Another symmetrical offering is the prusik knot. It holds position in either direction very well with just four coils.
I have not compared those knots with the climbing hitches. As I understand, climbing hitches hold well on a certain point of the main line only when -and because - they are loaded, and they are easily transported upwards or downwards when they are not. The bends/stopper/hitches - whatever we may call them - presented previously in this thread, as well as the last ones, tend to stay in place even after the ends of the attached line are not loaded any more. However, the main difference is elsewhere...The knots presented in this thread do not work on a straight, tensioned line, because they are based upon a more or less curved segment of it, to anchor the attached line. At those last knots, this curvature is imposed by the tightening of the attached line, i.e, we start placing the shape "8" knot of attached line on/around the straight main line, then we pull its two ends, and this operation deforms the main line as much as needed, to multiply the friction forces between the two lines. My purpose was this ; Find a knot tied with/on the attached line, that, when the main line is forced to curve inside it, the curvature is : 1 : Enough to offer the proper anchor so the attached line will not slip, and 2 : The curvature of the main line will not be straightened again, if, after the pull of the two ends of the attached line, the main line is tensioned much more forcefully than the attached line ( at about double the load, as it happens with the standing end of a loop, in comparison with the two legs of the loop).
I was amazed to see that the knots presented were successful in both of those tasks. I have not compared them in any detailed way, but it is clear that, although we start from about the same shape "8" knot on the attached line, we end with quite different knots, that should differ on their slippage characteristics. Great news !
Because we want to chose the best of them, and this difference of the end knot makes this much easier. My problem with knots that are e very similar, is that I can not chose which one is really better - and I am forced to keep all of them in the limited space of my brain...
So, I believe that those knots, based upon a more or less deformed main line, are very different animals than climbing friction hitches. And they have the advantage I have repeated many times, that climbing hitches do not : they can serve as knots for adjustable of fixed loops. I have stated that this iwas my main interest in the first place, to find a better mousetrap, sorry, bowline !
I do wonder what effect tensioning the white "pass through" main line will have on the couple you've just offered (#52-62)?
THAT is the crux of the matter !
I have seen that, after the attached line is tensioned and have succeeded to impose a curvature on the main line - be it an open helical segment or two 'bumps', a wave-like shape - those deformations of the main line tend to be permanent and stable. The existence of the attached line, even if it is not loaded, is enough to keep those necessary curves on the main line at their final state after the operation, i.e. that the deformation of the main line is, more or less, irreversible ! I say "more or less', because those knots are different, and in some of them this irreversibility is more assured than in others - and also because some straightening is expected. I have loaded the main line at double the load than at each of the two ends of the attached line, like it happens in a loop, and I have been satisfied with the results. I would love to perform the same tests with more slippery ropes, like the spectra/Dyneema non-coated ones, and see what happens there. volunteers are always wanted, and much welcomed !