Modular boundary models are a class of solid models which describe solids as collections of face-abutting object parts. The Face-to-Face Composition (FFC) model is a specific model belonging to this class which contains explicit information about connection and interference among object components. In the FFC model, juxtaposition and interference are represented through a graph-theoretic structure, in which nodes describe object components and hyperarcs connection and internal portions of the component boundaries. Necessary and sufficient conditions for an FFC model to be valid are defined in terms of its graph representation. The problem of producing valid FFC models from the decomposition of the FFC model of a given object into subparts is studied in connection with the generation of a production graph, which describes assembly and machining sequences, that can be extracted from an FFC model, in the form of an and/or graph.