non-orientable surfaces

Non-orientable surfaces are shapes where orientation, or the concept of "inside" and "outside," cannot be consistently defined. On these surfaces, if you move around, you might return flipped or mirrored without crossing an edge. A classic example is the Möbius strip, which has only one side and one edge, so objects on it can end up reversed. Non-orientable surfaces challenge our usual understanding of "left" and "right," and are important in mathematics and topology for understanding complex structures that lack a clear "sidedness."