  We show how spin networks can be described and evaluated as Feynman integrals
over an internal space. This description can, in particular, be applied to the
so-called simple SO(D) spin networks that are of importance for
higher-dimensional generalizations of loop quantum gravity. As an illustration
of the power of the new formalism, we use it to obtain the asymptotics of an
amplitude for the D-simplex and show that its oscillatory part is given by the
Regge action.
