The three-dimensional geometries of cavities and channels in four electrides are determined in detail with the aid of computer graphics methods. Previous theoretical and experimental studies support the view that electrons are trapped in cavities and interact through connecting channels. The magnetic coupling constants and the dimensionalities of the magnetic interactions are consistent in all cases with the cavity and channel structures of electrides. By combining structural information and theory, it may be possible to describe the overall electronic properties of electrides with a model of an electron gas in a complex "plumber’s nightmare box" whose geometry is given by the cavity and channel structures.