  Polytropes are both ordinary and tropical polytopes. We show that tropical
types of polytropes in $\mathbb{TP}^{n-1}$ are in bijection with cones of a
certain Gr\"{o}bner fan $\mathcal{GF}_n$ in $\mathbb{R}^{n^2 - n}$ restricted
to a small cone called the polytrope region. These in turn are indexed by
compatible sets of bipartite and triangle binomials. Geometrically, on the
polytrope region, $\mathcal{GF}_n$ is the refinement of two fans: the fan of
linearity of the polytrope map appeared in \cite{tran.combi}, and the bipartite
binomial fan. This gives two algorithms for enumerating tropical types of
polytropes: one via a general Gr\"obner fan software such as \textsf{gfan}, and
another via checking compatibility of systems of bipartite and triangle
binomials. We use these algorithms to compute types of full-dimensional
polytropes for $n = 4$, and maximal polytropes for $n = 5$.
