We present a new data structure known as Polygon Nesting Tree Data Structure that has the capacity to output a polygon nesting tree at the given height h of a polyhedron. The data structure can produce a set of polygon nesting trees which is then sent to a layered manufacturing printer to produce the object. The thickness of a layer is controlled by composing a number of nesting trees where a higher number of nesting trees would improve the resolution of the polyhedron. Furthermore, we show some results of the implemented polygon nesting tree data structure slicing several polyhedra. The newly developed data structure can be used to solve other related problems.