  We introduce a new spinfoam vertex to be used in models of 4d quantum gravity
based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the
conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis
constructed using SU(2) coherent states. This basis makes the geometric
interpretation of the variables transparent: they are the vectors normal to the
triangles within each tetrahedron. We study the condition under which these
states can be considered semiclassical, and we show that the semiclassical ones
dominate the evaluation of quantum correlations. Finally, we describe how the
constraints reducing BF to gravity can be directly written in terms of the new
variables, and how the semiclassicality of the states might improve
understanding the correct way to implement the constraints.
