The document describes a project called Branching Vaults that involves designing modular building blocks for constructing arches. There are three main modules - a cube, triangle, and variation piece - that connect in various configurations. The cube and triangle modules each have connections on some of their faces to allow aggregation. The project explores the evolution of the module designs and rules for how they connect to form arches using different arrangements. Physical models of the modules were created using both CNC hotwire cutting and 3D printing techniques.