Balloon Tangles

Tangles, or "regular polylinks," are made out of separate polygons, and are quite a puzzle to weave together. The tangle above is made out of six squares (twisted from one balloon each), and the instructions below will help you to tangle them up properly.

Once the balloons are in the proper entanglement, the entire tangle might be too loose, and not hold its shape. To fix this, you can make the lengths shorter, which is easily done by grabbing the corners of each polygon and twisting off a small amount. This also gives a nice asthetic effect which emphasizes the vertices. Below are two more views of the six-square tangle, one with twisted vertices and one without.

A simpler tangle to start with is made of 3 rectangles, also known as the borromean rings. This structure has the property that if you popped any one of the three balloons, the other two would not be linked together, yet all three together are linked.

With four balloons, you can make a tangle of four triangles:

For a real challenge, try six pentagons (160-size balloons are required if you want to make the pentagons from one balloon each, otherwise you'll have to make each pentagon out of two).

There are many other possible tangles. "Orderly Tangles" by Alan Holden is a good reference.