  We revise the classical continuum formulation behind the Spin Foam approach
to the quantization of gravity. Based on the recent applications of the current
EPRL-FK model beyond triangulations, we identify the tension with the
implementation of the 'volume' part of simplicity constraints, required for the
passage from the topological BF theory to gravity. The crucial role, played by
4d normals in the linear version of constraints, necessitates the extension of
the configuration space, and we argue to switch from normal 3-forms directly to
tetrads. The requirement of vanishing torsion leads to consider first an
unconstrained extended Poincare BF theory, which we characterize fully both at
the Lagrangian and Hamiltonian levels, paying special attention to its gauge
symmetries. The simplicity constraints are introduced naturally, in the spirit
of Plebanski formulation, and we give their tetradic version, dual to that of
using 3-forms. This brings us much closer to the geometric content of General
Relativity.

General Relativity and Quantum Cosmology;High Energy Physics - Theory