Origami: Truncated octahedron

truncated octahedron

Truncated Octahedron, designed by me.  I kept this on my office desk.

Today’s model is one of my earliest original designs.   This is a truncated octahedron, which is the shape you get when you take an octahedron, and chop off the 6 tips.

I was interested in designing a model with this particular shape, because it has some special significance in condensed matter physics.  There’s a certain kind of crystal structure, called the “body-centered cubic structure”, which looks like this:

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Origami: Double-pointed VWXYZ Squares

VWXYZ variation

Double-pointed VWXYZ squares, a design by me

Ah, so here’s a really old original design that I made in 2013.  The story goes that I have a copy of Meenakshi Mukerji’s Ornamental Origami, which has a chapter on planar models.  These are models where the folded form consists of multiple intersecting planes.  One of my favorite models of all time is Tung Ken Lam’s WXYZ Triangles, which consists of four intersecting triangles.  Later origamists would take this idea even further.  What if you had 5 intersecting planes, or 6 intersecting planes, or more?  So I made a bunch of planar models with different numbers of planes.

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Origami: Life inside

Life Inside, designed by Ekaterina Lukasheva

Ah, here’s a lovely origami model that I have not yet shared.  Not much to say about this one.  It’s a 30-unit model with icosahedral symmetry.  I used 3 distinct colors, and the petals are curled with a toothpick.

Origami: Spiral creases

A square sheet of silver foil paper, with 4 spiral creases radiating from the center

Four 45 degree spiral creases

This is going to be one of those origami posts where I talk way too much about math.  But before I get to the math, I will explain how you can make one of these things entirely with ordinary arts and craft tools.

“Ordinary tools” is the relevant bit here, since my understanding is that experts in curved-crease origami don’t use ordinary tools, they use things like vinyl cutters.  When I first tried making these, I could not find any instructions for how to make these models using ordinary tools (I later found an article by Ekaterina Lukasheva), so when I finally figured out a method, I wanted to share it.

Making a template

Before we draw the creases directly on the paper, we need to make a template.  The template ensures that each of the four curves are identical to each other.

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Origami: Star with spirals

star with spirals

Star with Spirals, designed by Meenakshi Mukerji

Meenakshi Mukerji featured some of my origami on her guest gallery page, including this model.  Then I realized I hadn’t posted this one on my blog yet, so here it is.

Regular readers have probably noticed that I feature an awful lot of models designed by Meenakshi Mukerji.  That’s because I have four of her books!  The Star with Spirals is featured on the cover of Origami Inspirations, which I would say is the best of the four.  Although, if you’re reluctant to commit, you might consider one of the Exquisite Origami books, which are cheaper because they’re in grayscale.

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Origami: Three-form

A model consisting of many little cubes attached together

Three-Form, a model designed by me.  Some of the component cubes are taken directly from Meenakshi Mukerji.

I was looking through my photos, and I realized that there are several large models that I never got around to sharing.  This is one of them.  The Three-Form consists of 24 little cubes, assembled into a larger mathematical design.

This one is inspired by General Relativity, Einstein’s theory of gravity.  At the time I was reading Sean Carroll’s textbook on the subject, and I was lamenting how difficult it was to visualize the mathematical concepts therein.

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Origami: Arrow Illusion, v2

Announcement: I now have a flickr account for my origami photos!  Now the images are bigger, and you can find them all in one place.  There are also lots of photos that I haven’t (yet) posted on my blogs.

Image is of two origami arrows in front of a mirror. Both arrows point to the right, but in the reflection, one of the arrows points to the left.

Arrow Illusion, version 2. An original design.  My hand is in the photo to show that this is a real mirror.

Over a year ago, I designed an origami arrow that points in the opposite direction when looked at in a mirror.  I wanted to revisit the design, and make it easier to fold, because this is basically the most popular origami thing I have ever done.  Below, I show detailed diagrams, and a sneak peek behind the curtain. [Read more…]