After making some of Palmer's twists I got excited about them and experimented for a while. The following pieces were all independently developed by me, although no doubt they are not original. All of them were made from 20cm coloured paper (including the diagrams!).
I started with the basics: the square twist, which I first met in Kawasaki's "Rose". A single twist (front and back).
A 2x2 square twist, front and back.
Extrapolation after that (major tesselations) seemed quite easy, and Kawasaki's "Rose Crystallisation" is a version of that so I went onto something else...
Equilateral triangle twists. It took me a while to work this out. But I finally managed to produce a single twist.
I also did a diagonal version of which you can see the top and the bottom.
The additional creases you can see on the above pictures show where I was experimenting trying to produce a tesselation. I worked out that, like the square tesselation, a tight tesselation was possible. I folded a 3-by-2 tesselation.
Then I drew some (bad) diagrams.
And then I folded a 7-by-4 tesselation.
After mastering triangle twists, I moved on to hexagon twists (since hexagons are made up of equilateral triangles). Firstly I produced a single closed hexagon twist, with a diagram following (the outside lines indicate the coverage of the twist).
After working some time on a tight hexagon tesselation (diagram following)...
... I decided that it simply wasn't possible. You just couldn't get all the crease lines to line up, even if you turned some twists upside down. So I went for an alternative method: make a square (or rectangular) tesselation with a hexagon twist in the middle. I ended up with this (note that this is actually the same piece of paper I used in the plain twist pictures):
I then diagrammed this rectangular hexagon-twist tesselation (2-by-2).
I then made a 3-by-3 hexagon-twist tesselation.
More recently (late 1999-2000), I've been working on an open-backed hexagon-twist tesselation, but haven't completed the main piece. I've also produced a cool-looking stacked square-twist but haven't scanned it in yet.
| /lib: Bill Clarke ( llib@computer.org) |
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| Last modified: Wed Jan 19 15:12:33 EST 2000 |
