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…]

Origami: Toroidal Cube


Toroidal cube

Toroidal Cube, a design by me

In case it’s not clear what’s going on in the photo, the model is in the shape of a cube, and we are looking at it directly onto one of the vertices.  However, the vertex has been cut out, and there is a triangular hole in its place.  There is also a triangular hole on the opposite end, so that you can see directly through the cube.  The triangles aren’t really triangles, but they look triangular from just the right perspective.

Today’s model was inspired by the regular toroid.  You may have heard of a torus, which is the shape of a donut, or a mug.  A toroidal polyhedron (aka a toroid) is a polyhedron which is also a torus.  A regular toroid is a toroidal polyhedron where each face has the same number of sides, and each vertex connects the same number of edges.

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Origami: Cube Plus Alpha

Cube plus alpha

Tomoko Fuse’s Simple Sonobe 12-unit Assembly Plus Alpha, from Unit Origami: Multidimensional Transformations

Fuse has a series of models that consist of basic polyhedra, with extra pieces of paper attached as embellishments.  This model is a cube (made of 12 pieces of paper) with a pyramid added to each face, and 3 spikes to each vertex.  All in all, that’s 42 pieces of paper.  This is a pretty neat idea.  Since it is made of three distinct types of units, it defies the usual convention of making modular origami from many identical units.

This one’s a fairly old model, apparently made in 2013.  I gave it away as a gift so I don’t know if it’s still living, or deceased.