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A combinatorial construction is used to analyze the properties of polyhedralproducts and generalized moment-angle complexes with respect to certainoperations on CW pairs including exponentiation. This allows for theconstruction of infinite families of toric manifolds, associated to a givenone, in a way which simplifies the combinatorial input and consequently, thepresentation of the cohomology rings. The new input is the interaction of apurely combinatorial construction with natural associated geometricconstructions related to polyhedral products and toric manifolds. Applicationsof the methods and results developed here have appeared in literature.

Operations on polyhedral products and a new topological construction of infinite families of toric manifolds