A Mobius strip has only one side. It can be made from a ribbon by making a half twist before joining
It was made famous by this picture of "Red Ants on a Mobius Strip" by M C Escher
This children's toy suggested to me that it might be possible to make a Mobius strip by wood turning
And this is the result before the pieces are glued together. There are two turned pieces cut into four
There is a "ring" piece (on the left) and a "disc" piece (on the right). They have the same cross sectional shape and the same sum of diameters
One quarter segment of each one is turned over. If the dimensions are just right, the cut ends will fit