Möbius Strip — Non-Orientable Surface
The Möbius strip has only one side and one edge. An ant walking along the center travels the full loop and returns on the "other side" without crossing an edge. Non-orientable surfaces cannot have a consistent normal vector field.
Euler characteristic χ = 0 (like a cylinder). Non-orientable: no consistent "inside" or "outside".
Cutting along the center line produces a longer, twice-twisted band. Cutting 1/3 from edge → two interlocked bands!