PET diamond loop

[xarax]

   I mean, as I follow the alternating over/under pattern, I forget to ignore the two eye legs, with which the Working End also meets in its path to the finish, so I lose the rime... One has to follow the alternating over/under pattern ( which is easy to remember ) but to be careful to ignore the crossing of the Working End with the eye legs.
   As I said in my second post, the difficult thing in tying a knot is not to manipulate the segments, but to remember their positions. Once one forms the two overlapping nipping loops, the correct path of the Working End within them is easy to remember almost everywhere, except in those two last crossings. If, after the "over" crossing at #5, one does not remember to ignore the subsequent crossing of the Working End with the eye legs, he will drive it "under" them, as he should, but then, following the over/under rime, he will now go "over" at the 6th and "under" the 7th.. One has to be careful and to ignore the eye legs - that was for me the most difficult point to remember.   

[Luca]

Hi Ruby and xarax,

I believe that, regarding the easiness of untying, this knot might be proven to be better than the also perfectly symmetric but already much more dense and compact Tweedledee bowline ( no "empty" space there whatsoever ), which runs the danger to become too tightly woven.

If I recall well, this loop was very difficult to untie for me even after being not so heavily loaded:the only hope it offered to me was to untie it via the standing end,which remained a little less locked than the other three strands that branch off from the knot's nub;nothing particularly annoying in my case, but if the standing end is 60 meters long or is attached somewhere, is not very comfortable ...
And if I recall well,the Tweedledee Bowline perhaps was not the champion of the ease of untying,but was much easier to untie than this loop,and(at least a bit) more easy than the Fig. 8 loop.

                                                                                                                             Bye!

[xarax]

   There is a difference between those two knots, the Diamond and the Tweedledee bend and loop : the Diamond does not have collars which one can grasp and flex back and forth, in order to loosen the nub. So, one has to do the next best thing, which I have found that it is quite effective in this case : push the pair of ends inwards, towards the centre of the globular nub, i.e. feed the nub with more material to make it less dense, and thus to loosen it. I prefer to grasp both eye legs AND both Standing and Tail Ends, and then push them towards each other, until the one pair of them starts to feed material into the nub.
   The nub itself of the Diamond does not get more tightly woven than the nub of the Tweedledee, it just lacks the "handles" from which one can manipulate it. I do not know what will happen when the "empty space" inside it will be filled with frozen snow, though... 
     

[Luca]

Hi xarax,

So, one has to do the next best thing, which I have found that it is quite effective in this case : push the pair of ends inwards, towards the centre of the globular nub, i.e. feed the nub with more material to make it less dense, and thus to loosen it. I prefer to grasp both eye legs AND both Standing and Tail Ends, and then push them towards each other, until the one pair of them starts to feed material into the nub.

Perhaps I could give a chance to the bend to be "fed", but today I succeded to load the loop(I deliberately left it "soft" and "empty" before loading it) in a "decent" heavy way(decent for me,not for Alan Lee or knot4u):I assure you that the loop is totally inappetent, because his stomach is completely blocked (is blocked in either sense: it was necessary to use some tool( a pointed plier used mostly as a wedge) to pull out something from his petrified stomach).This time I untied it via the tail end,at least initially,but then I still had to act even on the standing end,to be able to completely untie it(about fifteen minutes the total time(but also because at the beginning I tried to untie it only with my hands)).

                                                                                                                                      Bye!
     

[xarax]

   You keep trying to pull some segments outwards, when you should push some segments inwards. 
   Of course, this is possible only in the cases of stiff ropes - but those are the ropes we are most interested, the kernmantle climbing ropes, because we always try to find a secure bowline-like PET alternative to the beautiful, TIB, but not easily untied or PET rewoven fig.8 loop.
  (  I had tried to "simplify" this knot, by omitting the "elbow" crossings of the ends just before they exit the nub - but then the resulting bend/loop deforms very easily under loading, and loses its initial nice symmetric form = the ability to an even / smooth distribution of the tensile forces inside the knot s nub. )

[Luca]

Hi xarax,

But I understand what you have written at the reply #17,but when the knot's nub is petrified, there is no leg that can be pushed inwards ...
I can however imagine that,using some rigid,not compressible rope,the spaces can remain empty,allowing the knot to be untied with hands,and,who knows,maybe more easily than a Fig. 8;maybe the empty spaces can also help to absorb energies in case of fall.In my (static loading) not so serious(and not reiterated) tests I used my dirty old average rope( not very stiff,but not soft at all):the knot has jammed badly.

