Let M be a 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the (non-complete) hyperbolic metrics on M such that the boundary looks locally like an ideal hyperbolic polyhedron. We will give a description of the possible dihedral angles at the edges, and some partial results on the induced metrics on the boundary. As a by-product, we obtain an affine structure on the Teichmuller space of a surface of genus at least 2 with some marked points.