International Guild of Knot Tyers Forum

General => Practical Knots => Topic started by: Ruby on November 23, 2014, 04:50:14 AM

Title: PET diamond loop
Post by: Ruby on November 23, 2014, 04:50:14 AM


if the diamond knot is PET post eye tiable ,
then it may be a good practical end-of-line fixed loop knot?
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 04:52:04 AM
ABoK #787

Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 04:53:29 AM
wiki pic



retucked carrick bend
Title: Re: PET diamond loop
Post by: xarax on November 23, 2014, 06:21:01 AM
  if the diamond knot is PET post eye tiable ,
  then it may be a good practical end-of-line fixed loop knot ?

   I have not found a simple way to tie it in-the-(one) end... To be "practical", it should be not only "post-eye-tiable", but also "easily-tiable" !  :)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:29:20 AM
1. post eye

(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16614;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:30:17 AM
2. make 1st overhand loop using the standing part

   you can hold this crossing point A using left hand thumb and index finger during all the next steps



(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16598;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:31:04 AM
3. make 2nd overhand loop , over point A.
   hold tightly crossing point A


(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16600;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:31:47 AM
4. put the working end through the hole between the two loop. (elbow?) .

  hold all those (5) rope parts at crossing point A.


(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16602;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:32:22 AM
5. weave using working end.
    1 over, 2 under, 3 over, 4 under, 5 over, 6 under, 7 over
 
  hold tightly crossing point A during weaving


(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16612;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:33:01 AM
6. put working end throuth the center hole


(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16606;image)

.

(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16608;image)
Title: Re: PET diamond loop
Post by: Ruby on November 23, 2014, 08:33:43 AM
7. pull four ends to dress the diamond knot

end



(http://igkt.net/sm/index.php?action=dlattach;topic=5151.0;attach=16610;image)


left hand holds the crossing point A all the time, right hand does the weaving.

not  so easily-tiable.
but not too difficult, after practicing one or two times.
Title: Re: PET diamond loop
Post by: xarax on November 23, 2014, 09:15:50 AM
   "Easily-tiable" is referring to the required effort of the brain cells, not of the muscle cells !   :)
    The much easier to remember how to tie Tweedledee bowline (1) was criticized as overcomplicated for the average climber - and it may be, indeed. Therefore, I do not believe that anybody else except the two of us will tie this beautiful 3D rosette ! You have simplified the tying procedure a lot (*)( using less than a thousand words, I have to admit... :)), but not enough, I am afraid. It is a pity, because, judging from its form, I believe that this knot will be easy to untie, even after heavy loading ...

1. http://igkt.net/sm/index.php?topic=3989.msg28582#msg28582

(*) The alternating over/under pattern was a clever trick !
Title: Re: PET diamond loop
Post by: Dan_Lehman on November 28, 2014, 08:11:56 PM
   "Easily-tiable" is referring to the required effort of the brain cells, not of the muscle cells !   :)
Not so fast --it looks to be a mess of over/under reeving,
and the necessity to secure the inchoate knot until all
is done.

Quote
It is a pity, because, judging from its form, I believe
that this knot will be easy to untie, even after heavy loading ...

That hardly distinguishes it from the many bowlinesque
options one has, among many others, to boot, all of which
are more easily tied.

Now, I remain open to a personal reassessment after I've
taken time to work this all through --gave a cursory try in
cord of insufficient length for all the workings, so far.


--dl*
====
Title: Re: PET diamond loop
Post by: xarax on November 29, 2014, 02:07:45 PM
   I can not ignore the beautiful pattern of this knot, the perfect symmetry between the "nipping" ( before the eye ) and the "nipped" ( after the eye ) structures, and the way the segments are interwoven - meeting each other at the "right" angle ( 90 degrees, the right angle ) while, at the same time, leaving so much "empty" space in between them ( therefore, making the nub able to absorb a sudden heavy pull, without running the danger to become more compact, and jam ). 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. The clever way of tying it Ruby has devised, with the simple, easy to remember form of the first, before the eye, part, and the alternating over/under reeving of the Working End during the formation of the second, after the eye, part, reduces its complexity a lot. Moreover, I do not see any points during this particular tying procedure where one can do a mistake, like the one that can happen during the tying of the Tweedledee bowline (1).  Tying it the minimum number of times I need to tie in order to understand any knot ( 12... ), my greatest difficulty was always on the two last crossings, the 6th and the 7th : I believe that it is easy to make a mistake there, and go over/under instead of under/over, because the Working End crosses the two legs of the eye, and it is difficult to remember that those crossings should be ignored in the alternating over/under pattern... 
   In short, Ruby has done a great job, by pointing out a supposedly well known perfectly symmetric bend and loop ( which I, for one, had missed... ), and teaching a not-so-easy but also not terribly complex tying method. I believe this bend and this loop deserve a special place in any knot tyers collection, next to the Tweedledee bend and loop. Unfortunately, just like the Tweedledee bowline, the loop is not TIB, and I have came to believe that the versatility of a TIB end-of-line loop is also too much to ignore.

1. http://igkt.net/sm/index.php?topic=3989.msg28205#msg28205 
Title: Re: PET diamond loop
Post by: Ruby on November 29, 2014, 06:07:09 PM
...my greatest difficulty was always on the two last crossings, the 6th and the 7th : I believe that it is easy to make a mistake there, and go over/under instead of under/over, because the Working End crosses the two legs of the eye, and it is difficult to remember that those crossings should be ignored in the alternating over/under pattern... 
   ...


well, actualy last 2 crossings (the 6th and the 7th) and those in the next step ( 8th and 9th?) can be done in one step, 1 second.

because left hand is holding those crossing points all the time, using thumb and index finger.

just follow your thumb and index finger!  I think it's easy if you do it like this.
Title: Re: PET diamond loop
Post by: xarax on November 29, 2014, 06:41:01 PM
   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.   
Title: Re: PET diamond loop
Post by: Luca on November 30, 2014, 12:44:38 AM
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!
Title: Re: PET diamond loop
Post by: xarax on November 30, 2014, 06:10:52 AM
   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...  :)
     
Title: Re: PET diamond loop
Post by: Luca on December 01, 2014, 02:55:19 AM
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!
     
