Every semi-algebraic set is semi-algebraically homeomorphic to a simplicial complex. This result is well known for semi-algebraic sets over real closed fields. I will present the same triangulation result for semi-algebraic sets over a p-adically closed field, and some applications. Polytopes and simplexes over p-adic fields will be defined, by means of (very restrictive) linear inequalities on the valuations of their points.