Today, I present a set of octagonal boxes, designed by Tomoko Fuse.  Rather than providing a design with exact specifications, Tomoko Fuse tends to present several possible variations.  This design has cosmetic variations, which create different patterns of color; and structural variations, allowing you to create wide and short boxes, or narrow and tall boxes.  These boxes don’t have covers, but the idea is that you could make two boxes of slightly different width, and use the wider one as a cover for the narrower one.  I created a set of four of slightly different dimensions, so they could be nested (image below the fold).

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Today’s origami design is a relatively simple one, but I love simple stuff like this!  You just pleat a square back and forth diagonally across the paper, and then pinch it in the middle.

For this model, I used paper with diagonal stripes, so that the stripes approximately align with the folds.  This creates an iridescent effect, as the colors subtly change depending on your viewing angle.  Now, the stripes don’t align exactly with the folds, so there’s a bit of a subtle interference pattern as well.  I love the idea of making these subtle interactions between the paper patterns and the origami design, but I think it rarely aesthetically succeeds.  This is my favorite example.

I haven’t been posting much origami lately, because I haven’t been making any.  But I still have quite a number of models in my back catalog.  This is the Three Axis Woven Design, designed by David Huffman, later reconstructed and named by Erik Demaine.

This piece was painstakingly constructed as a gift for my grand aunt, who recently died.  She was an actress who played Asian characters circa the 1950s, and was a great appreciator of the arts.  She lived a full life.

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I haven’t really felt motivated to do origami since March.  But then I played Paper Mario: Origami King.  The game itself is whatever, but the art is great.  I love the premise of having origami be the villain of the story.  In a world where all the characters are made of paper, origami plays the role of zombie menace.

There’s a pretty wide range of origami, from traditional forms to stuff that’s only possible in fiction.  On the fantastical end are the Vellumentals (video contains spoilers).  On the realistic end is the origami castle, made of Sonobe units.  And then there are these two main characters:

These characters look nearly like real origami, but they’re not quite.  Or at least, it’s not possible to make them as simply as it is portrayed in the game.  I enjoy reverse-engineering origami, so I thought I’d give this one a shot.

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The Lens Tessellation is an example of curved-crease origami.  A relatively simple example of curved creases–so simple that a paper explaining the basic mathematics of curved creasing uses this model as a case study.  To make this model, I used a ruler and compass to draw out lines, a hand-cut stencil to copy patterns, and a ceramic stylus as a scoring tool.  I walked through some curved crease methods here.

Something I learned from the math paper, is that this crease pattern has multiple conformations.  If you poke and jab at the paper in the right spots, you can switch its conformation.  I have a photo below, where the left side is in one conformation, and the right side is in another conformation.  You can see the difference in the pattern of shadows on each side.  On the left side, the ripples of paper are horizontal, while on the right side, the ripples are oriented diagonally.

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This is a variant on the so-called waterbomb tessellation (a photo of which you can find somewhere in my blog archives).

A neat thing about the waterbomb tessellation is that it naturally curves into a sphere-like shape.  The tensions in the paper cause the tessellation to have an overall positive Gauss curvature,* like the surface of a sphere.  So I was thinking about how cool it would be to patch together multiple waterbomb tessellations, some concave up, and some concave down.  This here is the result.

*My understanding of differential geometry tells me that what determines the shape is mean curvature rather than Gauss curvature, but if you don’t know what that is then never you mind. ETA: On second thought I’m not sure this makes a lick of sense.

This is one of those origami models that other people seem to like much more than I do.  I think it’s over-designed.

I thought I’d have it recursively branch multiple levels, and at each level one of the branches would have a “mutation”.  You can see the pinwheel design on the upper right branch, the pink cube on the left branch. All this on top of the blue/orange/red/green color scheme.  I didn’t branch very many times because it didn’t seem structurally sound enough, and also I wasn’t too fond of it.  But still, some people like it.  If you like it, maybe you can tell me why.

My guess is that people like it for its intricate design.  I think it uses… *counts to self* …60 pieces of paper, each one 3.75 cm.  The whole model fits in my palm.  Each sheet is folded into a Sonobe unit, which is just very standard and flexible origami unit.  If I were to try it again, I would keep it intricate but reduce the design entropy.