  We introduce a collection of convex polytopes associated to a
torus-equivariant vector bundle on a smooth complete toric variety. We show
that the lattice points in these polytopes correspond to generators for the
space of global sections and we relate edges to jets. Using the polytopes, we
also exhibit toric vector bundles that are ample but not globally generated,
and toric vector bundles that are ample and globally generated but not very
ample.
