Origami: Six intersecting pentagonal prisms

Six intersecting pentagonal prisms

Six intersecting pentagonal prisms, designed by me.

I might be less active this month, so I thought I’d make up for it with an origami model you can dig into.  This model is called “Six Intersecting Pentagonal Prisms” because it’s literally made from six pentagonal prisms.  I’ve got some photos below the fold showing the step by step addition of each pentagonal prism.

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On color theory

This is a repost of an article I published on Tumblr in 2017.  As many things I publish there, it was written somewhat extemporaneously, but it stood out as something I wanted to eventually import here.

There are really two color theories, the scientific theory of color perception, and the aesthetic theory of choosing color palettes.

The former is quite interesting, containing some surprising facts: yellow is the brightest color, many shades of green can’t be produced by modern displays, white is defined arbitrarily.

The latter is a hodgepodge of various historical ideas and a collection of overgeneralized advice. When I’ve read about aesthetic color theory online my impression is that much of it is either already taught to children or else it is not very good. Here is my attempt to identify some non-bullshit principles of color theory.

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Origami: Skarmory

Skarmory, designed by Shintaro Miyamoto

I dabble in many kinds of origami, especially in the context of interacting with origami groups.  I created this model, because someone at the origami group was really excited about making Pokemon, and asked if anyone could help him with this one.  It was difficult because we didn’t know the folding steps, we only had a crease pattern.

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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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