Intersection cohomology simplicial blow up and rational homotopy Let X be a pseudomanifold. In this text we use a simplicial blow up to define a cochain complex whose cohomology with coefficients in a field is isomorphic to the intersection cohomology of X introduced by M. Goresky and R. MacPherson. We do it simplicially in the setting of a filtered version of face sets also called simplicial sets without degeneracies in the sense of C.P. Rourke and B.J. Sanderson. We define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular as announced above when X is a pseudomanifold we get a perverse local system of cochains quasi isomorphic to the intersection cochains of Goresky and MacPherson over a field. We show also that these two complexes of cochains are quasi isomorphic to a filtered version of Sullivans differential forms over the field Q. In a second step we use these forms to extend Sullivans presentation of rational homotopy type to intersection cohomology. For that we construct a functor from the category of filtered face sets to a category of perverse commutative differential graded Q algebras (CDGAs) due to Hovey. We establish also the existence and uniqueness of a positively graded minimal model of some perverse CDGAs including the perverse forms over a filtered face set and their intersection cohomology. Finally we prove the topological invariance of the minimal model of a PL pseudomanifold whose regular part is connected and this theory creates new topological invariants. This point of view brings a definition of formality in the intersection setting and examples are given. In particular we show that any nodal hypersurface in CP(4) is intersection formal