Quantum Gravity made from quantum polyhedra

The geometry of space at the Plank scale in Loop Quantum Gravity has a discrete structure. The grains of space have a quantum behavior and their semi-classical limit are classical euclidean polyhedra. The dynamics of the theory is encoded in transition amplitudes between geometries tessellated with polyhedra cells. I will review how the full space-time can be then thought as a collection of four-dimensional polytopes and how a discrete version of General Relativity is recovered in the semi-classical limit.