Continuing from my recent post, I’m exploring test-folds of geometric distortions to square tubes instead of the cylinders I’ve usually worked with. These two designs are very closely related to some designs I explored about 10 years ago and used in a diagonal shift vase about 5 years ago. These test-folds are actually based on pleats, not twists. The pleats can be trickier to work with because they don’t naturally hold themselves locked in place after you fold them, and they can tend to collapse partway but not all the way. For the first test-fold where the square tubes are aligned, either a pleat or a twist would work and give a very similar result.
The distances between the central convergence point and the tube work out such that the points on each flat face fall on a parabola. That’s less obvious here than for some of my previous examples where I had a 16-sided twist in a square tube.
The second test fold, with the square tubes rotated 45 degrees, only works with pleats. I attempted a version using a twist, and the paper lengths just don’t work – there are certain point pairs than need to be farther apart in 3D space than the length of the paper connecting them, which doesn’t work. But the pleated version works just fine. The rotated version is also fairly unstable because the top and bottom tubes are only really connected at the central convergence point and don’t rest on top of each other anywhere else. So as is, this wouldn’t work well in a vase because the top half would tend to tilt off to one side over time.
I’ll have more explorations that go into newer territory soon.
