I’ve been working recently on designing flat twists where the number of facets of the twist doesn’t match the number of facets of the paper tube. Of course, I also had to extend the math to diagonal shifts. I’ve designed a couple models with non-flat shape change twists, but the flat version opens up some new design possibilities. I’m looking forward to incorporating this into new designs and seeing where it takes me.
I’ve been playing recently with the math of twist-based designs where the twist has more sides than the tube, and recently developed an approach to create a flat twist with a mismatched number of sides. This model is a proof-of-concept of generalizing that math. Here, the model is based on a 12-sided tube, since 3 and 4 are both factors of 12. The sphere in the center is a standard curved-crease pleated form where all 12 facets are identical, similar to many people’s designs. The top face of the cube is very similar to my recent square-octagon flat twist, but generalized to 12 facets instead of 8. The base on the tetrahedron is similar.
I like this piece as a proof of concept because the pure geometric shapes don’t give a lot of room to hide imperfections. This gives me a good foundation to start thinking about how to incorporate these ideas into a series.
Two versions of the crease pattern for my recent test fold with an 8-sided twist in a square tube. The first is the twist version, which is similar to my typical folding style. The top and bottom square tubes are rotated 135 degrees from each other (3/8 of a circle, equivalent to a half twist minus one segment so that all the diagonal pleats go through the exact center of the tube).
Crease pattern: Square to octagon twist
The second is the pleat version, which matches the folded version I posted. The twist and pleat versions both have their own challenges in collapsing the folded form because even an 8-sided twist has 16 layers of paper (or 18 layers if you include the overlap segment) trying to converge at the same point.
Following up on my recent exploration of geometric distortions to square tubes, this test fold takes that exploration in a new direction. In my previous explorations of designs where the twist has more sides than the tube, I always had the issue that to make the paper lengths match up, the twist was never flat. That led to some limitations when trying to design models using those twists – the twist took up a lot of height in the model, and it was harder to make sure the model would be stable long-term and not want to tilt and drift as it aged.
This is the first successful test fold of a new approach to twists with mismatched numbers of sides. The twist is flat because the extra paper along each edge is tucked inside the model. The concept isn’t that much more complicated than what I’ve been doing in other designs, but it took quite a bit of geometry and algebra to get all of the paper lengths correct.
This is obviously only half of the full twist, but a second half could easily be stacked on top of it. Similar to some of my older explorations with the non-flat twists, it should be possible to stack different shapes on top of each other. I’ll have more to come on exploring this new direction further.
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.
Square tube with an octagonal twist – parallel
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.
This test-fold is essentially a recreation of one from 2015, re-learning how I folded the shape. From the original post:
Creating the twist is actually fairly straightforward – I would be surprised if it’s not a re-invention of someone else’s idea. I used the same angle between each box here, but any angle from 0 to 90 degrees would work with very minor changes to the crease pattern. It could also work for shapes with more sides, not just squares. Collapsing the stack of twists is a bit tricky and uses a lot of paper, so I’m not sure I would want to try a stack too much taller than this.
With a few more years of practice, I re-created the same basic design with cubes stacked at 45 degree angles, giving it a nice symmetry. I’m starting to post a series of test folds exploring variations of twists on square tubes and other simple geometric forms instead of the more cylindrical forms I’ve usually folded, so this made a nice, simple entry point to thinking in those directions.
This is the last piece in a mini-series I folded a couple years ago, playing with complementary painted and lacy patterns. The last piece was light and whimsical, but this piece shifts to solidity and structure. The painted surface and the lace pattern are modeled after the texture of tree bark, with irregular cutouts to suggest the crackling of the bark. The overall form of the vase is intentionally more substantial and weighty like a tree trunk, with more lace higher up suggesting more openness as in the upper parts of a tree.
Since I’m caught up now on older pieces, I’ll be posting about newer work soon!
This piece continues my exploration of lacy vases, shifting the visual language to circles. The overlapping circles in the painted design are reminiscent of the circles that bubbles leave behind on a surface and have a more playful feel than a lot of my work. All of the circles, in both the lace and the painted pattern, were hand-drawn free-form, so there are small inconsistencies and imperfections. Similar to the Sunburst lacy vase, the shape of the vase also echoes the round shapes in the painted and lacy textures. The shape is also a play on shapes common in scientific glassware, playing off of my multiple interests in art and science.
I’ll have one more piece in this mini-series to post soon.
This piece is a continuation of my lacy vase series, continuing the theme of creating complementing paint and lace patterns. Unlike the last form based on waves and curves, this piece is based on a sharper, more angular geometry. As the vase widens in the middle, a painted pattern of bright angular brushstrokes emerges from underneath the black lacy panels. The lace cutouts, the painted pattern, and the overall shape of the vase all reflect similar angularity. However, similar to my previous piece, the painted pattern gives a softer version of the same visual language as the lace does.
I’ll be continuing to explore similar themes in my next two posts.
