Hexaflexagons are traditionally made from paper. They are flat hexagons folded in such a way that they have more faces than you would expect. I find them fascinating and was inspired to make a knitted one by these videos from Vi Hart.
This pattern is for a tri-hexa-flexagon which has 3 faces that each appear in 2 unique ways making it a 6 sided flat object!
You will only need around 25g of DK weight acrylic to make one flexagon.
The pattern contains a detailed photo tutorial of the construction.
Here's a video of this hexaflexagon in action.
Also included is a pattern to make this Hexaflexagon cowl.