The generalization of Lattice Field Theory targeting in curved Riemann manifolds referred to as Quantum Finite Elements (QFE) requires geometrical tools.
A brief outline for the construction of a Simplicial Complex and
its Delaunay dual, the construction Finite Element of lattice action based on
the elegant Discrete Exterior Calculus (DEC) is given. The focus in on spheres and hyperbolic manifolds suited to radial quantization of conformal field theory and
the AdS/CFT correspondence respectively. The formalism aims to construct simlicial
actons for scalar, Dirac and non-Abelian fields.