Message #57

From: rbreiten <rbreiten@yahoo.com>
Subject: Re: Orientations of the centre cubes
Date: Tue, 25 Nov 2003 22:04:29 -0000

— In 4D_Cubing@yahoogroups.com, "rbreiten" <rbreiten@y…> wrote:

> There is still a bug in my sequence for rotating two adjacent faces
> of the internal cube a quarter turn each (wrote it down late late
> last night). I’ll work it out tonight and post it tomorrow.

Gah, I just forgot to write down a d2.

Here is a sequence which shows that our group G contains all even
permutations of the internal cube’s corners. I argued before that G
is a subgroup of this group, so it is in fact this group.

U.r2l2.D.rl’u2d2rl’f2rl’u2d2rl’b2.D’.r2.D2.fbrf’b’r2fbrf’b’r2.D2.l2
R.u2d2.L.rl’u2d2rl’f2rl’u2d2rl’b2.L’.u2.L2.fbuf’b’u2fbuf’b’u2.L2.d2

f2.D2.l u .r’b2r2br’b’r’b2luru’l’.u’l’.D.b’l2b2lb’l’b’l2fubu’f’.D
L2.d’r’.r’b2r2br’b’r’b2luru’l’.r d .L.l’u2l2ul’u’l’u2rblb’r’.L.f2

I used one U and one R for the "real" turns, and D and L in multiples
of 4 to restore stuff. I fixed up the 1-color cubies from the U
before doing R to make it a bit less tedious.

The first two longish subsequences are my other 3^3 supergroup
buddies that go along with the first longish subsequence in
yesterday’s U2 sequence. The last two lines are conjugated pair
flips to restore the edges as before.

Thanks for an interesting problem!