Origami: A nontrivial knot

Origami in the form of a trefoil knot

Knotted Toroid, designed by me.  Based on Thoki Yenn’s Umulius.

Although this blog has a standing ban on nontrivial knots, this piece of origami defies the ban because it knows it can get away with it.

I have two comments on this model.  First, I’ll explain how the choice of paper presents a philosophical problem.  Second, I’ll talk a bit about the inspiration for the model.

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Origami: Square Star and other tesselations


Square Star, by Ekaterina Lukasheva.  The squares are on the side, not visible in this photo.  Ekaterina has her own fancier photos here.

The past month has been astonishingly productive, in terms of origami.  I discovered that there was a nearby origami convention so of course I had to go.  Most people were doing one-piece origami, so of course I ended up trying a lot of one-piece origami myself.

I was, however, pleased to see some modular origami representation, and in particular there was Ekaterina Lukasheva, of Kusudame.me.  She gave a presentation on the connection between modular origami and origami tessellations.  And afterwards, as a demonstration of principle, she showed people how to make the Square Star, shown above.

I think perhaps few people understood her talk, but as someone who is interested in the design of both modular origami and origami tessellations, I for one found it inspiring.  Further discussion and origami below the fold.

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Origami: Hydrangea cube


A cube made from six copies of Shuzo Fujimoto’s Hydrangea

The instructions for the Hydrangea are freely available online in diagram or video form.  It’s not too difficult, except for one step (8:32 in video, #23 in diagrams) that involves inverting a pyramid, which is the source of all the wrinkles in above photo.  In theory, you can recursively add smaller and smaller petals ad infinitum, but for some reason I chose not to.  These flowers only go 3 levels deep, which is quite shallow but people seem to be impressed by it anyways.

This model was inspired by Origami Inspirations, by Meenakshi Mukerji.  She included a single photo of a cube made of Hydrangeas, and it was fairly easy to reverse engineer.

Origami: WXYZ Impostor

WXYZ IMpostor
WXYZ Impostor. The design is mine, but I include WXYZ units, designed by Tung Ken Lam.

Once a year, I run a little class to teach origami to kids. This year, one of the projects was to create the famous WXYZ model, which consists of four intersecting triangles (labeled W, X, Y, and Z). So I had been thinking about this model, and thought, I could design a variation on the theme. The result is shown above.

Once I had completed it, I realized I could not show this to the kids! It would just confuse them! The WXYZ Impostor looks like the model they were trying to create, but is slightly different in a way that is difficult to place. Check out the comparison below.
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Origami: Octopus

An octopus made of paper

Octopus, by Sipho Mabona.  It’s about 2 inches in diameter.

This model is a foray into “one-piece” origami.  Or at least, I like to think of it that way because I usually use multiple pieces of paper.  More specifically, this is the kind of advanced origami where they no longer give you instructions.  Instead, they simply show a square with all the folds (a “crease pattern”).  Check out the image below the cut.

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Origami: Bellflowers Ball

IMG_0872 (small)Bellflowers Ball, by Yuri Shumukov

As a gift, I got this new origami book called Origami Kusudama Garden: Delightful Paper Spheres.  But when I looked inside, I was dismayed.  This isn’t modular origami!  The flowers are all glued together, or sewn together.  Call me a traditionalist, but I prefer my origami to just have folding.

Of course, it turns out I was wrong.  Using sewing to make floral balls is in fact an old tradition, and modular origami is the modern innovation.  Well, okay, it’s worth a try, I thought.  I was also briefly tickled by the idea of assembling a dodecahedron using squares.

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Origami: Snub Cube

IMG_0679 (small)
Snub Cube with Windows, from Unit Origami: Multidimensional Transformations by Tomoko Fuse.

The snub cube is one of those fancy Archimedean solids, for when you’re bored with the Platonic solids.  Each vertex lies at the intersection of one square and four triangles.  All together, there are 24 vertices, 60 edges, 32 triangular faces, and 6 square faces.  And can you imagine, it’s only made of 12 sheets of paper? [Read more…]