I can’t see how an image produced by swirling gas can be equated to a Mobius strip, other than by a superficial resemblance.
Then we have a recent report here on a strange hexagon at Saturn's North pole >> [ ”Hexagon on Saturn” and ”Cassini Images Bizarre Hexagon on Saturn” ]
My speculation is that we see a hexagon, but it's really a Möbius strip of charged particles.
The Saturn hexagon appears to be a cloud and gas formation. It’s not a true object in the sense that that an ordinary Mobius strip is. While the latter is made of a thin rectangular solid comprised of a bunch of atoms bonded into molecules, stuck together into cells, which are stuck together into fibers, which are stuck together into the thin sheet, the Saturn “hexagon” is a bunch of atoms and molecules in gas form, some likely clumped into dust/smoke particles, but not a solid whole. Matter is constantly entering and leaving the formation, and moving within it. It’s no more really a “band” than are the various bands of Saturn’s rings, or a procession of cars on a busy highway is a “snake”.
Another problem with drawing an equivalence between a Mobius strip and Saturn’s hexagon is that the latter’s not shaped much like a strip of paper. Though overall shaped like a thin band with 6 somewhat strait segments and 6 sharp angles, the segments vary a lot in thikness, from about 100 to 1000 km in width. Observations have revealed them to extend about 100 (but not as much as 1000) km from their tops to their bottoms. Their shape, then, appears to be roughly that of a flattened cylindrical tube, with no sharp edges to allow them to be divided into a top and bottom face for the Mobius construction to make a single surface. Scrutinizing the JPL images reveals no sign of the (single) distinct edge that defines a Mobius strip. In short, it’s hard to make a decent Mobius strip out of a garden hose – especially one that’s made out of wind and clouds.
The Mobius strip analogy might be more applicable if the wind direction within the Saturn formation showed a distinct pattern of alternating up and down at adjacent sharp corner (under high magnification, the corners don’t appear all that sharp, with radiuses of at least a couple of tens of kilometers, but still, clearly, a lot of air is changing direction more abruptly than usual). This would indicate that the formation was in a sense “folded” rather than curved. Visual examination of the images doesn’t appear to suggest this, and, AFAIK, Cassini’s instruments capable of imaging this don’t include ones capable of directly measuring wind velocity (eg: doppler radar). It’s imaging radar is, I believe, intended for surface mapping, not velocity measurement – though it’s unwise to underestimate the flexibility with which mission staff – some very smart folks - can use their instruments.
What’s forming Saturn’s strange “hexagon” is a fascinating mystery, on a par, I think, with that of Jupiter’s Great Red Spot. We’ve got to be careful to avoid finding patterns that aren’t really there, however – the human brain seems optimized to finding such patterns, even when it must be excessively inventive to do so.