Klein Bottle

Klein bottle is a four-dimensional shape without an interior or exterior. If you follow a line down its surface, similar to a Möbius strip, you will pass through both directions before coming back to the beginning place. A real Klein Bottle can only fully exist in four dimensions since it does not intersect itself. Yet, this may be thought of as the 3D “shadow” of a 4D Klein Bottle—the closest we can get in our world. It is the ideal present for a math or science aficionado.