2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171179We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-compact symmetric spaces of semi-simple Lie groups.31pages, new version contains a few typos corrected, and a minor modificationDifferential Geometry30F60 (Primary); 51F15, 53C21 (Secondary)text