Message #674

From: rev_16_4 <rev_16_4@yahoo.com>
Subject: Re: My solution
Date: Fri, 22 May 2009 16:31:05 -0000

— In 4D_Cubing@yahoogroups.com, "Kyle Headley" <kygron@…> wrote:
>
> I had speculated that in a (3+)^5 the 1-color cubies
> could be rearranged in place. This may be the reason
> that certain parity issues don’t come up (thought I
> haven’t fully read that section of the group postings
> yet).

Actually, Kyle, On a 3^n, the 1 color cubies are immovable in relation to each other. (Their "orientation" can be changed…) Look at a 3^3. If yours has red and orange 1 color cubies opposite of each other, you’ll never be able to move them to sides next to each other. This applies to all 3^n. With n>4 this is extremely difficult to visualize.

As for the m^n (m>3 and even, n>2), the 1 color cubies CAN be "rearranged" in place. This is due to the multiple same color cubies. This is also the reason parity issues do seem to come up (but can be trivial to solve with an unrestricted move set).

The easiest example of parity issues is with the 4^3. The rearranging of the 1 color cubies is what allows the apparent single flipped edge on a 4^3. (An odd number of quarter twists of center slices is what creates it)

Happy n-cubing!

-Levi