  In this article, using combinatorial techniques of mapping class groups, we
show that a Stein fillable integral homology $3$-sphere supported by an open
book decomposition with page a $4$-holed sphere admits a unique Stein filling
up to diffeomorphism. Furthermore, according to a property of deforming
symplectic fillings of a rational homology $3$-spheres into strongly symplectic
fillings, we also show that a symplectically fillable integral homology
$3$-sphere supported by an open book decomposition with page a $4$-holed sphere
admits a unique symplectic filling up to diffeomorphism and blow-up.
