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.

Origami: Lilia

The Sparaxis, a spiky ball that fits in my hand

Lilia, by Ekaterina Lukasheva. I’m not sure I got the name right, but I’m absolutely sure about the author.

In the past year I’ve been dabbling a lot into other kinds of origami, such as traditional origami, tessellations, and minimalist designs.  But still, it’s good to make some modular origami models.  This is a kusudama model of very standard design.  30 units, 5 colors arranged symmetrically.  Although, I actually made 2 of the 5 colors identical, which is a cheeky way of making it slightly asymmetrical.  This was made as a gift for a relative.

Origami: Curvature experiments

Pizza wedge model sitting on top of a copy of "Folding Techniques for Designers: From Sheet to Form" by Paul Jackson

Pizza Wedge, a design/experiment by me

I acquired a copy of Folding Techniques for Designers: From Sheet to Form, by Paul Jackson.  It has a rather unusual, but refreshing perspective.  Basically, it tries to avoid the origami tradition entirely, and instead focuses on folding as an element of design.  Several chapters are occupied by simple ideas about pleating paper.  The reader is encouraged to experiment, and this is just one basic experiment.

The Pizza Wedge is not technically challenging to create, but its simple and abstract nature leads one to contemplate the little details.  One emergent property of the paper is the negative curvature (i.e. the saddle shape).  When you crease a paper back and forth, on the macro scale the paper compresses in one direction.  When I added the “crust” of the pizza, that suppressed the creases, which has the effect of stretching the paper on one side.  The stretching and compressing leads to negative curvature.

I include a second experiment below the fold.

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Tessellation symmetry

This is (the last) part of my series about symmetry in origami.

A tessellation is a set of tiles that fill up a 2D plane. And I do mean the entire 2D plane, infinite in extent. When we talk about origami tessellations, these are models that could hypothetically fill a 2D plane, if we had an infinite amount of paper. In practice, an origami tessellation is finite, but for the purposes of discussing symmetry, we will imagine them to be infinite.

example origami tessellation

An example of an origami tessellation, the Rectangular Woven Design by David Huffman

Previously, I only discussed two kinds of symmetry transformations: rotation, and reflection. However, many tessellations have repeating patterns, and this in itself is another form of symmetry. Are there other kinds of symmetries that we forgot? Let’s take an inventory of all the possible kinds of symmetry transformations.

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