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
> If we define "symmetry level" as the number of distinct patterns
>generated by rotating the cube through it's 24 different orientations
>space then most known antipodes are symmetry level 6. Thus the lower
>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.
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
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 <-