But there is still another problem: theoretically the Diamond knot is perfectly symmetric, but physically I can not get this, because, once completed, the knot assumes actually a lower symmetry, as its faces do not look symmetric, as in theory seems that it should be;and, in fact, with regard of the position of the ends and the legs of the loop with respect to the asymmetry that appears, the same loop can be transformed in one or another way,as in the pic below.
So, we are talking about the same loop?

                                                                                                                                   Bye!

[xarax]

...when the knot's nub is petrified, there is no leg that can be pushed inwards ...

  You can push a petrified leg more easily than a liquefied one ! 
  The two pair of ends themselves are not squeezed  as they enter/exit the knot s nub. The interweaved surrounding segments, which travel in those "orbits" around the central area with the "empty" space, form kind of a protective "cocoon" around the two "necks", which, although itself is tightly woven, it does not constrict the legs as they enter/exit the nub. Any resistance to a push inwards is generated by the "elbow" crossing between them ( i.e., the "elbow" twisting of the Standing End around the Tail End, and of the on-going eye leg around the returning eye leg ), NOT by their own constriction by the surrounding nub.
   Now, you may mean that, when the segments of the surrounding "cocoon" are tightly interwoven, even if the legs do not encounter any major resistance at the entry/exit areas, they nevertheless will be immobilized deeper inside the nub, at the areas when they merge with the "cocoon". In that case, when you push the legs you will not be able to feed more material into the nub, because the tightly woven "imploded" "cocoon" will fail to "explode" even a little bid.
   I use rather slippery ropes, so the knots tied on them can reach their "final" form, and become very compact, even under a not-so-heavy loading ( compared to the strength of the rope itself ). This enables me to generate tightly woven knots, but perhaps also enables me to untie them more easily than the same knots tied on rougher, "used" ropes, like this not-so-white-any-more rope you use. See the picture of the knot at reply #13. Judging from its size, you can see that the knot is tightly woven, yet I encountered no difficulty at all in pushing the legs inwards and forcing it to "explode" outwards. Perhaps this Beal conyoning rope (1) is much more slippery than the ropes you had used ( ? ). 

1.  http://www.bealplanet.com/2014/anglais/corde-pro-canyon.html

...theoretically the Diamond knot is perfectly symmetric...

  No, it in not perfectly axially symmetric, if that is what you mean. There are only two segments going inwards and two going outwards, so the nub woven around them is more "flattened" along the one direction than along the other ( so the nub s cross section along the axis of the knot is elliptical, not circular ). I do not know what one can weave with a double-line one, when we will have four segments at each end - perhaps such a knot will become more axially symmetric, indeed. 

[enhaut]

Hi Ruby,

Thanks for showing us this Diamond loop.
It looks great, but I fear it would not stand still in high slippery material because it only uses friction as a stopping mecanism. But I can be all wrong here.

I took the liberty to reproduce the Diamond's pattern for more clarity.
Hope you dont mind.

Picture = Diamond Loop's route

[Luca]

Hi xarax,

(referring to the reply #21)
Here are two different loops that one can talk, they are shown at reply #20. What I really mean in regard to the symmetries is that,looking at the Diamond knot,we can identify two opposite faces identical to each other + other two opposite faces identical to each other: each of these four faces intrinsically is not symmetric; then there are two other opposite faces,from each of which come out  two legs of the knot's nub:each of these two faces is intrinsically symmetric, but these two opposite faces are geometrically different from each other.
So,taking as an example the image of the knot at reply #13,if the eye is formed with the two strands on the left is a distinct loop from the loop that is obtained if are the two strands on the right that form the eye(but the two loops are topologically identical in this case,due to the high symmetry of the "theoretical" knot from which the "diamond" is obtained);and in the case where the knot is used as a bend, with this geometry the bend obtained is asymmetric.
This also results in the fact that the two pairs of "legs" that enter in the knot's nub, enter into it in a different way: a pair remains more "immersed" in the knot'nub, but the other pair remains "squeezed" closer to the surface(and yes,the more immersed legs are those that eventually allowed me to untie(with a tool!)the jammed knot)

                                                                                                                                        Bye!

