(continued) As you suggest another way of asking the question is 'what are the combinatorial conditions needed to get a special Ford spine?'

Yes, I want the faces to be hyperbolic polygons glued isometrically together along the edges. So I guess I am looking at is a decomposition of a 2-sphere with hyperbolic polygons glued together by isometries. Each vertex is either trivalent or quadrivalent. To give a bit more detail -- the special spine is actually obtained by decomposing the Haken manifold along a hierarchy such as that used by Waldhausen and Johannson.

The reason I am looking at it like this is that I can explicitly construct a class of special spines for manifolds that (from geometrization) do admit hyperbolic structures, but I was wondering if I can give some sort of condition on my construction of the special spine that picks this out.

Thanks Ian for the reply, appreciate it. What I was actually looking for though was some sort of notion for an "angled special spine" with conditions on the singular 1-skeleton which if satisfied give me a angle structure on the dual triangulation. In particular I was wondering if I assume that the special polyhedron defining the spine was a hyperbolic polyhedron, does this say something about the existence of an angle or hyperbolic structure on the manifold.