Paper Folding
We have made Christmas themed (www.think-maths.co.uk/festive-fold-cut and Halloween themed (www.think-maths.co.uk/fold-and-cut-bat) fold and cut resources over the years.
Erik Demaines website (mathematician who worked on fold and cut): https://erikdemaine.org/foldcut/
A video about the fold and cut theorem:
Mobius Loops
Here is the mobius loops investigation sheet.