A new approach is introduced to reduce the number of nodes of a polyhedral model according to several conditions which allow to produce high quality simpli®ed geometries. The simpli®ed polyhedron must satisfy everywhere a geometric restoration criterion based on an error zone assigned to each node of its initial model. These error zones can be speci®ed by the user or automatically set up using the accuracy characteristics of the digitizing device. Moreover, speci®c criteria are used to preserve the shape of the object during the simpli®cation process both from geometric and topologic points of view. Indeed, the uses of such polyhedra require a good geometric quality without topologic and geometric singularities. The simpli®cation process is based on a node removal method. A new strategy is developed to produce the simpli®ed polyhedron using front propagations and multiple remeshing schemes which take into account the discrete curvature characteristics of the object. Such an approach allows to increase the node reduction of the initial polyhedron and produces a smoothing e ect on the simpli®ed geometry. The front propagation technique also leads to a better preservation of the shape of the object. Examples illustrate the behaviour of the simpli®cation algorithm in terms of data reduction,quality of the simpli®ed geometry and shape preservation of objects.