Message #969

From: "dicekid@rocketmail.com" <dicekid@rocketmail.com>
Subject: Re: [MC4D] Checkerboard
Date: Sat, 10 Jul 2010 08:09:28 -0000

Hi deustfrr,

I thought about this checkerboard pattern for myself a while ago and I think the way you
want to turn the cells will not work.
I’m not sure but maybe some of the experts can correct me if I’m wrong.
But what I think you need, is the possibility to turn 1 cell in a way that all the
neighbouring cells will switch their "faces" (is this the right word here?) with the
opposed cell. You can do this for 4 of the 6 neighbouring cells, but not for all. At least
not in a way that they will switch the faces with their opposite cell.

In a 2D or 3D cube this is possible. So if you turn an edge on a 2D cube around 180°, you
just switch the colors of the corners of the 2 neighbouring edges.
On a 3D cube it’s the same if you turn a face around 180° you switch the edges of all the
neighbouring faces to their opposite face….
Now in 4D…. we just can’t turn the cell around 180° and switching all the faces of the
neighbouring cells, so that they will end up on ther opposite cell.

At this point I have some question on the experts here. Is such a turn completely
forbidden in a mathematical way? Or are we missing a possibility to turn the faces of the
4D-cube? And is the "easy" checkerboard-solution with the 180° twists only possible for 2D
and 3D and not for higher dimensions?

I hope, I didn’t confuse you too much.

Have a nice weekend,
Denny

— In 4D_Cubing@yahoogroups.com, "deustfrr" <deustfrr@…> wrote:
>
> Wait so, do you click on the 3 coloured edges or the 2 coloured faces once? I posted this in the first place because MC4D updated and the log files wouldn’t work!
>
> old checkerboard:
> MagicCube4D 2 0 24 3
> 161616161616161616161616161
> 707070707070707070707070707
> 525252525252525252525252525
> 434343434343434343434343434
> 343434343434343434343434343
> 252525252525252525252525252
> 070707070707070707070707070
> 616161616161616161616161616
> 122 122 314 314 610:2 610:2 414 414 622 622
> 410:-1 122 122 216 216 614:2 614:2 516 516 622
> 622 414:2 414:2 54:2 54:2.
>
> new first three-coloured series:
> MagicCube4D 3 0 8 {4,3,3} 2
> 0.6520850785553989 -0.3815055016364071 0.6551630350886356 0.0
> 0.7574805810228947 0.36403966358641016 -0.5419393810280918 0.0
> -0.0317524754722722 0.8496638603336303 0.5263678416700018 0.0
> 0.0 0.0 0.0 1.0
> *
> m[ 25,1,1 105,1,1 25,-1,1 132,-1,1 25,1,1 105,-1,1 25,-1,1 132,1,1 m].
>
> I’m just posting examples
>
>
> — In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@> wrote:
> >
> > Hello deustfrr,
> >
> > You perform 180 degree twists by clicking on the edge pieces. These are
> > the ones that look like the 2-colored pieces on the normal 3D Rubik’s
> > cube. To perform twists on the invisible "outer" face you can either
> > first rotate it into view by ctrl-clicking anywhere on one of the
> > non-center faces, or you can hold down the ‘3’ key while clicking a
> > sticker of its opposite face, in this case the inner-most one.
> >
> > You may find that second method to be useful for twisting of all face
> > pairs in a consistent way by clicking twice on just one of each pair,
> > once normally and once with the ‘3’ key. An even faster method might be
> > to hold the ‘2’ key instead to twist just the middle slice which will
> > cut your twist count in half. Even without that, the current record for
> > a 3^4 checkerboard is 24 twists so an 8 twist method would be quite an
> > improvement!
> >
> > Welcome to the 3D cubing group,
> > -Melinda
> >
> > deustfrr wrote:
> > > Hi everybody, I just wanted to ask how to make a checkerboard pattern
> > > on a 4D and 5D cube.
> > > On a 2D cube you turn every edge 180, 4 turns
> > > On a 3D cube you turn every face 180, 6 turns
> > > On a 4D cube you turn every cell 180, 8 turns? How do you do that?
> > > For me, even though I talk about 4D so much, I can’t understand
> > > something as easy as this! :(((or at least I think that’s supposed to
> > > be easy)
> > > using my notation, the turns should be U, D, L, R, F, B, N (near) and
> > > T, but I don’t know which faces to click on.
> > > hope you respond
> >
>