  Fix two lattice paths $P$ and $Q$ from $(0,0)$ to $(m,r)$ that use East and
North steps with $P $ never going above $Q$. Bonin et al. show that the lattice
paths that go from $(0,0)$ to $(m,r)$ and remain bounded by $P$ and $Q$ can be
identified with the bases of a particular type of transversal matroid, which we
call it a lattice path matroid.
  In this paper, we consider properties of lattice path matroid polytopes.
These are the polytopes associated to the lattice path matroids. We investigate
their face structure, decomposition, triangulation, Ehrhart polynomial and
volume.
