  We introduce the concept of a handlebody decomposition of a 3-manifold, a
generalization of a Heegaard splitting, or a trisection. We show that two
handlebody decompositions of a closed orientable 3-manifold are stably
equivalent. As an application to materials science, we consider a mathematical
model of polycontinuous patterns and discuss a topological study of microphase
separation of a block copolymer melt.
