Message #1204

From: schuma <mananself@gmail.com>
Subject: Re: Siamese
Date: Mon, 18 Oct 2010 22:51:28 -0000

Hi everyone,

Another type of constraints other than the bandaging is to restrict the rotation of a cell from the original octahedral group to a certain subgroup. For example, one possible rule is: in every step, it is not allowed to make 90 degree turns around face centers or 180 degree turns around edge pieces. Only 180 degree turns around face centers or 120 degree turns around corners are allowed. This rule restrict the possible rotations of a cell from the octahedral group down to the tetrahedral group. I don’t know if there is a universal UI design that works for all the shapes in MC4D. But this type of restriction is mathematically more appealing to me, because it preserves more symmetry than bandaging. The 3D analog in a 3x3x3 Rubik’s Cube is to allow only 180 degree face turns for each face.

Nan

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:
>
> On 10/16/2010 7:05 PM, jasmon brian wrote:
> > Hey Melinda, It’s Jon,
> > I finished the siamese hypercube. I started with a solved 3^4 and
> > scrambled the red and blue sides for 100 twists as random as I could.
> > I then solved the puzzle from there, turning only the red and blue
> > sides. I attached the file for consideration.
> > I would also like to suggest that you edit your program to be workable
> > with other bandaged hypercubes! Even having the program not
> > scramble/twist certain sides, at request, would be nice.
> > Jon Scott
>
> Jon,
>
> That was a really clever exercise! I hope you don’t mind that I’m
> including the rests of the group on this thread so that other interested
> puzzlers can also offer new insights and suggestions.
>
> Regarding additions to MC4D, I try to keep out all features that require
> coding for special case puzzles, so if we were to add the ability to
> bandage cubes, then we need to make sure that it’s possible to bandage
> any puzzle. The main question then becomes a UI design problem of how to
> most naturally describe such a puzzle, and to a lessor degree, how to
> display the bandaging. Right now we describe puzzles by giving a
> Schläfli symbol plus an edge length. To add bandaging constraints I
> expect would mean adding a third, optional chunk of information to
> describe how you want it bandaged. I can’t think of an obvious and
> general way to do that, but I’d guess that there are probably ways to do
> that having to do with face numbers.
>
> Another thing people could do right now would be to create a bunch of
> interesting scrambled versions of different bandaged puzzles just like
> you did for this one. The process is a little tedious but only needs to
> be done once for any particular configuration. From there people can
> just use these hand-created scrambles and simply avoid twisting any of
> the forbidden faces. That won’t cover all possible bandagings but should
> be good enough to have fun exploring quite a few interesting ones. So
> that others can get the full effect, here is what your log file looks
> like with only your scrambling twists considered to be fully scrambled:
>
> MagicCube4D 3 2 0 {4,3,3} 3
> -0.7781653457506625 0.312535051866865 -0.54477567495927 2.925835719544026E-9
> 0.6274075122099996 0.426340681158958 -0.651608346486887
> -3.525863967809649E-16
> -0.02860958397480492 0.8488553851767048 0.5278503829318464
> 7.375303054792201E-18
> -2.276784185734973E-9 9.144260743002593E-10 -1.5939238952932422E-9 -1.0
> *
> 100,1,1 206,1,1 100,1,1 194,1,1 103,1,1 207,1,1 105,1,1 214,1,1 95,1,1
> 194,1,1
> 105,-1,1 202,1,1 105,1,1 214,1,1 87,-1,1 207,1,1 105,1,1 207,1,1 105,1,1
> 212,1,1
> 105,1,1 214,1,1 105,1,1 207,1,1 87,1,1 194,1,1 87,1,1 196,1,1 105,1,1
> 207,1,1
> 83,1,1 205,1,1 105,1,1 202,1,1 102,1,1 210,1,1 81,1,1 202,1,1 103,1,1
> 210,1,1
> 98,1,1 210,1,1 87,1,1 210,1,1 87,1,1 207,1,1 105,1,1 207,1,1 100,1,1 194,1,1
> 87,1,1 207,1,1 100,1,1 212,1,1 100,1,1 212,1,1 105,1,1 212,1,1 105,1,1
> 212,1,1
> 87,-1,1 202,-1,1 98,-1,1 202,1,1 98,1,1 190,1,1 105,1,1 212,1,1 105,1,1
> 212,1,1
> 105,1,1 207,1,1 105,1,1 202,1,1 105,1,1 194,1,1 105,1,1 205,1,1 105,1,1
> 195,1,1
> 105,1,1 210,1,1 103,1,1 212,1,1 105,1,1 212,1,1 105,-1,1 202,-1,1
> 103,-1,1 207,1,1
> 105,1,1 207,1,1 100,1,1 206,1,1 100,1,1 194,1,1 87,1,1 206,1,1 100,1,1
> 205,1,1
> m|.
>
> Neat stuff Jon. Thanks for sharing this.
> -Melinda
>