  Let GF denote the rational points of a semisimple group G over a
non-archimedean local field F, with Bruhat-Tits building X. This paper contains
five main results. We prove a convergence theorem for sequences of parahoric
subgroups of GF in the Chabauty topology, which enables to compactify the
vertices of X. We obtain a structure theorem showing that the Bruhat-Tits
buildings of the Levi factors all lie in the boundary of the compactification.
Then we obtain an identification theorem with the polyhedral compactification
(previously defined in analogy with the case of symmetric spaces). We finally
prove two parametrization theorems extending the BruhatTits dictionary between
maximal compact subgroups and vertices of X: one is about Zariski connected
amenable subgroups, and the other is about subgroups with distal adjoint
action.
