It is the *geometry*, not the *topology* of the fig. 8 knot that is utilized here. Any S shaped knot can serve as a base for such a loop. So, instead of knots topologically equivalent to the fig. 8 knot, we can use simpler S shaped knots, topologically equivalent to the overhand knot, or even to the unknot. All we need is,

a : to form, as a base, a geometrically S shaped knot on the standing part, and,

b : to pass the working end through this knot two or three times ( two times, as at the # 0 and #4 loops, three times, as at the # 1, #2 and #3 loops).

If we could possibly achieve essentially the same thing using a simpler base knot, which would be much easier to untie, why should we use the fig.8 knot ? An S shaped overhand knot would probably produce equally secure loops.

Without probing distinctions between "geometry" & "topology"

in knotting, here, suffice it to say that this set of knots arises

from working the commonly given

*fig.8* shape ("geometry")

into an altered form and then <... --variations of the set>.

Yes, one can do such general working with other bases,

but so what? (Casting the

*Eskimo bowline* into this shape I think

distorts that knot's real

*geometry* more so than does this set's

use of the

*fig.8* . The "S" is hardly essential, either,

generally;

but it is particular to this set, and the idea set off upon in exploration.)

This

*fig.8* set has a characteristic enclosure of the SPart's

eyeleg exit/entry by the turn of the SPart that is lost, e.g.,

in that

*Eskimo bowline* diagram.

I see (slowly) that a version that I verbally sketched in the OP's

thread is his #0 with the tail's path reversed; it's not all so clear

to me which should be preferred --#0 is surely better on

*ring-loading*.

And both of these I think are better bets at easier loosening than

others --in that their brief entanglement of the tail allows it to be

used qua lever for loosening--, though I've not played much with

the full set.

--dl*

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