IMMEDIATE AND OBVIOUS : It is a CYLINDRICAL KNOT It is a TWO COMPONENTS (each being SINGLE-STRAND) CYLINDRICAL KNOT It is a REGULAR CYLINDRICAL KNOT as in each BIGHT-NEST the BIGHTS are in perfect alignment and each NEST makes use of ALL the BIGHT-RIM on a given KNOT BORDER It is a SYMMETRIC REGULAR CYLINDRICAL KNOT ( on each KNOT BORDER there are the same number of BIGHT-RIM ) It is a fully complete and harmonious HERRINGBONE PATTERN
Copyright Charles HAMEL aka nautile 2012 Nov
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So let us see the CORDAGE ROUTE of this REGULAR SYMMETRIC NESTEDBIGHT CYLINDRICAL KNOT with a HERRINGBONE PATTERN Fig 2 Fig 3
The two components seem identical and superimposable one onto the other at the price of a small lateral sliding move over one INTER-BIGHT DISTANCE
Each COMPONENT is a SINGLE-STRAND 2-PASS
11L 9B SYMMETRIC IRREGULAR NESTED-BIGHT CYLINDRICAL (IRREGULAR because the BIGHTS in a BIGHT-NEST do not use each of the BIGHT-RIM available )
Copyright Charles HAMEL aka nautile 2012 Nov
page 3 on 7
Fig 4 each component cordage route shown alone
Fig 5 FIRST-RETURN CORDAGE ROUTE for each component
Two identical components it are. ( FORGET linearity and NEVER forget CYCLIC / PERIODIC and you will see they are identical )
Copyright Charles HAMEL aka nautile 2012 Nov
Fig 6
page 4 on 7
Copyright Charles HAMEL aka nautile 2012 Nov
Fig 7 the mirror knot cordage route
Fig 8 the two cordage route compared side by side
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Copyright Charles HAMEL aka nautile 2012 Nov
page 6 on 7
Fig 9 the two cordage route compared side by side
One has a DELTA = 1 ( Type 1 ) the other a DELTA = A – 1 = 3 – 1 = 2 ( Type 2 )
In the HERRINGBONE-PINEAPPLE CYLINDRICAL KNOT sub-class : SEMI-PERFECT HERRINGBONE-PINEAPPLE CYLINDRICAL KNOT characteristics are :
∆1 = 1 ( Type 1 ) ∆2 = A – 1 ( Type 2 )
condition is met
condition is met ( 3 – 1 = 2 ) B (18 ) and Ltotal (22) have a common divisor greater than 1 condition is met (2) 22 = 2 * 11 18 = 2 * 3 * 3 L total = x + 2A – 2 = 18 + (2*3) – 2 = 22 condition is met L total = Σ Lcomponent = 11 + 11 = 22 condition is met *
We know that my knot is a SEMI-PERFECT HERRINGBONE-PINEAPPLE CYLINDRICAL KNOT
Copyright Charles HAMEL aka nautile 2012 Nov
page 7 on 7
Just take away ONE BIGHT-NEST so that B* and Lcomp are coprime hence SINGLE-STRAND and you get a PERFECT HERRINGBONE CYLINDRICAL KNOT B* = 5 A = 3 Btotal = 15 Lcomp = Ltotal = 22
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