  Describing the combinatorial structure of the tropical complex $C$ of a
tropical matroid polytope, we obtain a formula for the coarse types of the
maximal cells of $C$. Due to the connection between tropical complexes and
resolutions of monomial ideals, this yields the generators for the
corresponding coarse type ideal introduced in a recent paper of Dochtermann,
Joswig and Sanyal (2010, preprint arXiv.org:1001.0237). Furthermore, a complete
description of the minimal tropical halfspaces of the uniform tropical matroid
polytopes, i.e. the tropical hypersimplices, is given.
