An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a renormalized sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e.g., triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is projectively equivalent to the Turaev–Viro model.