Prince Rupert's Cube visualization

thingiverse

Prince Rupert's Cube is a mathematical problem from centuries past that claims a cube with sides of length 1 can allow a slightly larger cube to pass through its enclosed space. Additional information on this topic can be found at these links: https://wiki2.org/en/Prince_Rupert%27s_cube+Newton and https://geekhaus.com/math103_fall2017/2017/10/05/open-project-prince-ruperts-cube/. The optimal solution to the Prince Rupert's Cube problem is a cube with sides of length 1.0606601, which is the largest cube that can pass through a cube with sides of length 1 at an angle of 22.5 degrees, or 1/16th of a full circle. My visualization of the Prince Rupert's Cube deviates from the optimal solution due to the need for small amounts of plastic to hold the outer part together in one piece. Other visualizations have employed loops of plastic to secure the pieces, such as the model linked above, but this approach uses an intersection angle of 45 degrees and a cube with sides of length 1.03, which is not the optimal solution. In contrast, my version utilizes an angle of 23 degrees and requires a cube with sides of length 0.99 to facilitate a working, three-dimensional printable real-world model. This model consists of three components: the outer and inner parts of the cube, which can be assembled to form a complete cube, and the solution, which is the cube that passes through the hole. Printing Notes: These files are designed for printing with sides of length 100mm (4 inches), but the models are only 1mm in size, so you will need to scale them up by 100 times, or 10,000 percent, for successful printing. Scaling by a different amount may result in parts that cannot be assembled and do not function properly. The small size of the models also explains why they appear to have textured surfaces on Thingiverse, but in reality, they are smooth. I've included the OpenSCAD file if you need to modify the models.