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Fragmented objects are encountered in a variety of diverse engineering and scientific fields including industrial inspection, customized medical prosthesis design, forensic science, paleontology, and archaeology. The arbitrarily broken pieces must be reassembled and new material often added to complete the process of shape reconstruction. To prevent physical damage of the pieces during reconstruction and enhance shape visualization scientists have begun to exploit 3D data acquisition and graphical modeling tools. An algorithm for enabling free-form shape reconstruction from digitized data of fragmented pieces is described in this paper. The method exploits the topological structure and learning algorithm of a 3D self-organizing feature map (SOFM). The lattice of the SOFM is a spherical mesh that maintains the relative connectivity of the neighboring nodes as it transforms under external forces. The weight nodes of the lattice represent vertices of the constituent elements in the facetted surface model. The technique is illustrated by reconstructing two clay objects with closed geometries from several fragmented parts.