The internet (in this case Instagram) sometimes delivers to you by pure chance (or deliberate algorithm) inspiration that is timely:

A recent work (a square-tube based mobius strip) by Henk van der Vorst sparked a curiosity that led me to damaging a few A0 sheets of Kraft paper to explore a tubiform corrugation, and then work out something to do with it.

There is something interesting (for me, recently) in corrugations, and Henk’s work uses simple right-angle hinges, first documented by Paul Jackson, to use a large-scale fanfold without the tiresome necessity of reversing sections of the crease, and allowing you to curve that fanfold onto itself in an interesting way.

I discovered I could hinge on proportions of 6 and 3, making rectangular tubes that articulate and bend in very interesting (the kids would call it “satisfying”) ways.

I fashioned a bunch of different sizes to test the proportions and see just how small I could fold it reliably and accurately. On the large test folds I glued the seam – not sure why, but as I got smaller, the seam just seemed to keep itself shut and become invisible – especially when the tube was twisted.

A Trefoil knot is historically interesting – it is like a set of interwoven mobius strips, and originally was associated with the “Holy Trinity” : the Father, the Son, and the holy GOAT, or something similar. Renditions of it exist in historic engravings, statuary, heraldic depictions – even common images like the Girl Guide logo/symbol … thing.

I cut a 9cm x 1.5m strip of Kraft paper, divided it longitudinally with creases spaced at 3cm, 1.5cm, 3cm, 1.5cm to form the rectangular tube, and then began dividing the strip on the short distance smaller and smaller until I could reasonably go no smaller – the divisions ended up being about 5mm. Allocating these divisions alternately mountain and valley to make a really WIDE fanfold.

I pre-creased the hinges using the long lines as a guide, and then, carefully and as accurately as I could while watching Eurovision replay broadcasts, I collapsed one hinge at a time. As the tube closed in on itself, each subsequent hinge becomes harder to collapse accurately – at this scale I found I was adjusting it with tweezers to ensure the corners were as close to 90 degrees as possible.

The resultant tube was deliciously flexible and it seemed to want to tie itself in knots – so I complied and decided a trefoil was just possible with this length tube. To join the ends I inserted the pleats of one end inside the other – this locked the structure by paper tension and pretty soon after that I lost where th join was because the “seam” lay in the valley rather conveniently.

This was a lot of fun, but really punishing on my hands – I have made sooo many typing mistakes in this post (subsequently fixed mostly) because my hands are stiff and joints swollen. The continued cold damp weather is not helping, but you get that sometimes (well, I do).