Richard Stanley showed that order polytopes have a unimoudlar triangulation. In particular, this implies that they are integrally closed/normal.

One can generalize order polytopes to marked order polytopes, where the smallest and largest elements are not always 0 and 1 respectively, but other integers, and the poset do not have unique top and bottom.

For example, Gelfand-Tsetlin polytopes can be realized as the construction above, and it is quite easy to show that these particular polytopes are integrally closed.

*However, is it known if ALL marked order polytopes are integrally closed?*

*Reminder:* A convex polytope $P$ with integer vertices is integrally closed if
we have that each integer point $p$ in $kP$ can be expressed as
$p=p_1+\dots+p_k$ where each $p_i$ is an integer point in $P$.