Message #219
From: Remigiusz Durka <thesamer@interia.pl>
Subject: My gallery, n-vectors,2^5, etc.
Date: Wed, 15 Mar 2006 16:58:57 +0100
Roice wrote:
>cool :)
>I think your pics under the category "Roice’s Solution" would be useful explanation tools. I have a 3D cube I’ve pulled the corners off of that I use to help people ignore >these pieces when I’m teaching them to solve edges. If you were interested, we could try to incorporate your pictures into the hypercube solution.
##) Sure! You are free to take what you want from my page. Did you see http://genezis.station76.pl/Hypercubes/During%20work/slides/I%204C.jpg ?
I use something like that to see what will happened when I use sequence (I’m basing this on my folded pointing finger and my thumb ;) Maybe later I will make some foto ;) (Remark that I joined this objects with top face in different way…I REALLY don’t know WHY! ;) (1b,2c,3c). I did it on the beginning my solving and I just used that…Hmmm)
Anyway:
(I called this 4-vector (4C Serie)…I have also 3-vectors (3C Serie) and also 2-vectors (2C) … (n-vector ,where n is number of colours which are connected)
(of course it has nothing to do with real vectors and 4-vectors as well that we know from physics and mathematics-> http://en.wikipedia.org/wiki/Four-vector )
I think that is very effetive way to show how Series work..
I PROMISE THAT SOON I’LL MAKE SOME PHOTOS with my vectors in action…
(I want to do "Remi Solution" in polish version;) of course basing on "Roice solution" (if I have permission) but using my vectors)
>Your emails have had me thinking about the n^5 some more the past couple days. Unfortunately, I’ve sort of come to the same conclusion I have in the past, which is >that there is not an elegant way to present it.
##) All my thinking is on this pictures…
Mostly http://genezis.station76.pl/Hypercubes/2x2x2x2x2/slides/Interface.html
With this interface we don’t get clean twists…but it’s probably the cleanest way we have…
Taking the ‘base’ in gray hypercube and connecting it with ‘co-base’ (purple hypercube) we have clean 6 connections…(5 BLUE ARROWS and green 4-cube).
The last two connection are through two 4-cubes LEFT and RIGHT (I’m still talking about Interface on my picture)
(I have problem with figure out from which side of face they will be connected…But maybe it will be simple…)
-> for example :
(top side) of (top face) of the gray hypercube with (bottom side) of the (top face) of the purple hypercube…through LEFT 4-cube
(top side) of (bottom face) of the gray hypercube with (bottom side) of the (bottom face) of the purple hypercube…through RIGHT 4-cube
and connetion could be along axis (base)-(co-base)
It could be visible enough to handle this relativly easy ;)
I must meditate on this more ;)
(Please excuse my vocabulary! and using some maybe inappopriate words ;) I’m doing my best to show what I think…(thx good for pictures ;))
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 guess I haven’t given up completely though. As you say, somebody has to try ;)
##) SO there are at least 3 persons => you, me, micheal wizner,….
>If there is a way, I think we’d need to nail down how the 4D rotations would take place to twist faces, which has been discussed some in the past.I think a first step >towards a better understanding would be a 5D cube program (not permutation puzzle, just cube) that would let us play with the 3D, 4D, and maybe a limited subset of >the 5D rotations.
##) Even showing 10 separated hypercubes mixing will be very…stimulated to further work..
I’m looking forward to see THIS!
RemiQ