[xarax]

...the two pairs of "legs" that enter in the knot's nub, enter into it in a different way

   So that is what you are trying to say all this time !    Obviously, if we start from the ( face-symmetric ) Diamond mat ( shown in the attached picture ), we can tie either the loop shown by Ruby, or its reversed - as it happens in any symmetric mat turned into a bend or a loop. However, that does not mean that the base mat itself is not symmetric - the same happens in the case of the many symmetric variations of the retraced fig.8 knot, but we do not characterize them as a-symmetric !
   Now, you may argue that the reversed loop, where the Standing/Tail Ends of the knot shown by Ruby become the eye legs, and vice versa, will behave differently, and perhaps will not clinch so tightly under heavy loading. Who knows ? The only way we can tell is to actually test the two knots. Under moderate loading, I have not noticed any major differences.

...in the case where the knot is used as a bend, with this geometry the bend obtained is asymmetric.

   Noope ! (*) Starting from the face-symmetric Diamond mat shown in the attached picture, the derived two bends are as symmetric as they can be ( because they are also face-symmetric ) : the red and the blue lines follow identical paths relatively to each other.
   (*) Unless you are talking about the bend based on the compact nubs of those two loops ( which are globular, and not flat, as the initial mat )... However, I believe we always start from the knots of the bends, which are symmetrically loaded, and we turn them into the corresponding knots of the loops, which are not, only afterwards. ( In the knots of the loops we have three of the four limbs loaded. A symmetric loading requires two or four loaded limbs ).   

[Luca]

Hi xarax,

The mat that you show is what I have called (quite improperly) "theoretical knot" .
If someone wrote that "this base mat itself is not symmetric",please let me know where to find him, because I have to pull his ears!
I,for example,have written (perhaps poorly) exactly the opposite:the sense of what I wrote is that this base mat is higly symmetric,more symmetric than the Diamond knot that can be derived from it.
So,what is that I am trying to say all this time?
Mainly the obvious fact that, for example, using the PET method(that I find very easy to remember) by Ruby for the Diamond loop is not obvious what will be the loop that will be obtained between the two loops(the one+the "opposite" to this one) shown at reply #20,because, after the tying,is a pure question of dressing in order to determine what will be the final loop.
This is an obvious consequence of the fact that the level of symmetry of the Diamond knot(naively described at reply #23) is lower than that for example of the Tweedledee knot.
Another consequence of this fact is that the bend shown at reply #13, with that geometry,is not symmetric like the Tweedledee bend, and is not symmetric even like another less face-symmetric bend,because,with that geometry,the bend has no hope of being symmetrically loaded,if the bend is the bend version of the loops,ie loaded by one strand on the left and the appropiate strand of the other link,on the right.
If you load the base mat you show above by loading  the over-left-red strand and the under-right-blue strand(or viceversa),the bend that you will obtain(less symmetric than the base mat,but however symmetric),is not even remotely similar to the Diamond bend that you show at reply #13.

                                                                                                                           Bye!

[xarax]

...this base mat is highly symmetric, more symmetric than the Diamond knot that can be derived from it.

