 2-faces. We provide a proof of this result that bypass
homological arguments, which seem to be the most widely known proof. As a
corollary, we obtain a result of Blind & Blind (1994) stating that graphs of
polytopes are bipartite if and only if graphs of every 2-face are bipartite.
