  We provide a brief overview on the application of the exterior calculus of
differential forms to the ab initio formulation of field theories on random
simplicial lattices. In this framework, discrete analogues of the exterior
derivative and the Hodge star operator are employed for the factorization of
discrete field equations into a purely combinatorial (metric-free) part and a
metric-dependent part. The Hodge star duality (isomorphism) is invoked to
motivate the use of primal and dual lattices (a dual cell complex). The natural
role of Whitney forms in the construction of discrete Hodge star operators is
stressed.
