Hexa Flexa Cowl
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 large tri-hexa-flexagon which has 3 faces that each appear in 2 unique ways making it a 6 sided flat object, which when opened up makes a perfect cowl.
The pattern contains a detailed photo tutorial of the construction and also instructions on lining the cowl for a more sculptural piece of neckwear.
Also included is the pattern for a mini hexaflexagon, pattern details here.
Here's a video of the mini hexaflexagon in action.