  In this paper, we study the stable homotopy types of
$\mathbf{F}^4_{n(2)}$-polyhedra, i.e., $(n-1)$-connected, at most
$(n+4)$-dimensional polyhedra with 2-torsion free homologies. We are able to
classify the indecomposable $\mathbf{F}^4_{n(2)}$-polyhedra. The proof relies
on the matrix problem technique which was developed in the classification of
representaions of algebras and applied to homotopy theory by Baues and Drozd.
