Nautile aka Charles Hamel's personal pages
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Added 2013 July

up a heap of absurd and mistaken notions and that I canNOT countenance despite liking the person intellectual curiosity because it is
polluting minds. )  :



The THK nature is NOT GRADABLE :
it  IS A THK OR it IS NOT  A THK but there is ABSOLUTELY NO
possible QUASI-THK just as there is no quasi positive number or quasi-even number.

There is no quasi THK except if deliberately ignoring the structural mathematical characteristics of  THK and deciding to call THK just about anything.

This soap box ranting of mine is  in relation with  a post from friend Struktor in the IGKT- forum of which some ( surprised by the notion ) persons apprised me after I got a private mail from Struktor asking me a question but not telling of this post.
Struktor went public then I will answer in my site in the hope that some persons will be saved from adhering to absurd notions.

This Struktor's grid  IS ANYTHING BUT a THK grid.

I really don't know how with the tiniest acquaintance with Cylindrical Knots (Schaake) someone may dare to think THK about it, the more so with "quasi" appended to it.

Some persons thrive on constantly attempting to make things clearer while some other thrive on bending backward to make them as obscure as possible.

Is the motivation for diffusing so an absurd notion as  QUASI-THK a  QUASI
contrast illusion
? the more obscure the environment the brighter you seem to be ?

Struktor, by mail, posed to me this question ( but without using this absurd quasi THK heading) before I learned of his post ( of which he did not spoke ) through a third party.

[open quote]
How to describe this knot?
[end quote]

To this question I must make some observations
( I was away from home for a few days and could not immediately respond to Struktor
directly but learning of his public post I deem necessary to answer on a place accessible to public to try and block some poor souls from being contaminated with such notions as are exposed.)

That Struktor diagram  seems to me to be specially 'gauche' or , may be though I doubt it, specially made to trick the observer by obscuring essential characteristics.
Obscuring  due to the very outlandish * topology* used. Not only that but it makes the tyer's work a lot more difficult than strictly necessary : looks to me  more like a Art Nouveau wrought iron project than a grid for a knot.

I was trained in sciences and in "experimental method" so to get a reasoned and factual answer I had to find a moment to lay cordage along that tracing and as I suspected from the first half  second of seeing it that the result, laid cordage GEOMETRY  as opposed to the grid TOPOLOGY,  is different  from what the grid seems to show.

No offence meant but I ( and a number of my correspondents with me) often wondered  if Struktor is  simply a polymath just dabbling now and then with knots but without any  in depth and really extensive practical experience with them  or if he has several hundreds of knots in his hands as  "experience" like most of those I deal with in a regular fashion.
Why that interrogation ? : this intelligent person has a real knack to draw the most unfriendly grids for a "practical" knot tyer ;-) 

[open quote]
Conical or cylindrical
How to describe this knot?
[end quote]

Struktor question to me, as it stands, is really without any possible answer as it undecidable
(at least for me...)

First point :  friend Struktor is not showing a KNOT  (geometry) but the diagram of a knot (topology) which make  two entirely different logical planes that must not be confused one with the other.

It is impossible to have a meaningful discussion if logical planes get mixed up as this create perfect misunderstanding through total absence of possible common ground.

I just hope that he did not even test his creation in the cordage because that would show a surprising lack of knowledge of Schaake's work and of Ariane for someone saying that he has the mastery of The Braider main points ! (well after years of regular study I cannot even begin to boast that)

If from his question I understand :

How to describe this knot's GRID?
***Then he must know as well as me that the question is "meaningless" so is without any answer since the grid shows the topology and not the geometry.
It is meaningless to describe a topology when one want to discuss the geometry, the 3D real life structure is geometry*not* topology like the gris is.

Has is well known any NESTED-BIGHT CYLINDRICAL KNOTS can cover a
cylinder OR a sphere or other volume so there is no definite answer unless one refers to the fact that  the cordage rouge during its laying can be put on a cylinder.
This route and coding can certainly be laid on a cylinder so in that particular restricted meaning it can be said "cylindrical" which is not really a great progress.

*** if the question put to me is "does this grid represents a "cylindrical" Knot as theorised by Schaake then  the answer to be given in a reasoned factula fashion will have to wait for the *geometry* of it to appear in my hands.

Let us see several hypothesis.
If I understand the question as meaning:
How to describe this knot once it is laid in cordage but not yet dressed and set ?
Then there is still uncertainty as  we may be speaking of TOPOLOGY if the cordage is still on its laying support with the pins still in place, or we may be speaking of GEOMETRY if
--- the laid cordage route has been taken off its support ,
--- the slack has been taken off almost in totality without being  really hard set.

