It can be demonstrated that the tessellations of squares, of equilateral triangles, and of regular hexagons are all orientable on the two dimensional plane. However, these three classes of plane surfaces are not orientable on the one-sided, single edge Möbius surface. Since orientability is defined by certain directional properties commonly shared by two adjacent plane figures such that if one direction is going forward the other is going backward. This alternating directional property always holds for every two adjacent plane figures. Consequently, it is one of the exclusive properties for defining orientability.


The topology of the Möbius surface is more suitable for describing the unidirectional property of time for the external physical reality. Moreover, for the internal physical world of the microcosm of quarks and leptons, these directional properties are commonly shared at a point instead of along a line segment of multi-dimensional spacetime as the contact point of spacetime charges of H-pluses and H-minuses. Hence, spacetime quantization can be described by using the two distinct directions of spacetime orientation of spacetime charges analogous to the use of spinors in quantum mechanics for describing the quantized spin of elementary particles.