This is a Mobius strip with an arrow which can travel around to show you that the Mobius strip is a nonorientable surface.

When the arrow comes back to the original location, it's flipped!

Read more about (non)-orientable surfaces on Wikipedia:
https://en.wikipedia.org/wiki/Orientability

Print instructions

This is 3d printed in a single go, with the arrow 3d printed in place around the Mobius strip.

This requires a multimaterial printer and the ability to use soluble supports.

If you want one printed for you, I currently have these listed for sale on Etsy:
https://www.etsy.com/listing/779933609/mobius-strip-with-arrow-3d-printed-math