  We introduce topological notions of polytopes and simplexes, the latter being
expected to play in p-adically closed fields the role played by real simplexes
in the classical results of triangulation of semi-algebraic sets over real
closed fields. We prove that the faces of every p-adic polytope are polytopes
and that they form a rooted tree with respect to specialisation. Simplexes are
then defined as polytopes whose faces tree is a chain. Our main result is a
construction allowing to divide every p-adic polytope in a complex of p-adic
simplexes with prescribed faces and shapes.
