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Let Σ g be a closed orientable surface of genus g ≥ 2 and τ a graph on Σ g with one vertex which lifts to a triangulation of the universal cover. We have shown that the cross ratio parameter space C τ associated with τ , which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to τ , is homeomorphic to R 6g−6 , and moreover that the forgetting map of C τ to the space of projective structures is injective. In this paper, we showdoi:10.2140/pjm.2006.225.287 fatcat:w5rassowfzf6xkqpc6lydfkqnq