Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron X X and a simple polyhedron X 0 X_0 that is obtained by collapsing from X X . Then we prove that there exists a canonical way to equip internal regions of X 0 X_0 with gleams so that two 4-manifolds reconstructed from X 0 X_0 and X X are diffeomorphic. We also show that any acyclic simple polyhedron whose singular set is a union of circles can collapse onto a disk. As a consequence of these results, we prove that any acyclic 4-manifold having shadow complexity zero with boundary is diffeomorphic to a 4 4 -ball.