  Geometric frustration arises whenever the constituents of a physical assembly
locally favor an arrangement that cannot be realized globally. Recently, such
frustrated assemblies were shown to exhibit filamentation, size limitation,
large morphological variations, and exotic response properties. These unique
characteristics can be shown to be a direct outcome of geometric frustration.
There are, however, geometrically frustrated systems that do not exhibit any of
the above characteristics. The epitome of frustration in condensed matter
physics, the Ising anti-ferromagnet on a triangular lattice, is one such
system. In this work, we provide a framework for directly addressing the
frustration in physical assemblies and their expected energy scaling exponents.
We also present a new spin model that exhibits cumulative geometric frustration
and use the newly devised framework to analyze it.
