  A cosmological polytope is a lattice polytope introduced by Arkani-Hamed,
Benincasa, and Postnikov in their study of the wavefunction of the universe in
a class of cosmological models. More concretely, they construct a cosmological
polytope for any Feynman diagram, i.e. an undirected graph. In this paper, we
initiate a combinatorial study of these polytopes. We give a complete
description of their faces, identify minimal faces that are not simplices and
compute the number of faces in specific instances. In particular, we give a
recursive description of the $f$-vector of cosmological polytopes of trees.
