In 1858, mathematician August Ferdinand Möbius discovered a surface with only one side. Take a strip of paper, give it a half-twist, and join the ends. What was two-sided becomes one.
A walker on this surface can travel forever without crossing an edge, yet will visit both "sides" — because there is only one side.
Watch the glowing point trace the surface. It will complete one loop and find itself on the "opposite" side, then loop again to return. Two journeys to come home.
Non-orientable. One-sided. A small twist that breaks our intuitions about inside and outside.