Non-orientable parametric surface — one edge, one side
The Möbius strip is parametrized as: x=(R+s·cos(nt/2))cos(t), y=(R+s·cos(nt/2))sin(t), z=s·sin(nt/2). With n=1 (one half-twist) it has one face and one edge — an ant can traverse every point without crossing an edge. Drag to rotate.