  For any marked poset we define a continuous family of polytopes, parametrized
by a hypercube, generalizing the notions of marked order and marked chain
polytopes. By providing transfer maps, we show that the vertices of the
hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The
combinatorial type of the polytopes is constant when the parameters vary in the
relative interior of each face of the hypercube. Moreover, with the help of a
subdivision arising from a tropical hyperplane arrangement associated to the
marked poset, we give an explicit description of the vertices of the polytope
for generic parameters.
