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Techniques for extracting detailed, complete descriptions of polyhedral objects from light-stripe rangefinder data are described. The descriptions are in the form of 3D faces, edges, vertices, and their topology and geometry. A range image is first segmented into edge points. A line drawing is then obtained by fitting linear segments to the points in the image, and refining the segments to eliminate gaps. Faces are then generated from the line drawing. Interestingly, although the final description is in 3D. most of the processing is done in the 2D image space. This paper describes one part of a larger project whose goal is to obtain a full symbolic description of a scene from range data obtained from multiple viewpoints.