Mobius Turk's-head knots      

I developed a method of manufacturing knots in the shape of the head of the Turkish Mobius strip. It has the advantage that it allows these nodes to plait on normal tools used for ordinary Turkish head knots. The idea is to add extra bights, which only serve to simulate the half turn on the cylinder, or a plane and disappear after pulling the knot and Mobius strip molding. This method works well for an even number of laps of the leads. For an odd number of leads, the order of interlaces can be locally broken, that is why I didn't take them under consideration.

I did not make a separate index for Mobius Turk's Head knots, because you can use the index for the ordinary Turk's Head knots, adding extra bights. Easy to see that for even leads we have formula: extra bights = leads / 2

I wrote the program to draw schemes of these knots, which is available from: Diagram1 download

For parity lead: extra bights = lead /2 = 12/2 = 6

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Mobius clockwise (B35L12S1M)

Used tool

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Appendix

Mobius Turk's Head knots for the odd number of leads.

I wrote the program to draw schemes of these knots, which is available from: Diagram2 download

I used a single (universal) way to make turk's head knots in the shape of Mobius strip for the odd number of leads. For this purpose, I applied a double crossover strip which goes along the middle of the strip symmetrically.

The method works well for any odd, having more than 3 numbers leads.

Again, I used additional bight, which serves only to simulate a roundhouse on the cylinder, or plane and disappear after enlisting the knot and the formation of a Mobius strip.

This enables the creation of the knots on the tools used normally the make usual turk's head knots (example) .

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As it is well known Mobius strip has only one edge. For an odd number of leads, the sum of bights on this edge is odd as well. That's what my picture explains :

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For more information:

Moebius-strip_RELEASED_CORRECTION.pdf

FAIRE-UN-RUBAN-DE-M%D6BIUS-fr.pdf

Moebius-TheBraider-p356-367-EN.pdf

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