  We prove that the extension complexity of the independence polytope of every
regular matroid on $n$ elements is $O(n^6)$. Past results of Wong and Martin on
extended formulations of the spanning tree polytope of a graph imply a $O(n^2)$
bound for the special case of (co)graphic matroids. However, the case of a
general regular matroid was open, despite recent attempts. We also consider the
extension complexity of circuit dominants of regular matroids, for which we
give a $O(n^2)$ bound.
