Date: Wed, 20 Dec 95 08:44:16 -0400
From: Jerry Bryan <jbryan@pstcc.cc.tn.us >
~~~ Subject: Re: Physical Cubes and Models Thereof
```On Wed, 20 Dec 1995, der Mouse wrote:
```

The only facelet for which invisible orientation changes are even
possible is the center facelet on an odd-order cube. Other facelets
always have a fixed orientation with respect to the center of the face
they're on at the moment. (On the 4x4x4, for example, if you mark
every facelet for orientation, you will find that each center facelets
always has the same corner to the face center, regardless of which face
it's on.)

I believe Der Mouse is entirely correct for the physical cube case (which
is the case I was talking about). Imagine a 99x99x99 or some such large
cube, and for each facelet except the face center itself mark the corner
closest to the face center. Any slab quarter-turn preserves the fact that
all marked corners remain closest to the face center. There are two cases
-- a face slab, and any inner slab. But both cases work. In the case of
a face slab, the orientations of the facelets on the face of the slab do
change, but the orientations change in lock step with the positions of
the facelets.

In the case of a mathematical model, Evisceration also preserves facelet
orientation, if I understand correctly how first Singmaster and then Dan
Hoey defined Evisceration. However, Inflection and Exflection do not
preserve facelet orientation. Could (or should) the definitions of
Inflection and Exflection be broadened to include and preserve facelet
orientation?

``` = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)                jbryan@pstcc.cc.tn.us
```