  The polytopic definition introduced recently describing the topology of
manifolds is used to formulate a generating function pertinent to its
topological properties. In particular, a polynomial in terms of one variable
and a tori underlying this polynomial may be defined that generates an
individual cohomological count. This includes the de Rham complex for example,
as well as various index theorems by definition such as homotopy. The degree of
the polynomials depends on the volume used to define the region parameterizing
the manifolds; its potentially complex form and L-series is not presented in
this work. However, the polynomials and the relevant torii uniformize the
topological properties in various dimensions; in various dimensions this is
interesting in view of known topologies.
