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Hello, I am Peter Jung, a physicist from Cologne University.

Only a couple of days ago I got very much interested in the Cube. At wikipedia I found a note that the diameter of the Cube group is not yet known, and a link to this site.

Great work!

Sniffing into the problem, it seems to be quite complex. But some ideas that came to me these days I could not find. That's the purpose of this visit: To ask whether attempts have been made along these lines of thought, and if so, what is the outcome. And if not, I would like to contribute some analysis.

Some ideas for how to possibly proove that the diameter of the Cube-Group would be X.

Hi, I am new to the Cube problem, so probably the ideas are not new, or too naive, but I could not find them anywhere. This is possibly due to my lack of knowledge of terminology. (My background is theoretical solid states physics.)

Thus I would like to share these ideas with you, which you hopefully find useful, or can tell me that these ideas are not new or possibly that they are useless. I kindly ask you to comment. I just go ahead...

How could one calculate the diameter of the Group?

Let A be a random permutation. I start by choosing a (not optimal) path from id to A, say in quarter turn metric, with A=prod_i(ai) (i=1,...,N) where ai in {U,U',D,...}.