  We derive the Gauss-Codazzi equation in the holonomy and plane-angle
representations and we use the result to write a Gauss-Codazzi equation for a
discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This
allows us to write operators acting on spin network states in (2+1)-dimensional
loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional
intrinsic, and 2-dimensional extrinsic curvatures.
