  We investigate the geometry of the space of N-valent SU(2)-intertwiners. We
propose a new set of holomorphic operators acting on this space and a new set
of coherent states which are covariant under U(N) transformations. These states
are labeled by elements of the Grassmannian Gr(N,2), they possess a direct
geometrical interpretation in terms of framed polyhedra and are shown to be
related to the well-known coherent intertwiners.
