My friend Kim and I started learning to knit at the same time. I am still at K1P1, while she has gone on to this:

and

Here is what Kim wrote about the above green basket:

This mossy mobius basket was knit with brown wool yarn and a green novelty yarn held together while knitting. After being knit, the basket is then felted by placing it in a washing machine with hot water. The combination of moisture, heat and agitation cause scales on the wool fibers to open up and interlock with each other. This process creates a strong, felted fabric that can then be shaped and allowed to dry.

The basket begins as a mobius strip. This is a loop made with a flat surface that has one twist in it. This shape is called a mobius strip and has only one edge and only one side. This shape is a mathematical phenomenon discovered by August Ferdinand Mobius (1790-1868) who was a German astronomer and mathematician. He helped establish a study in geometry called topology, which deals with geometrical figures that are pulled and twisted out of shape in various ways.

Like the mobius strip, the basket has only one edge and one side. If you place your finger along the rim (or edge) of the basket you can follow along the edge all the way around the handle and back to your starting place. Likewise, if you place your finger on the side of the basket, you can run your finger along any surface of the basket (both inside and outside) without crossing the edge. Cat Bordhi is the knitter who made the pattern for knitting mobius baskets and she currently has two knitting pattern books published that use mobius designs.