Delucchi, Emanuele Hoessly, Linard 2020-03-25 We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik (2010).In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid.- We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics.- We characterize the metric trees for which the fundamental polytope is simplicial. application/pdf https://folia.unifr.ch/global/documents/308717 https://folia.unifr.ch/documents/308717/files/del_fpm.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ejc.2020.103098 info:eu-repo/semantics/openAccess License undefined European Journal of Combinatorics. - 2020, vol. 87, p. 103098 info:eu-repo/classification/udc/51 Fundamental polytopes of metric trees via parallel connections of matroids http://purl.org/coar/resource_type/c_6501