  Quantum geometric maps, which relate SU(2) spin networks and Lorentz
covariant projected spin networks, are an important ingredient of spin foam
models (and tensorial group field theories) for 4-dimensional quantum gravity.
We give a general definition of such maps, that encompasses all current spin
foam models, and we investigate their properties at such a general level. We
then specialize the definition to see how the precise implementation of
simplicity constraints affects features of the quantum geometric maps in
specific models.
