Message #221

From: Roice Nelson <roice@gravitation3d.com>
Subject: Re: [MC4D] My gallery, n-vectors,2^5, etc.
Date: Fri, 17 Mar 2006 01:31:07 -0600

>
> (Please excuse my vocabulary! and using some maybe inappopriate words ;)
> I’m doing my best to show what I think…(thx good for pictures ;))
>

No worries, you’re doing great. Your comments have lead to some fun thought
exercises, and your pictures have really made the discussion possible.
Without them, we wouldn’t have had a good base for trying to talk about the
puzzle.

> I must say that interface will be good for 2^5 but in case n^5…
> WOW…3^5 It will be 2160 hyper-4-sticers…
>
> (I managed with 5^4 (1000 hyper-4-sticers) and 20x20x20 (it has
> 20x20*6=2400 stickers) but I’m terrified with vision of complex of 2160
> stickers conected in weird way
>
> (I’m not afraid number of stickers but the connections in this collosal
> system…)
>
> => ONLY "bunch of hyperfaces all over the screen" …
>
> 10 seperated hypercbes 3^4 ->>>>>> unbelievable!!! hard !!! My head would
> explode…
>

I wanted to correct something, and use this for a little further
discussion. The 3^5 would not have 27*8*10 = 2160 4-stickers. It would
only have 3^4*10 = 810 of them. The 2160 number is based on 3D cubies, so
you were not counting the right parts. That was like counting the 2D faces
of the 3D stickers of MagicCube4D. The good news is you’ve already done
puzzles with lots more stickers :)

Anyway, this got me thinking that maybe it would be better to draw the
stickers as little hypercubies instead of how they are drawn in your
pictures. I am not sure it would *have* to be this way. In both the 3D and
4D puzzles, stickers were always completely connected, so it might be nice
to do that here if possible. But when moving to the 4D puzzle, we had to
sacrifice visual connections between the adjacent stickers - their areas
don’t touch. So perhaps moving to the 5D cube would need to involve the
further sacrifice of not even having the stickers themselves be fully
connected!? I’m not 100% sure which way would be better.

I do think the highlighting that was added to the most recent Java version
of MagicCube4D would be a HUGE help with a 5D puzzle, reconnecting all that
had to be split apart to fit everything into a measly 2 dimensions.

Roice