If I understand the question as meaning
How to describe this knot once it is laid in cordage *and* faired and set?
Then it is still without answer since we do not know what will appear if we give it a core or if we let it "somehow collapse" in some "natural" shape.

It was IMPERATIVE for me to put it in cordage to reveal the GEOMETRY of this awfully cumbersome TOPOLOGY.

I put Struktor's grid on this "tool" and got that geometry by laying the cordage.
( it is in a "relaxed" or "exploded" state, not tightened )

I replace it on a small cylinder and put back some pins to get a more friendly AND
honest topology candidly showing itself.

Armed with that it was child play to make a new topological grid for this geometry.


It is 7 LEAD yes but certainly not 8 BIGHT since it is 16 BIGHT/
--- 4 bight on BIGHT-RIM N1
--- 4 bights on BIGHT-RIM N2
--- 8 bights on BIGHT-RIM N3
On the other KNOT EDGE
--- 8 bight on BIGHT-RIM N1
--- 8 bights on BIGHT-RIM N2

: the Number of BIGHT-RIM is different in the two KNOT-BORDER.
one has 3 BIGHT-RIM, the other has 2.

NESTED-BIGHT : there are BIGHTS "hanging" on BIGHT-RIM that are NOT perfectly
aligned with the outermost BIGHT servig as nest.

Plus NON REGULAR or IRREGULAR because there are different "groups" of BIGHT according to the BIGHT-RIM they are hanging from. and they are not "regularly aligned "in neatly stacked  nests.
If you want to see some example just have a quick look at page 2 to 5 of

For me, (in the vertical cylinder frame of reference with BIGHT-BORDER at TOP and BOTTOM)  the ODD-numbered Half-Period go \  from BOTTOM-RIGHT to TOP-LEFT and EVEN-numbered  Half-Period go   /     from TOP-RIGHT to BOTTOM-LEFT.

If you observe attentively the picture of the real knot you will see that its geometry clearly shows HALF-PERIODS that have their 'summit pin' inside the knot itself :
NESTED-BIGHT ; the changing in direction  of a supposed Half-Period which goes upward or downward before getting to the opposite Bight-border sign the nature of EVEN or ODD Half-period which does not begin or end on one of the outermost Bight-Rim.

First I compared the two grids and found ( would be astonishing to get the same number of crossings just by chance) the same number of crossings in both :
56 crossings all told , 24 in the Nested-Bight zone and 32 (different repartition in the two grids) for the remaining contingent.

I then used ARIANE to draw my topology as a verification of my hand drawn grid.
in square grid
in isometric grid

Comparison of the three grids :  just try to find which is the more obscure.

Then I made a new knot using my own grid and made a comparison between the two knots : identical geometry despite the hugely different topologies that served for their laying.

Here it is in hard set version as a knot should be shown and using not trick to give it
a particular appearance that is not its 'spontaneous' one.

End of my ranting...

err NO !
I almost forgot :
 here is how to take people on a fool's ride : Reidemeister's moves.

See how the two grids , Struktor's and mine,  are topologically equivalent but one is an
illusionist trick hiding all the relevant information.

Here is how to correct Struktor grid and give it an honest (does not hide anything , no trick) appearance.

By all means do ( for exploration ) this knot in several diameter of cordage ( from 3  mm to 15 mm ) as the rendering of a knot dependends on the size of the cordage, try it to in flat lace  ( gutted paracord and hard set on a core ( to flatten it ).

If you are not sure that a knot is cordage diameter diameter ( and support diameter ) then I suggest :
a Constrictor knot with kitchen string on a pencil
a Constrictor knot with kitchen string around a 1 liter bottle
a Constrictor knotin 15 mm string around a glass
a Constrictor knott in 15 mm string around a 50 cm tree trunk or a barrel
and see how they behave...


Added 2013 30th


In Bats-belfry_16 read the topic
Making a better job than ASHLEY did on some of his knots.
ABoK#2216   ;   #2217   ;   #2218   ;   #2219 (1391)   ;   #2222   ;  #2232

Ashley worked there following the principle " why make it simple when you can make it complicated ?" and very ill advised he drew flat ( mat ) grids for knot that really are "volume" and not mat as they are covers for the surface of some volumes.

Using the same process I have redrawn Struktor 'PENTA' conical knot for use on a
cylinder as 98% of knots-tyers I know very much prefer that way of doing thing (usual method, less deformation in the knot, no need to stress it to make it go form "flat" to "relief...)
You have there the two grids. = the mat from Struktor and the cylindrical from me.

and this one is for the "hexa"

Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2014 -(each year)

Url : http://charles.hamel.freeL .fr/knots-and-cordages/B