The Möbius strip is a non-orientable surface with only one side and one edge. An ant walking along its full length would return to its starting point having traversed both “sides” without ever crossing an edge.
Classic Möbius strip (non-orientable)
x = (R + w·v·cos(n·u/2)) cos(u)
y = (R + w·v·cos(n·u/2)) sin(u)
z = w·v·sin(n·u/2)
u ∈ [0, 2π], v ∈ [−1, 1], n = 1