Abstract
This is a continuation of an early paper [Adv. Appl. Math. 47(2011), 158-172] about matroid base polytope decomposition. We will present sufficient conditions on a matroid M so its base polytope P (M) has a sequence of hyperplane splits. These yield to decompositions of P (M) with two or more pieces for infinitely many matroids M. We also present necessary conditions on the Euclidean representation of rank three matroids M for the existence of decompositions of P (M) into 2 or 3 pieces. Finally, we prove that P (M1 ⊕ M2) has a sequence of hyperplane splits if either P (M1) or P (M2) also has a sequence of hyperplane splits.