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For a Riemannian polyhedra, we study the geometry of the unit ball for theunidimensional stable norm (stable ball). In the case of a unidimensionalRiemannian polyhedra (graph), we show that the stable ball is a polytope whosevertices are completely described by combinatorial properties of the graph. Westudy then the realizable forms as stable ball of Riemannan manifolds ofdimension larger than three. For a Riemannian manifold $(M, g)$ fixed, we showthat a broad class of polytopes can appear as stable ball of metrics in theconformal class of $g$. We use for that a polyhedral technique.Comment: 13 pages, in Frenc

Sur la forme de la boule unité de la norme stable unidimensionnelle