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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.