Thread: "Corners in 3^4?"

Just interesting - what is the length of the shortest known operations for =
corners in 3^4?
I have:=20
- 12-twists for 3-loop of corners;
- 16-twists for twist of single corner
- 18-twists for 3-rotations of two corners.
(unfortunately I can't use them in my algorithms - only half of last sequen=
ce can be used).
Is there something better?

Andrey

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>
> @matthew
> P.S. Remi mentioned different 'steering' for the 2^4 in the new MC4D, did I
> miss something?
>
> @andrey
> What was with 2^4 in older versions? Only rotations around the diagonals?
> If so, it was very different puzzle (with the different set of positons -
> all cubies remained in their 8-orbits). Or there was another kind of
> difference?
>


So I think what Remi was referring to is the following...

In the previous MC4D, the 2^4 was limited to rotations aligned with the
coordinate axes, that is, the 90 degree ones. And unlike the higher order
puzzles, where you clicked on the sticker was important (the particular
sticker "facet").

Where you click on the sticker is still important in the latest version, but
things are a little stranger (I think neither Melinda nor I like the
complications that arise from special casing the 2^4). The current
implementation is such that if you click on the sticker facets towards the
interior of a hyperface, you can get the corner (120 degree) rotations as
well. The other thing about the new version is that you can create macros
on the 3^4 having twists of any type, then apply those macros to the 2^4.
But not only is this an awkward way to make moves, it's further complicated
by the macro definition clicks (which would all need to be of the
corner-click variety to get this to work). I suppose we could make the 2^4
macro definition clicks not depend on the particular sticker facets, but
that is the way things look to work now.

Btw, since I'm posting, let me add my congrats to the new record holders,
especially to Matthew since he took the record I liked to hold ;) I don't
think my approach is capable of getting anywhere near 250, so I don't have
plans to try. If I become motivated to take short solutions further, it
would be a different line of study I think, one involving computers and
learning about how the current 3D optimal algorithms are done. And in such
a scenario, those efforts wouldn't qualify for the HOF anyway. I tried to
find a funny quote about newer generations replacing older ones without
luck, but in any case, nice job!

Cheers,
Roice

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