One thing I recently realized about the cube. In a simulation, or in reality, the configuration of the cube can be completely described by the orientation of the 20 movable pieces. The location of a piece is actually determined by it's orientation.
For example, if you wanted to make a 3d model you might make a bunch of little cubes each centered in their own object space and then translate them to their location in the cube. If you do that, you have to track the orientation AND location of each piece. However, if you center the entire cube at the origin and then place each piece in its place relative to that origin, all "moves" simply rotate a piece around some axis which both changes their orientation AND moves them relative to the cube center. As such, position is redundant information.
I'm not sure how relevant this is, but to me it seems to point to alternative ways of finding a solution via computer.
But this is probably very old news to people who study the cube.
For example, if you wanted to make a 3d model you might make a bunch of little cubes each centered in their own object space and then translate them to their location in the cube. If you do that, you have to track the orientation AND location of each piece. However, if you center the entire cube at the origin and then place each piece in its place relative to that origin, all "moves" simply rotate a piece around some axis which both changes their orientation AND moves them relative to the cube center. As such, position is redundant information.
I'm not sure how relevant this is, but to me it seems to point to alternative ways of finding a solution via computer.
But this is probably very old news to people who study the cube.