Discussions on the mathematics of the cube

A question about the commutator subgroup

We all know that commutators can be used to generate half of the Cube group G. My first question is: Can all elements of the commutator subgroup themselves be written as commutators? i.e., the problem is to determine whether the set of commutators is closed under multiplication; it need not be in general, but is it true here?

If it is closed in this case, then a natural question to ask is How do we write a given element of the commutator subgroup as a single commutator?

On the other hand, if the set of commutators is NOT closed under multiplication, then how many elements of G can be written in commutator form?

Two directional serch for cube solutions...



I was wondering if anyone has ever build a bi-directional tree search for solving specific cube positions.
Let me explain.

Suppose one starts with a solved cube (3x3x3) and find all the configurations after one rotation, and so on say until 10 or 11 rotations. The resulting tree will contain a large number of nodes, but not completely unreasonable.

Now suppose you wish to find the shortest solution for a specific configuration. You may start building another tree similar to the above and look for collisions between nodes of the two trees. After exploring say 10 or 11 levels of the tree it is very likely that the two trees will connect and the shortest path can be obtained.

Back from the dead

Service is back up, fixed ip address is 216.138.229.145, enjoy :)

Server will be down for a short time

I'm changing to a better ISP with a fixed IP address. The current service will go down sometime on July 5th, 2004 and should be back up by the 6th.

www.olympicube.com need cube lovers opinion on which cube to produce first

olympic cube 6a
83% (19 votes)
olympic cube 6b
17% (4 votes)
Total votes: 23

www.olympicube.com


www.olympicube.com


new cube family are ready to born

My responses to questions posted on various news groups

Google canned search" Many on the links from earlier posts are no longer active.

Cube Lovers Archives Found

Thanks to the diligence of Josef Jelinek I'm pleased to announce that the original cube-lovers files have been found. They are available by anonymous ftp at cubezzz.duckdns.org or by clicking on the link to left.

Cube-lovers, a rebirth (Hopefully)

Hi folks,

I'm sure many of you can remember the old cube-lovers mailing list. It started in 1980 and lasted until Feb 2000. Cube-lovers was the "creme deLa creme" of all cube discussions, with topics ranging from hypercubing to God's Algorithm calculations there was never anything else quite like it.

Cube-lovers seemed to breathe it's last in Feb of 2000, but cube discussions continue on the internet. Many Rubik's Cube sites have appeared on the internet but the discussions and topics were fragmented and nowadays the discussions are dominated by speed cubing. Interesting to be sure, but not quite the same as the ol' cube-lovers list.

Exhaustive Search of the Cube will happen

Within 3 years
7% (1 vote)
Within 5 years
7% (1 vote)
Within 10 years
7% (1 vote)
Within 25 years
29% (4 votes)
More than 25 years
43% (6 votes)
Never
7% (1 vote)
Total votes: 14