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On 01/06/95 at 23:51:00 mark.longridge@canrem.com said:

As I understand it, the format Martin uses in GAP is to represent

the 3x3x3 cube by assigning each individual facelet an unique

number like so (by the way, the following part is all from the

GAP documentation).---------------------------------------------------------------------- +--------------+ | 1 2 3 | | 4 top 5 | | 6 7 8 | +--------------+--------------+--------------+--------------+ | 9 10 11 | 17 18 19 | 25 26 27 | 33 34 35 | | 12 left 13 | 20 front 21 | 28 right 29 | 36 rear 37 | | 14 15 16 | 22 23 24 | 30 31 32 | 38 39 40 | +--------------+--------------+--------------+--------------+ | 41 42 43 | | 44 bottom 45 | | 46 47 48 | +--------------+

Note that this model does not include the face centers. That is, it

is G[C,E] rather than G[C,E,F]. 56 numbers would be required to

include the face centers. The distinction between 48 facelets and

56 facelets bears on the nitpicky question of whether the set C of

rotations is a subgroup of G or not. What I don't see is how to

model the Supergroup in GAP. It looks like you would have to

label each Face center with four numbers so you could see the

rotations of the Face centers, but that seems like overkill.

I call this kind of model a facelet model

rather than a cubie model, and the twists and flips are implicit in

a facelet model. I would think that the twists and flips would have

to be made explicit in a cubie model. Dan Hoey reported to me once

that he had an error wherein his corners turned themselves inside

out. I can't totally picture how that happened, but it was related

to the fact that he was using a cubie model with a little

multiplication table for the twists.

I have always used a facelet

model, except that I number the corners from 1 to 24 and the edges

from 1 to 24 for historical reasons. That is, I started with corners

only or edges only, and have only lately put the two together. It

really does not create any problems for me to use the same numbers

for both edges and corners because the edges and corners

are stored disjointly, as are the edge and corner permutations

for quarter and half turns, and as are the edge and corner

permutations for rotations and reflections.

When I write the model out to disk, I only write out 8 corner facelets

and 12 edge facelets. For example, I only write out the front and

back corner facelets. This saves space and converts the model from

a facelet model to a cubie model, with the twists implicitly encoded

rather than being explicitly encoded via multiplication tables. It

also automatically establishes a frame of reference by which a

proof of conservation of twist and flip can be accomplished.

... I don't know how a normal 4x4x4 could be represented though.

I fail to see the problem. Just number the facelets. The only

problem would then lie in deciding what the generators are -- i.e.,

which kind of slice moves do you accept. You would also have to

decide whether to model the invisible 2x2x2 inside, but again if you

did, just number the invisible facelets and include their movements

with your generators.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU