The knot ( stopper ) shown at the front row of the table, is the third knot shown at (1). I call it "both bights, half-untwist to fig.8" knot"
, trying to describe verbally how we arrive from this knot to the fig.8 knot. Most people call it with another, wrong (
) name, that might be improved a little bid, as " 2 fig. 9 s knot"
( because it resembles the shape of two
9 s, each put in a point-symmetric configuration to the other ). They say that, the retraced knot of it makes a very secure bend, more secure than the retraced fig. 8 bend. While this claim sounds reasonable, judging from the more convoluted and wider curves that the standing parts follow in this knot, I am not sure that it is supported by extensive experimental evidence. And I am sure that it is not tested against all different dressings of the retraced fg. 8 bend, shown at (2). I believe it is used, as a bend, in caving and canyoning, because the lines are wet, muddy and get very slippery in those environments. I do not know how people prefer to dress it at those situations - like the knot shown at the first attached picture, or the same knot, dressed differently, shown at the second attached picture, or in any other way...
Now, one can, indeed, see the "Helical bend" shown at (3) as a sub-set, so to speak, of a retraced knot as the 3D printed one, shown in the picture. As I have said there, this was not the path I have followed to arrive at this bend, not at all. However, it is interesting to start from the complete retraced knot (shown in the attached pcture) , and try to figure out how we can simplify it, omitting some parts or modifying some others. For some more convoluted bends, that can possibly be used with/on very slippery materials, see (4).