Thank you for your warm opinions about my post.
One day, while making a Turk's head knot, I made a mistake and instead of a ring, I created a perfectly symmetrical Mobius strip.
I was really surprised and interested by this new possibility, let's call it: Turk's head Mobius knot.
I decided to define the rules of making this kind of Turk's head knot ( shape of Mobius strip)
Looking for regularity, I was generating normal Turk's head knots of even number L (Lead) using my own program.
Next, I was cutting them and gluing them together again ( virtually) after turning both ends - angle 180 degrees,
by analogy to a normal way of making paper Mobius strips.
What have I noticed? A one strand knot B5L4S1
http://narval.republika.pl/b5l4s1.jpgcan be changed into a one strand Mobius strip described above ( cutting, turning, gluing)
To my surprise also two strand knots can be changed into a one strand Mobius strip B10L6S2
http://narval.republika.pl/b10l6s2.jpgAs you know, Mobius strip has only one edge.
It is not possible for me to create ( by this method of cutting and turning a normal knot) an odd number of bights on this one edge.
After this introduction, I can ask the right question :
Does a case with an odd number of bights on the edge of Turk's head Mobius knot exist?
WM