  Gelfand-Tsetlin polytopes are prominent objects in algebraic combinatorics.
The number of integer points of the Gelfand-Tsetlin polytope
$\mathrm{GT}(\lambda)$ is equal to the dimension of the corresponding
irreducible representation of $GL(n)$. It is well-known that the
Gelfand-Tsetlin polytope is a marked order polytope; the authors have recently
shown it to be a flow polytope. In this paper, we draw corollaries from this
result and establish a general theory connecting marked order polytopes and
flow polytopes.