   Noope !  It is more symmetric than some Diamond knots that can be derived from it ( as the globular Diamond loop, where three limbs are loaded ), but it is not more symmetric than others ( as the two planar, face symmetric Diamond bends, where two limbs are loaded  ). It is the mat, the "theoretical" knot, the knot which should be considered as the base knot. This knot is symmetric, albeit less symmetric than the Tweedledee knot, indeed - which is "triply symmetric" ( according to the nomenclature established by Miles ).
   Now, this symmetric mat can be loaded symmetrically, i.e., by two or four limbs, and generate symmetric knots, or asymmetrically, i.e., by three limbs, and generate asymmetric knot, as it should have been expected ! The Tweedledee loop is also asymmetrically loaded, but there the geometrical distortion of the base knot, the Tweedledee mat, is not so pronounced and visible, and it may even be unnoticed. In the case of the Diamond mat, the asymmetric loading ( by three limbs ) forces the nub to curl, and finally settle in this globular form of the Diamond loop. We should not be fooled by the stability of some loop knots, as the Tweedledee bowline ( or, for that matter, of the fake, so-called "Zeppelin loop" ), and believe that they are symmetric... They are not. Eventually, under heavy loading, this asymmetry will be manifested. In the case of the Diamond knot, it happens that the parent Diamond mat is very unstable, and sensitive to the asymmetric, three-limbs loading, and takes this globular form immediately, even under a light loading.     
   What I have pointed out is that, usually, one does not go to the knot of bend starting from the knot of the loop, but starting from the knot of the mat. If you follow this sequence, you will never arrive at the globular form of the knot of the loop, and use it as a bend !
   

...the level of symmetry of the Diamond knot... is lower than that for example of the Tweedledee knot.

   Right. However, that does not mean that the Diamond knot is a-symmetric ! 

... the bend shown at reply #13, with that geometry, is not symmetric like the Tweedledee bend ...[it] has no hope of being symmetrically loaded,

   Right. Now I understand what you are saying... Therefore you have to derive the two face-symmetric bends from the mat, not from the loop. The correct sequence is : mat ---> bends ---> loop, not mat ---> loop ---> bend.

...the bend that you will obtain... is not even remotely similar to the Diamond bend that you show at reply #13.

   Correct. The label of the picture in Reply#13 is misleading. I should had labelled it as " Diamond loop ( detail )". It is a good thing to have a knot-tyer-angel who saves you from those mistakes ! 

[Luca]

Hi xarax,

The base-mat at reply #24,for how it looks,when turned upside down should present the exact same intrinsically symmetric face.
The problem is that,in the practice,this identity of faces is a little hard to get, because this knot is itself very unstable,and,moreover, if one not achieves a perfect "balance of identity" between the two faces,will be even more difficult to notice that also the "four sides", the "edges" of the flat faces, become intrinsically symmetric.
Then, if one transforms the Diamond knot(I mean the "classic" Diamond knot,ie the "unloaded" lanyard knot) into the flat "neutral" base-mat(which is not exactly the mat visible in the third pic at reply #2 http://igkt.net/sm/index.php?topic=5151.msg33717#msg33717 ),this happens (with a little patience and luck ... I make the example of this transformation also because it is in this way that I personally have obtained the base-mat):the two opposite faces that in the Diamond knot are intrinsically symmetric,but that are different respect to one another,continue to be intrinsically symmetric and become identical respect to one another.And the 2+2 opposite faces that in the Diamond knot are intrinsically asymmetric,but are identical respect to one another,becomes intrinsically symmetric and continue to be identical respect to one another.
Therefore I believe that the base-mat has an higher level of symmetry than the level of face-symmetry of the Diamond knot and the two bends partially reversed to each other,obtained by loading two limbs of this base-mat.

                                                                                                                                                      Your little guardian chick 

[xarax]

... this knot is very unstable..

  It is, indeed, but only when / if  it is loaded asymmetrically, i.e., when it is used as an eye-knot. The "flat" symmetric bend is not more unstable than the ( simpler, but "similar", in a sense ) Mike s small fancy bend and the Axis knot ( M. A22 ), shown at :
  http://igkt.net/sm/index.php?topic=3585
 

... the base-mat has an higher level of symmetry than... the two bends ...obtained by loading two limbs of this base-mat.

  Moreover the one bend ( where, in the unloaded base-mat, the Standing Ends are parallel ), is more symmetric than the other, ( where they are perpendicular). To get the most symmetric knot, you have to load evenly all the four limbs.

[capellagroup]

I agree with Xarax about the glorious symmetry of this knot.  There are odd bits of cord all over my house, truck, boat and elsewhere, all tied in a loop.  I've never tried tying it in 2 separate pieces of cord.  I tie it PET (love that acronymic description!) all the time.  It's just how I learned to tie it out of some book I can't remember. (Grandfathers ar allowed to forget whatever they want.)  I will try the method tuted above and see how I go.  But after all, it's just a Carricked loop.