  In 1986 Stanley associated to a poset the order polytope. The close interplay
between its combinatorial and geometric properties makes the order polytope an
object of tremendous interest. Double posets were introduced in 2011 by
Malvenuto and Reutenauer as a generalization of Stanleys labelled posets. A
double poset is a finite set equipped with two partial orders. To a double
poset Chappell, Friedl and Sanyal (2017) associated the double order polytope.
They determined the combinatorial structure for the class of compatible double
posets. In this paper we generalize their description to all double posets and
we classify the 2-level double order polytopes.
