Archives

I have received permission to post Dan Hoey's taxonomy of symmetry groups of Rubik's Cube.  Also, I will relate Dan's taxonomy to Shoenflies symbols as implemented in Herbert Kociemba's Cube Explorer.  (Go to http://kociemba.org/cube.htm and then click on Symmetric Patterns.)  To that end, some preparatory comments are in order.

In order to define any terminology for the symmetry groups of Rubik's Cube, it's necessary first to define some terminology for the symmetries of the cube.  To the best of my knowledge, no standard terminology has been adopted by the Rubik's cube community for the symmetries of the cube.  The terminology I'm going to use is very similar to some terminology I have seen before, but I can't remember the reference.  It may have been Christoph Bandelow's book, Inside Rubik's Cube and Beyond.  In any case, if I can find the reference I want to give proper credit.