Abstraction is one of the most important concepts in computer science. It has been realized in object oriented programming as the form of class hierarchy. In this paper, new abstraction levels are introduced. This abstraction level can be applied in many fields of computer science, including computer graphics, image processing, database systems and design automation. In this paper, the new abstraction level is applied to shape modeling. The abstraction level consists of homotopy, topological spaces, cellular structured spaces and Euclidean spaces. A teacup is used as an example of shape modeling using these abstraction levels.