Summary: An algorithm is presented for constructing a topologically and geometrically valid Domain Delaunay Tetrahedrization (DDT) of an arbitrarily shaped solid model with quadric curved faces (including objects with holes and nonmanifold objects). The algorithm operates on the boundary representation (B-rep) of the solid, and makes extensive use of properties of the Delaunay triangulation. This algorithm also includes a mechanism for transferring neighborhood information from the solid model to the elements of the tetrahedral model. Neighborhood information is used for identifying tetrahedra to be included in the DDT, and — in combination with geometric criteria — for ensuring that the DDT approximates satisfactorily the curved faces of the solid.