# 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

> >

>