On the interpretations of a polyhedral figure

A polyhedral figure is a drawing that an observer interprets as the representation of a solid, or solids, with planar faces. The aim of this paper is to furnish a mathematical model that represents all conceivable interpretations of a polyhedral figure, for the purpose of testing the consistency of each one. Various types of inconsistency are thus defined, and the relationship between the consistency and realizability of an interpretation is discussed.