  We study restricted chain-order polytopes associated to Young diagrams using
combinatorial mutations. These polytopes are obtained by intersecting
chain-order polytopes with certain hyperplanes. The family of chain-order
polytopes associated to a poset interpolate between the order and chain
polytopes of the poset. Each such polytope retains properties of the order and
chain polytope; for example its Ehrhart polynomial. For a fixed Young diagram,
we show that all restricted chain-order polytopes are related by a sequence of
combinatorial mutations. Since the property of giving rise to the period
collapse phenomenon is invariant under combinatorial mutations, we provide a
large class of rational polytopes that give rise to period collapse.
