Prince Rupert's Cube visualization

Prince Rupert's Cube is a mathematical problem from a few centuries ago. It claims that a cube with sides of length 1 can allow a slightly larger cube to pass through the space it encloses. You can find more information in these links:

https://wiki2.org/en/Prince_Rupert%27s_cube+Newton
https://geekhaus.com/math103_fall2017/2017/10/05/open-project-prince-ruperts-cube/

The optimal solution to the Prince Ruper's Cube is another cube with sides of length 1.0606601, which is the largest cube that can pass through a cube with sides of length 1. It passes through at an angle of 22.5 degrees, which is 1/16th of a full circle.

My visualization of Prince Rupert's Cube is not the optimal solution due to the need to have small amounts of plastic still present to hold the outer part together in one piece. Other visualizations have used loops of plastic to hold the pieces together, such as the one linked above, but that solution is not the optimal solution because it uses an intersection