  We introduce the basic elements of SO(n)-local theory of Regge Calculus. A
first order formalism, in the sense of Palatini, is defined on the metric-dual
Voronoi complex of a simplicial complex. The Quantum Measure exhibits an
expansion, in four dimensions, in characters of irreducible representation of
SO(4) which has close resemblance and differences as well with the Spin Foam
Formalism. The coupling with fermionic matter is easily introduced which could
have consequences for the Spin Foam Formalism and Loop Quantum Gravity.
