A Möbius band, a.k.a. Möbius strip, is a nonorientable surface (has only one side) with a boundary. In 1999, it was pointed out to Sarah-Marie Belcastro that K6 embeds in the Möbius band. K6 is the complete graph on six vertices; in other words, take 6 points and join each pair of them by an edge. Over the 2001-2002 school year, Belcastro designed and knitted a Möbius-band scarf with K6 embedded in it. Here is one of the finished products. Credit: Sarah-Marie Belcastro