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Mark gaffs again: > I'm now sure (I think) that it is really: > > all edges flipped + 4 X > (with the 4 X on sides F, R, B, L which should match Dan's diagram)

* sign * No, I see I entered the position into my program wrong.

A central reflection of the edges with respect to the faces is

simply 6 X or checkerboard order 2, solvable in 12 qtw or 6 htw.

So the edges-only antipode is: all-edges-flipped + 6 X.

Jerry Byran quote:

>Dan Hoey is correct. Mirror-Image-of-Start is at level 12.

>Edges-Flipped is at level 9. Mirror-Image-of-Start-and-Edges-Flipped

>is at level 15. And, of course, Start is at Level 0. This exhausts

>the list of configurations with order-24 symmetry.

Ok, only 9 qtw.... it's got to play havoc with corners. I got it now.

* Hmmm, what are all the possible orders of symmetry? *

Also I note my "Symmetry Level" is the opposite of Jerry's Order-N

symmetry:

> If we define "symmetry level" as the number of distinct patterns

>generated by rotating the cube through it's 24 different orientations

in

>space then most known antipodes are symmetry level 6. Thus the lower

the

>number the higher the level of symmetry. The least symmetric positions

>have level 24, and this is very common. The most symmetric positions

>have level 1, the two positions START and 6 X order 2.

Of course all-edges-flipped I never included, as at the time I was

looking at the square's group.

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As a small postfix to my cyclic decomposition article, I found the

following patterns. I'm fond of pattern 16 myself. I am looking for

CD-type processes for 6 X order 3 and 6 X order 6. I find when I

am physical cubing (as opposed to computer cubing or old fashioned

mental cubing!) it really helps having a CD-type process memory-wise.

Memorizing the computer generated processes is like memorizing

prime numbers.

p161 Mark's Pattern 16 (F1 R1 L1 B1) ^3 + F2 B2 D2 F2 B2 T2 (18) p162 2 X, 4 H full (F1 T2 B1) ^4 (12) p163 4 ARM Full (F2 T1 B2) ^4 + T1 D3 (14) p164 4 Y's Rotated (F1 T2 D2) ^6 + F1 (19) p165 2 Swap, 4 H full (F1 L2 T2 R2 B1) ^2 + L2 R2 T2 D2 (14) p166 2 H adj swap (F1 L2 T2 R2 B1) ^2 + L2 T2 R2 D2 L2 T2 (16)

No doubt these are compressible and hence not as efficient, but if

you consider ease of execution....

-> Mark <-