  A discretisation of differential geometry using the Whitney forms of
algebraic topology is consistently extended via the introduction of a pairing
on the space of chains. This pairing of chains enables us to give a definition
of the discrete interior product and thus provides a solution to a notorious
puzzle in discretisation techniques. Further prescriptions are made to
introduce metric data, as a discrete substitute for the continuum vielbein, or
Cartan formulation. The original topological data of the de Rham complex is
then recovered as a discrete version of the Pontryagin class, a sketch of a few
examples of the technique is also provided. A map of discrete differential
geometry into the non-commutative geometry of graphs is constructed which shows
in a precise way the difference between them.
