How small can you make it by folding up?
How many different sorts of triangle can you produce?
Can you produce four equal triangles?
What is the quickest way to produce a square?
Can you fold all the other quadrilaterals?

Or by folding a long sheet of paper ...

piece of paper folded to make long shape

What can you produce?
Other knots?
More folds?

Have a look at this /mathsf/journalf/sep03/stage4new.html#709">Dodecawhat 15+ problem. The question itself is too tricky, but you may like to try paper folding to make a dodecahedron.