One last try!! What I meant was the 12 sided frob built out of
pentagons. And after refering to better and better dictionaries I
discovered this thing is called a pentagonal dodecahedron, and I
meant the faces to be the points of rotation. Perhaps McKeeman
thought I meant the rhombic dodecahedron, and subsequent messages
got me confused and I jumped the gun without thinking very
heavily.

Woods: Could you please send the manipulations for "baseball,"
"snake," and "cube-in-cube" for the benifit of those who do not
have Singmaster. Please use prime notation (R' instead of (lower
case) r) for counterclockwise twists since that seems to be the
notation currently in use in this list.

In general, my opinion is that it would be nice if people would
send along the short algorithms that are known. ZILCH's 50 and 70
qtw algotithms are a little too long, but anything under 36
should probably be sent. I know it may be a spoiler, but (1)
there seem to be several configurations mentioned and perhaps
some people don't have time to find nice fast ways to get there,
(2) it reduces needless duplication of effort, (3) parts of the
algorithm (or the algorithm itself) might serve as a subroutine
for other algorithms under development.

On the concept of the higher order "cubes:"
N dimensions
has a reasonable geometric interpretation (maybe it
doesn't have to have this condition?)
built out of some number of "cubies" of dimension N
Each "cubie" is in turn a "cube," perhaps of a different
order than the larger cube (eg, a 3x3x3 cube
whose cubies are 5x5x5)
Each "cubie" of the "cubie" is a "cube," ad infinitum as
desired
In addition to all this, each faclet is a "cube" of
dimension N-1, ad infinitum (at least until the
dimensions run out!!)

The thing I am doing is trying to PHYSICALLY construct a higher
order (flavor: dimension 3, cubical, order 5, cubies are "atomic"
(ie, not cubes in themselves), faclets are atomic). Personally, I
think half the fun is being able to hold one of the beasties and
mung it by twisting.

ACW: I think it would be instructive to have an short intro to
Group Theory for Cubist. This would benefit newcomers to the
mailing list, and people who hack the cube and want to know some
of the theory behind the cube. (5-10K characters if you can keep
it down to that. If not, send it when machines are generally
lightly loaded.) I vote: plase do.