Take a set with six elements and consider all possible matchings (partitions into 2-element sets). A little thought or counting should convince you there are exactly 15 matchings. Now, we can define a peculiar incidence geometry on those set: the “points” of the geometry are these 15 matchings, and two “points” are on the same “line” precisely when they have a 2-element set in common. When you try to draw this geometry, you may end up with the symmetric configuration above, which exhibits various nice features.

The result is sometimes known as the Cremona–Richmond configuration but is more commonly referred to as the doily. In this geometry, every point is incident with three lines and vice versa (the configuration is self-dual). Moreover, the doily is triangle-free, making it the smallest non-trivial example of a generalized quadrangle.

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Bridges Tessellation designed by Hannah Horng | Crease Pattern 

I ended up playing around with the tessellation that I designed and came up with a lot of variations, my favorite of which is the Whipped Cream based on Meenakshi Mukerji’s Whipped Cream Star. I folded it with Elephant Hide just to see what it felt like and it was amazing. You can try and figure out the variations, or just play around with the base as much as you like!

The length of the bridges is entirely up to you, so enjoy!

05-23-2013

Inner Storm

The idea that the human body and mind is in some sense a temporal reflection is beautiful, perplexing and terrifying to me.

It’s disappointing how poorly we parse these reflections. To some extent we can forgive ourselves—the reflection itself is a hopelessly incomplete representation.

Even so, I can’t help but wonder if we are getting better, or if we will.

imglib

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Fibonacci Sculptures - Part II

These are 3-D printed sculptures designed to animate when spun under a strobe light. The placement of the appendages is determined by the same method nature uses in pinecones and sunflowers. The rotation speed is synchronized to the strobe so that one flash occurs every time the sculpture turns 137.5º—the golden angle. If you count the number of spirals on any of these sculptures you will find that they are always Fibonacci numbers.

© John Edmark