In surface modeling, it is important to reconstruct the smooth connecting surface for the polyhedron vertex and edge rendering. The general method by using the spherical and cylindrical surfaces do not possess the geometric continuity. This paper proposed a geometric modeling method of reconstruction vertices and edges with smooth surface for the polyhedron corner rendering with high order geometric continuity. The proposed method is based on the principle of the theory of geometry continuity through a geometry drawing algorithm. The reconstructed surface can be connected neighboring surfaces with G1 geometry continuity. The results show that the reconstructed surfaces can polish and render the polyhedron corner with good geometry continuity property.