Provan and Billera defined the notion of weak k‐decomposability for pure simplicial complexes in the hopes of bounding the diameter of convex polytopes. They showed the diameter of a weakly k‐decomposable simplicial complex Δ is bounded above by a polynomial function of the number of k‐faces in Δ and its dimension. For weakly 0‐decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non‐weakly 0‐decomposable simplicial polytopes. Our examples are in fact polar to certain transportation polytopes.
