  A cosmological polytope is defined for a given Feynman diagram, and its
canonical form may be used to compute the contribution of the Feynman diagram
to the wavefunction of certain cosmological models. Given a subdivision of a
polytope, its canonical form is obtained as a sum of the canonical forms of the
facets of the subdivision. In this paper, we identify such formulas for the
canonical form via algebraic techniques. It is shown that the toric ideal of
every cosmological polytope admits a Gr\"obner basis with a squarefree initial
ideal, yielding a regular unimodular triangulation of the polytope. In specific
instances, including trees and cycles, we recover graphical characterizations
of the facets of such triangulations that may be used to compute the desired
canonical form. For paths and cycles, these characterizations admit simple
enumeration. Hence, we obtain formulas for the normalized volume of these
polytopes, extending previous observations of K\"uhne and Monin.
