The Möbius twist needs to appear finished everywhere. An example is crocheting a twisted hat brim. Placing the hat at one angle needs to appeal at other angles.
Think of it this way. Never wear pajamas all day when at home. You never know when your friends might visit. Always look dressed to impress. In this case, all angles must look presentable. This applies to designs for your head or any part of your body: your wrist, arms, hands. The designs include twisted: hats, infinity scarves, neck warmers, fingerless gloves, socks, etc. That's a possible idea. Hmm.
The list of similar stitches front and back are: Crab Stitch