Wikipedia says, "The Möbius band is a surface with only one side and one edge." We will construct some Möbius bands and verify this observation. But is it possible for a Möbius band to have two sides? We will see that the number of sides of a geometric object is not an intrinsic property of the object but instead depends on the space around it. In 1946, Martin Gardner wrote a short story about topologists who folded themselves into no-sided Möbius bands. Where can we find one of these?