Topological Geometry is the rich field of mathematics that exists in many branches of engineering sciences in addition; it is used in various real-life applications. In this paper, we concentrate on the application of M¨obius surface as a new model of Geometrical Topological Structure (GTS).
The M¨obius strip, since its discovery, has captured the imaginations of mathematicians and engineers everywhere, and it continues to fascinate modern generations with its non-orientability properly and one-sidedness.The concept of the M¨obius Band also appears to be used in
many fields such as M¨obius House. The Geometrical Topological structures of the M¨obius surface has great potential as an architectural forms that is difficult to visualize and investigate without the aid of digital technologies. The M¨obius strip, since its discovery, has captured the imaginations of mathematicians and engineers everywhere, and it continues to fascinate modern generations with its non-orientability properly and one-sidedness. Also, we show that there exists some models from rubber sheet geometry that can be applied to design processes.