I have been investigating different kinds of Rubik's Cube patterns and their symmetry families for the last couple of years and I have discovered a great deal of information that I have seen nowhere else. It was long ago noted that the ways you can twist corners on a Rubik's cube closely paralleled the ways you can construct particles with quarks. So far, nobody has pursued this as far as I can tell. I have found many more ccorrespondences than this and indeed I am acquiring a deep understanding of the often subtle and complicated ways seemingly simple Rubik's patterns relate to each other. My discoveries are best understood by comparing the different families of particles that theoretical ophysicists have come up with or hypothesized may exist. Basically, I identify a symmetrical pattern on the Rubik's cube as being equivalent to a subatomic particle. What kind of particle depends on the symmetry of how the colors are exchanged and the kind of orbit the cube must be in for that pattern. If this seems simple, consider the 6-way checkerboard pattern that everybody knows, you just need 3 half slice moves to make it and it has reflection symmetry on all 3 axes through the centers. I have met few people who know any others than this one. It might surprise you to know that there are 28 other possible checkerboard patterns (counting color permutations) on a given Rubik's cube falling into 5 different symmetry families. The reason's behind this are what I am investigating,

It is best if you use one of the speed type cubes. I use the Rubik's Speed Cube, in fact about 6 different ones so I can study different symmetry versions of the same basic pattern side by side, You should be able to disassemble the cube and reassemble it into a different orbit. It is also nice if you can pry off the center facelets and exchange opposite ones to creeate mirrored patterns. The speed cubes seem to be the ones you can do this with. The Rubik's New Cube is not designed to be disassembled and is not really useful for this purpouse.

I keep finding more and more things about Rubik's cube patterns and I would appreciate it if somebody would be interested in assisting in the work of discovery. I am especially interested in anyone willing to look for the rarer patterns in the Magnetic Monopole andG.U.T. families.

Anyway,

Let me know if you are interested! Math Bear ^,..,^