We present a novel geometric model for robot mapping suited for robots equipped with a laser range finder. The geometric representation is based on shape. Cyclic ordered sets of polygonal lines are the underlying data structures. Specially adapted shape matching techniques originating from computer vision are applied to match range scan against the partially constructed map. Shape matching respects for a wider context than conventional scan matching approaches, allowing to disregard pose estimations. The described shape based approach is an improvement of the underlying geometric models of todays SLAM implementations. Moreover, using our object-centered approach allows for compact representations that are well-suited to bridge the gap from metric information needed in robot motion and path planning to more abstract, i.e. topological or qualitative spatial knowledge desired in complex navigational tasks or communication.