Bandaged Cube Explorer is a js tool for exploring the configurations of a bandaged 3x3x3 Rubik's cube.
Bandaging is a way of modifying a twisty puzzle to create a new challenge. Here is a nice video about it that also sets up the idea of a graph of bandaged states: https://www.youtube.com/watch?v=7ke6momBndU
When I started this project, I quickly ran into https://github.com/paulnasca/paul_cube_bandaged_graph/ . I'm especially thankful to Paul for the csv he collected.
When I started this project I wanted it to be compatible with the existing naming scheme for bandaged cubes that was used by others - but I had a hard time finding documentation for it. The big idea is that there are 56 bonds that could be present which would bind together two adjacent cubies. We can store those 56 bits of information in a bit-set and then use bitwise operations to quickly check or set the state of the cube. But which bits go with which bonds?
The bottom two images contain the same information but from different perspectives. I found both useful while writing this program.
The second one shows what I call the "pin model". In this model, we imagine shoving a pin through a sticker until it binds one cube to the one below it. This is useful for checking if a face can be turned. A face is turnable when none of the stickers on it have a pin in them.
The lowest image is what I call the "cuts model". In this model, we think of every split between pieces on the cube as being able to be invalidated by a bond. When a bond is present, the corresponding line segments go away. This model was handy for drawing legends showing what a bandaged signature should look like.