PET diamond loop

[Luca]

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!

[Luca]

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!

[xarax]

...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

[Ruby]

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

[Ruby]

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.