2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109875We 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.14 pages, 1 figures, proceeding of the Albert Einstein's International Conference 18-22 July 2005General Relativity and Quantum CosmologyHigh Energy Physics - LatticeHigh Energy Physics - TheoryMathematical Physicstext