  Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the
simplicity constraint? What is a complete form of the partition function
written in terms of this parametrization? We prove that the EPRL map is
injective for n-valent vertex in case when it is a map from SO(3) into
SO(3)xSO(3) representations. We find, however, that the EPRL map is not
isometric. In the consequence, in order to be written in a SU(2) amplitude
form, the formula for the partition function has to be rederived. We do it and
obtain a new, complete formula for the partition function. The result goes
beyond the SU(2) spin-foam models framework.
