Many math puzzles and game rely on the mathematical study of shapes and spaces called **topology**.

Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting. Tearing, on the other hand, is not allowed!

Some of the shapes involved include polygons and circles which can be manipulated in space to create different shapes. These are a great way for students to explore 2-dimensional shapes in 3-dimensional space.

**Trihexaflexagons** are ingenious paper contraptions that change their faces as they are folded and flipped. Watch this series for a humorous history of hexaflexagons.

In this activity, students make a paper foldable that changes its faces as it is manipulated.