Cutting cubes

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 came up with a simple symmetric lock as shown in the CP.



But that's not all! 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.



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.