So, I've been obsessed lately with mobius knitting. Yes, you can knit a mobius band. No, it's not easy, and I'm pretty sure that Cat Bordhi was brilliant in her insanity of how she created the mobius cast-on.
I've finished 4 projects, but the last 2 were little mobius baskets with the mobius half-twist for the handle. Although you could really play with the twist and put it anywhere (it would make the bowl part unusable, since it's part of the single side, but you COULD).
It's pretty cool, the geometry behind the mobius baskets... it's just a deformation of the knitted band. I have another cat bed on the needles.. hopefully this will be the "just right" one. (the first was too small, the second, too big)