Almost 10 years ago I had some fun making ambigrams (a word or words that have some sort of symmetry—rotation, reflection, etc.) of my name. I posted some examples on this blog.
Möbius bands have the surprising properties that they are one-sided and have only one edge. This inspired me to write the words MÖBIUS and BAND as ambigrams—in particular, as ambigrams that appear the same after a 180° rotation.
Then I created a Möbius band with the words running along the band.
If you want to make your own, you can download this printable pdf.
However, after I made the Möbius band, it occurred to me that we don’t actually need a Möbius band to achieve this effect with the ambigram. In particular, if you tape the band together as a cylinder, it still looks the same when it is flipped over.
Now, if you were really good, you could create a version of MÖBIUS and BAND that have the 180° rotation and look the same in a mirror. Then you could write the words on a transparent Möbius band. . . .