  Networks and their higher order generalizations, such as hypernetworks or
multiplex networks are ever more popular models in the applied sciences.
However, methods developed for the study of their structural properties go
little beyond the common name and the heavy reliance of combinatorial tools. We
show that, in fact, a geometric unifying approach is possible, by viewing them
as polyhedral complexes endowed with a simple, yet, the powerful notion of
curvature - the Forman Ricci curvature. We systematically explore some aspects
related to the modeling of weighted and directed hypernetworks and present
expressive and natural choices involved in their definitions. A benefit of this
approach is a simple method of structure-preserving embedding of hypernetworks
in Euclidean N-space. Furthermore, we introduce a simple and efficient manner
of computing the well established Ollivier-Ricci curvature of a hypernetwork.
