Knit your own Moebius ZigZag using these clearly-written instructions by knitwear designer Jackie E-S of HeartStrings FiberArts.
Moebius ZigZag features a dramatic shaped edge and reversible diagonal lace stitch, making the single-sided moebius wonder even more wonderful.
The Moebius ZigZag Scarf is a continuous one-sided surface that is formed from a rectangular piece of knitting! In effect, there is no inside or outside to this scarf. It is simply a loop with a half twist that will rest comfortably folded about your head or neck. The knitting goes quickly and makes a great gift, too. Wear it as a head covering, or a scarf, or even a shoulder wrap.
Preview sample cover page

36" loop, 10" overall width, 200 yards sport or DK weight yarn. 5 stitches/inch, size US 8 / 5.0 mm needles suggested. Pattern adjusts easily in width and length, as well as other yarn weights. Flexible, easy, and fun! Shown in a kid mohair/merino/baby alpaca boucle yarn.Written stitch instructions.
Tip: For a variation, you can easily make a regular reversible scarf by omitting the step to join the start and finish of your knitting. Just use your favorite method of casting on and casting off.
The photo in the Additional Images section features the Moebius ZigZag Scarf worn as a vest front style. Knitted in Heritage Yarns Rayon Boucle color What a Wonderful World.