  We discretize the Hamiltonian scalar constraint of three-dimensional
Riemannian gravity on a graph of the loop quantum gravity phase space. This
Hamiltonian has a clear interpretation in terms of discrete geometries: it
computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt
equation takes the form of difference equations, which are actually recursion
relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the
Hamiltonian generates the exact recursion relation on the 6j-symbol which comes
from the Biedenharn-Elliott (pentagon) identity. This fills the gap between the
canonical quantization and the symmetries of the Ponzano-Regge state-sum model
for 3d gravity.
