------=_NextPart_000_0012_01C64851.BFCA60E0
Content-Type: text/plain;
charset="ISO-8859-1"
Content-Transfer-Encoding: quoted-printable
Roice wrote:
>cool :)
>I think your pics under the category "Roice's Solution" would be useful ex=
planation tools. I have a 3D cube I've pulled the corners off of that I us=
e 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 t=
he hypercube solution.=20
##) 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 wi=
ll make some foto ;) (Remark that I joined this objects with top face in di=
fferent way...I REALLY don't know WHY! ;) (1b,2c,3c). I did it on the begin=
ning my solving and I just used that...Hmmm)
Anyway:
(I called this 4-vector (4C Serie)...I have also 3-vectors (3C Serie) and a=
lso 2-vectors (2C) ... (n-vector ,where n is number of colours which are co=
nnected)
(of course it has nothing to do with real vectors and 4-vectors as well tha=
t 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 "Roic=
e solution" (if I have permission) but using my vectors)
>Your emails have had me thinking about the n^5 some more the past couple d=
ays. 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.=20=20
##) All my thinking is on this pictures...=20
Mostly http://genezis.station76.pl/Hypercubes/2x2x2x2x2/slides/Interface.ht=
ml=20
With this interface we don't get clean twists...but it's probably the clean=
est way we have...
Taking the 'base' in gray hypercube and connecting it with 'co-base' (purpl=
e 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 t=
alking about Interface on my picture)=20
(I have problem with figure out from which side of face they will be conne=
cted...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 th=
e (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=3D2=
400 stickers) but I'm terrified with vision of complex of 2160 stickers con=
ected in weird way=20
(I'm not afraid number of stickers but the connections in this collosal sys=
tem...)
=3D> ONLY "bunch of hyperfaces all over the screen" ...
10 seperated hypercbes 3^4 ->>>>>> unbelievable!!! hard !!! My head would e=
xplode...
>I guess I haven't given up completely though. As you say, somebody has to=
try ;)=20
##) SO there are at least 3 persons =3D> you, me, micheal wizner,....
>If there is a way, I think we'd need to nail down how the 4D rotations wo=
uld 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 progr=
am (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 t=
o further work..
I'm looking forward to see THIS!
RemiQ
------=_NextPart_000_0012_01C64851.BFCA60E0
Content-Type: text/html;
charset="ISO-8859-1"
Content-Transfer-Encoding: quoted-printable
| 12px Courier New, Courier, monotype.com; padding: 3px; background: #ffffff;= |
------=_Part_4314_32428962.1142580667830
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
Content-Disposition: inline
>
> (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 though=
t
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=3D2400 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...)
>
> =3D> 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 =3D 2160 4-stickers. It would
only have 3^4*10 =3D 810 of them. The 2160 number is based on 3D cubies, s=
o
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 an=
d
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
------=_Part_4314_32428962.1142580667830
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
Content-Disposition: inline
px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">(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 lea=
d to some fun thought exercises, and your pictures have really made the dis=
cussion possible. Without them, we wouldn't have had a good base=
for trying to talk about the puzzle.
px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">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-stic=
ers) and 20x20x20 (it has 20x20*6=3D2400 stickers) but I'm terrified with v=
ision of complex of 2160 stickers conected in weird way(I'm not afraid number of stickers but=
the connections in this collosal system...)
=3D> ONLY "bunc=
h 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 discu=
ssion. The 3^5 would not have 27*8*10 =3D 2160 4-stickers. It w=
ould only have 3^4*10 =3D 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 ne=
ws is you've already done puzzles with lots more stickers :)=20Anyway, 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 pictu=
res. 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 b=
e nice to do that here if possible. But when moving to the 4D puzzle,=
we had to sacrifice visual connections between the adjacent stickers - the=
ir areas don't touch. So perhaps moving to the 5D cube would need to =
involve the further sacrifice of not even having the stickers themselv=
es be fully connected!? I'm not 100% sure which way would be better.=
=20I do think the highlighting that was added to the most recent Java ver=
sion 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.=20Roice
------=_Part_4314_32428962.1142580667830--