## Interdimensional Cubes

Submitted by cubex on Fri, 09/10/2004 - 08:04.As a thought experiment consider the case of the familar 4x4x4 cube with a 2x2x2 cube embedded inside it, instead of the usual mechanism. I'll call this the "Interdimensional 4x4x4 cube" for lack of a better name. Now clearly if we turn the slices of the 4x4x4 cube it would have an effect on the internal 2x2x2 cube. Now moving the slice adjacent to the U face and moving the slice adjacent to the R face this would be the equivalent of turning the internal 2x2x2's U face and R face.

My question is: Is it possible to reach all the positions of the internal 2x2x2 without having any constraints on the 4x4x4 cube? How many positions are there?

My question is: Is it possible to reach all the positions of the internal 2x2x2 without having any constraints on the 4x4x4 cube? How many positions are there?

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## A question about the commutator subgroup

Submitted by Mike G on Thu, 09/02/2004 - 08:43.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?

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?

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## Two directional serch for cube solutions...

Submitted by crepeau on Wed, 07/14/2004 - 09:06.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.

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## Back from the dead

Submitted by cubex on Wed, 07/07/2004 - 13:04.Service is back up, fixed ip address is 216.138.229.145, enjoy :)

## Server will be down for a short time

Submitted by cubex on Thu, 07/01/2004 - 10:55.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

Submitted by greekcubes on Mon, 06/28/2004 - 14:13.olympic cube 6a

83% (19 votes)

olympic cube 6b

17% (4 votes)

Total votes: 23

## www.olympicube.com

Submitted by greekcubes on Mon, 06/28/2004 - 14:07.## My responses to questions posted on various news groups

Submitted by web2k on Sun, 06/27/2004 - 12:59. Google canned search" Many on the links from earlier posts are no longer active.

## Cube Lovers Archives Found

Submitted by cubex on Fri, 06/25/2004 - 04:53.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)

Submitted by cubex on Thu, 06/24/2004 - 10:19.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.

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.

» 5 comments | read more