We present a formalism for the computer representation of three-dimensional shapes, that has as its goal to facilitate man-machine communication using verbal, graphic, and visual means. With this method, pieces may be assembled hierarchically using any of severalways of specifying attachment. The primitives of the representation are generalized cylinders, and the creating of assemblies may make use of the axes inherent in the primitives. Generic models may be described that may leave some parameters or dimensions unspecified, so that when a specific instance of the model is described, those parameters may either be explicitly specified or take on default values. The axes of local coordinate frames may be given symbolic names. A set of computer programs translates descriptions of objects into polyhedral models and line drawings.