This paper describes an efficient method for reconstructing a solid model by generating its boundary surface from a wireframe model. This method utilizes a wireframe that is topologically a 2-connected planar multigraph, which can be interpreted as a solid in multiple ways. First the graph is decomposed using triconnected component decomposition; all solutions are then generated combinatorially. Each solution is a set of face loops representing a closed 2-manifold of genus 0. After giving a surface geometry for each face loop, the solutions are pruned according to prescribed geometric simplicity criteria. A method for extending the algorithm to deal with general disconnected wireframes is also described. This approach is characterized by not using geometry for reconstructing 2-manifold topology; geometry is used for discarding geometrically invalid solutions and prioritizing remaining ones. Therefore, negative influence of geometric errors is minimized and even wireframes having incomplete geometry can be handled. The algorithm provides an easy and intuitive method of geometric modeling as well as a conversion tool for existing wireframes.