We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and polyhedral meshes. The mimetic inner products are locally built in a recursive way on each k-cell and, then, globally assembled. This strategy is similar to the implementation of the finite element methods. The effectiveness of this approach is documented by deriving mimetic discretizations and testing their behavior on a set of problems related to the Maxwell equations.