An orderly tangle

A paper version, I haven't made this yet, just cut the pieces.

Hi

After a few weeks of trying, I have managed to make my first "orderly tangle" or "regular polylink" which is a type of link (lots of loops tangled up) made by rotating and interlinking regular polygon shaped loops on the face of a solid. These shapes are described in a book by Alan Holden called (unsurprisingly) Orderly Tangles.  I have written and submitted an article on twin edge polyhedral links and knots (see my last post ) , and during the review process, Holden's work was recommended to me. After resubmitting the article and also seeing online examples, I decided to have a go myself. There are articles by George Hart describing paper and other tangles here and here , but the one I made was based on Alan Holden's work. From here I might be able to work out the maths of the things and could go on to make them from other materials (beer cans being seem to me the most obvious).

Anyway my steps were - 

* Get a copy of Orderly Tangles, I needed to do this for my article anyway.

* Work out what I wanted to make. (This was an easy choice, I had made topologically similar cubes before)  

* Look up the dimensions needed and stick to the proportions - I used 1/4" = 10mm as a scale.

* Replicate the squares Holden used in a 2-part 3d print - 2 identical C shapes plug into each other.

* Attempt assembly without jig (really hard, I mucked around and made "other stuff" with the 12 pieces instead.

* Go back to the original photo and work out the proportions of a jig - it could be based on a 16mm square rod about 100mm long.

* Design and print a cross-shaped jig that could come apart from inside the polylink

*  Strap 2 squares to the jig with rubber bands, and keep putting more squares on as per the photo. To assemble the last square in I had to crop the pin on each side by about 5mm, the fit was too tight otherwise.

* Disassemble the jig et voila!

Regards Steve Nurse

For 3d print files see https://www.thingiverse.com/thing:7366096