A jump system is a set of lattice points satisfying a certain "two-step" axiom. A Manhattan set is the convex hull of a two-dimensional jump system. Taking multiple Manhattan sets, in layers, forms a three-dimensional object. We determine under what conditions this object is, in turn, a jump system.
Cuomo, J., Nwasokwa, N., & Ponomarenko, V. (2005). Jump systems and laminated Manhattan sets. Australasian Journal of Combinatorics, 31, 135-143.
Australasian Journal of Combinatorics