Title: Re: PET diamond loop
Post by: xarax on December 01, 2014, 09:07:49 AM
   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. )
Title: Re: PET diamond loop
Post by: Luca on December 02, 2014, 02:13:02 AM
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!
(http://)
Title: Re: PET diamond loop
Post by: xarax on December 02, 2014, 05:35:28 AM
...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. 
Title: Re: PET diamond loop
Post by: enhaut on December 02, 2014, 07:38:15 PM
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
Title: Re: PET diamond loop
Post by: Luca on December 03, 2014, 03:01:06 AM
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!
Title: Re: PET diamond loop
Post by: xarax on December 03, 2014, 09:36:49 AM
...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 ).   
Title: Re: PET diamond loop
Post by: Luca on December 04, 2014, 12:09:50 AM
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! >:( ;D
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!
Title: Re: PET diamond loop
Post by: xarax on December 04, 2014, 04:37:30 AM
...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 !  :)
Title: Re: PET diamond loop
Post by: Luca on December 06, 2014, 02:49:59 AM
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  ;)

Title: Re: PET diamond loop
Post by: xarax on December 06, 2014, 04:12:17 AM
... 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.
Title: Re: PET diamond loop
Post by: capellagroup on December 07, 2014, 06:52:14 AM
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.
Title: Re: PET diamond loop
Post by: Luca on December 08, 2014, 03:19:03 AM
Hi 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.......     ........To get the most symmetric knot, you have to load evenly all the four limbs.


This highly symmetric mat,like some other highly symmetric knot,needs to be carefully dressed and setted to express "visually" its symmetry, and yes, if loaded, the only way to maintain its visual symmetry is to load it in a perfectly balanced way by his four limbs.

The Mike's small fancy bend is a symmetric knot,with his own type of symmetry(the 3+3 opposite(intrinsically asymmetric)faces are symmetrical to each other),and as a bend is symmetrically loaded.
The Axis knot,with that geometry in the linked pic,in itself,as an unloaded lanyard knot,is a symmetric knot,and is symmetric exactly(or roughly,but in broad terms the situation is the same:1+1 opposite faces intrinsically symmetric,but different to each other(although apparently very similar,in this case),and 2+2 opposite faces intrinsically asymmetric,but identical to each other)as is symmetric the unloaded Diamond knot.
But the consequence of this situation is inexorable:the Axis bend,with that geometry(I tried to fumble in order to obtain a neutral, more symmetric base,but I did not get results in this regard),loaded by the left-white rope and the right-orange rope or viceversa,is a bend asymmetrically loaded.


... 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).

I do not know:to me, as they appear geometrically, it seems that roughly have the same type of symmetry, that seems to me to be roughly the one I described for the Diamond knot.But I'm ignorant about the science of geometry, so it is likely that I am missing something:for example, comparing the capsized #1428 with the capsized #1439,I can not really say which is the more symmetric,as they appear to look at them.

                                                                                                                                           Bye!

Title: Re: PET diamond loop
Post by: Luca on December 08, 2014, 03:53:57 AM
Hi capellagroup,

I agree...about the glorious symmetry of this knot. 

I agree(with all those who know this knot,I think)about the glorious beauty of the geometry of this knot,but I think that its symmetries are not much more glorious than those of a capsized Carrick bend,and that are less glorious than those of a no-capsized/loaded Carrick mat.

                                                                                                                                    Bye!
Title: Re: PET diamond loop
Post by: xarax on December 08, 2014, 05:42:29 AM
...in order to obtain a neutral, more symmetric base...

   Have a look at the knots shown at :
   http://igkt.net/sm/index.php?topic=3585.msg22193#msg22193
   http://igkt.net/sm/index.php?topic=4293.0

Title: Re: PET diamond loop
Post by: Ruby on December 14, 2014, 10:32:53 AM
if begin with 3 loops, you'll get a bigger diamond, but the over-1-under-1 pattern would change to over-2-under-2.

begin with 4 loops? over-3-under-3.

more decorative, less practical.


but the over-1-under-1 pattern normal diamond is the best, both decorative and practical, famous and well-known.

perfect ;D
Title: Re: PET diamond loop
Post by: Ruby on September 10, 2020, 03:53:32 PM
hello, just to add some words.

this is actually a THK, turks head knot, 3 Leads,4 Bights.
the basic pattern is repeatedly over one, under one.

basic move is:
2 loops,
then under 1 over 1, center,  under 1 over 1
 
to extend this method, like this:

3 loops,
then under 2 over 1, center,  under 2 over 1
then under 2 over 2, center,  under 2 over 2

then you get a bend, or a PET loop, of a THK, turks head knot, 5 Leads x 6 Bights.
the basic pattern is repeatedly over 2, under 2.  someone calls it Gaucho knot.

to extend this method again, like this:

4 loops,
then under 3 over 1, center,  under 3 over 1
then under 3 over 2, center,  under 3 over 2
then under 3 over 3, center,  under 3 over 3

then you get a bend, or a PET loop, of a THK, turks head knot, 7 Leads x 8 Bights.
the basic pattern is repeatedly over 3, under 3. someone calls it 3 pass Gaucho knot.


once you find the rule or law, you ll find it?s quite easy,  and, much fun.