Message #56

From: rbreiten <rbreiten@yahoo.com>
Subject: Re: [MC4D] Orientations of the centre cubes
Date: Mon, 24 Nov 2003 22:42:22 -0000

— In 4D_Cubing@yahoogroups.com, David Vanderschel <DvdS@A…> wrote:
> So did I. Oddly, Jay had posted the same comment back
> in September:

It seemed so familiar that I checked to make sure I wasn’t replying
to an accidental double post.

Anyway, let u f r d b l refer to clockwise quarter turns of up,
front, right, down, back, and left faces of 4^3 cube as usual, and
let U F R D B L refer to clockwise quarter turns of the layer
adjacent to the face with lowercase name (so uU == dD plus a spatial
reorientation). Let u’ and u2 refer to anticlockwise quarter turn
and half turn of the u face, etc.

To rotate just the up face of the internal cube a half turn, perform

U2.f2r2.U2.rl’du’fb’r2f’bd’ur’lf2.U2.r2.U.r’f2r2fr’f’r’f2ldrd’l’.U2.d’
f2d2fd’f’d’f2uldl’u’.U.f2

The first U2 is our half turn of internal u face along with some
naughty stuff in the shell, and the rest unscrambles all the naughty
stuff without permanently affecting the internal cube.

The first longish subsequence rotates the center four 1-color squares
of the f and r faces a half turn while leaving the rest of the cube
fixed. When conjugated by U2, this restores the 1-color cubies to
their original positions. The only tricky point is that exponent
counting seems to show that f and r faces end up rotated a half turn
total, but the conjugation by U2 kind of distributes these half turns
to the l and b faces in a way that makes everything work out (try it
on paper, or if you can bear to look at it, mark up your 4^3). The
last U2 is really U’U’, and the last two longish subsequences are
edge pair flips (the same one in the bottom face and two in the
middle layer), that when conjugated by U and U’ respectively, restore
the middle edges that were disrupted by the first U2.

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.

I’m testing these at work via

http://www.nrr.co.uk/rubik/cuboid/?planes=444

which has the nice property of taking keyboard input (left my cube at
home). It uses shift for anticlockwise and ctrl for inner layer.
But I do need to get *some* work done today.