Sunday, August 6, 2017

Cutting cubes

First off, I recently attended the Convention for Creators in Lyon, France and it was a bit of a surreal experience. I had looked at the guest list in advance and was surprised to only see a few names I didn't recognize. As Daniel Chang put it, "At most conventions, you want to meet with two or three particular folders. At this convention, you want to see everyone." Afterwards, I was fortunate enough to travel with Robert Lang, Dave Brill, Beth Johnson, Shuki Kato, Gen Hagiwara, Ondřej Cibulka and Alex Szarry-Gomez to Nicolas Terry's home and visit his shop, and I visited the Escuela Museo Origami Zaragoza in Zaragoza and the OAS (Origami Always Succeed) group in Barcelona.

Among the many ideas I had during the convention, one was to create an Instagram account: @rymacorigami.

In my last post I mentioned that I had been thinking about folding simple but interesting geometric shapes. I guess that I still had the k-dron in mind, because I decided to try making another cube bisection. I realized that bisecting a cube to two equal pieces has to involve the central point inside the cube and some symmetry about that point. Based on this, a simple way to get the pieces involved was to draw lines from the central point out to the corners of the cube. Alternating between connecting to an upper corner or a lower corner gave a simple saddle point geometry which wasn't hard to find the references for because of the √2:√3/2:√3/2 triangles.

The lock on the bottom of the model took a bit of playing around with. At first I wanted to use half of the cube width, but it ended up too weak. Eventually, Roman Remme (also in Lyon) came up with a simple symmetric lock as shown in the CP.

Pointed saddle cube bisection

Pointed saddle cube bisection

But that's not all! On my flight back home, I realized that there was another way to make a saddle point in a cube. Instead of having edges directly to the centre of the cube, I could have a flat square in the centre with equilateral triangles connecting to the corners. Here is the resulting CP:

The references are 15 degrees from the corners, which can be folded quite easily as mentioned in my last post. The lock for the bottom of the cube was the same as before. From the side, the result reminds me of the 元宝 (yuanbao), an old form of Chinese currency.

Flat saddle cube bisection

Flat saddle cube bisection

Because both models were based off the same geometric shape, I decided to call the first a pointed saddle cube bisection and the second a flat saddle cube bisection. The best part of these models is being able to take the two pieces apart and fit them together. Here is a video from my Instagram page:

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