16 colors was easy. When I understood what is the actual role of small tria=
ngles, first stage (stars around centers, then corners) was smooth enough, =
and then simple 4-twist commutators were all I need to resolve edges. I eve=
n haven't needed special operation for re-orientation of edges :)
With 9 colors first stage was equally easy, but edges are too much connec=
ted. The best thing that I could develop was 22-twist commutators for 3-cyc=
le of edges and 10-twist for re-orientation of the couple of edges. And I h=
ad to remember them in normal and mirrored forms in all orientations of the=
plane. Terrible...
Anyway, results are 1254 twist for 16 colors and 1630 for 9 colors.
Nice puzzles!
Andrey
Hi,
I just finished my {6,3} 9 colors, 3 layer factor =3D 1.29903810567 (the sw=
eet spot Roice provided). For the edges, I used a 10-move commutator for 3-=
cycle, which is not too bad. It's actually easier than I expected yesterday=
. I notice you said your 3-cycle is 22-twist but re-orientation is 10-twist=
. That's a little weird. For me re-orientation is usually two 3-cycles.=20
Nan
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> 16 colors was easy. When I understood what is the actual role of small tr=
iangles, first stage (stars around centers, then corners) was smooth enough=
, and then simple 4-twist commutators were all I need to resolve edges. I e=
ven haven't needed special operation for re-orientation of edges :)
> With 9 colors first stage was equally easy, but edges are too much conn=
ected. The best thing that I could develop was 22-twist commutators for 3-c=
ycle of edges and 10-twist for re-orientation of the couple of edges. And I=
had to remember them in normal and mirrored forms in all orientations of t=
he plane. Terrible...
> Anyway, results are 1254 twist for 16 colors and 1630 for 9 colors.
> Nice puzzles!
>=20
> Andrey
>
Yes, it's strange for me too.
Let's mark centers as
..G.H.I
.D.E.F.
A.B.C.
I've started with commutator [A,E']. Among other things it moves three edge=
s around center D and changes orientation of two of them. So when I made [[=
A,E'],D^2] (10 twists), it was pure reversing of edges DF and DG. But I fai=
led to make pure 3-cycle from it.
Then I tried [A,E]. Again, it moves 9 edges, and the best I made from it wa=
s 5-cycle [[A,E],C^2]. Third commutator converted it to 3-cycle:=20
[[[A,E],C^2],D^2]. Not very good, but enough for solving.
Andrey
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Hi,
>=20
> I just finished my {6,3} 9 colors, 3 layer factor =3D 1.29903810567 (the =
sweet spot Roice provided). For the edges, I used a 10-move commutator for =
3-cycle, which is not too bad. It's actually easier than I expected yesterd=
ay. I notice you said your 3-cycle is 22-twist but re-orientation is 10-twi=
st. That's a little weird. For me re-orientation is usually two 3-cycles.=20
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "Andrey"
> >
> > 16 colors was easy. When I understood what is the actual role of small =
triangles, first stage (stars around centers, then corners) was smooth enou=
gh, and then simple 4-twist commutators were all I need to resolve edges. I=
even haven't needed special operation for re-orientation of edges :)
> > With 9 colors first stage was equally easy, but edges are too much co=
nnected. The best thing that I could develop was 22-twist commutators for 3=
-cycle of edges and 10-twist for re-orientation of the couple of edges. And=
I had to remember them in normal and mirrored forms in all orientations of=
the plane. Terrible...
> > Anyway, results are 1254 twist for 16 colors and 1630 for 9 colors.
> > Nice puzzles!
> >=20
> > Andrey
> >
>
Your reorientation algorithm is interesting. Using your notation, my 3-cycl=
e is [[C,E],D] =3D (C,E,C',E'),D,(E,C,E',C'),D'. D can be replaced by D2, D=
3, D', etc to get some variations.=20
Nan
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Yes, it's strange for me too.
>=20
> Let's mark centers as
>=20
> ..G.H.I
> .D.E.F.
> A.B.C.
>=20
> I've started with commutator [A,E']. Among other things it moves three ed=
ges around center D and changes orientation of two of them. So when I made =
[[A,E'],D^2] (10 twists), it was pure reversing of edges DF and DG. But I f=
ailed to make pure 3-cycle from it.
> Then I tried [A,E]. Again, it moves 9 edges, and the best I made from it =
was 5-cycle [[A,E],C^2]. Third commutator converted it to 3-cycle:=20
> [[[A,E],C^2],D^2]. Not very good, but enough for solving.
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Hi,
> >=20
> > I just finished my {6,3} 9 colors, 3 layer factor =3D 1.29903810567 (th=
e sweet spot Roice provided). For the edges, I used a 10-move commutator fo=
r 3-cycle, which is not too bad. It's actually easier than I expected yeste=
rday. I notice you said your 3-cycle is 22-twist but re-orientation is 10-t=
wist. That's a little weird. For me re-orientation is usually two 3-cycles.=
=20
> >=20
> > Nan
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Andrey"
> > >
> > > 16 colors was easy. When I understood what is the actual role of smal=
l triangles, first stage (stars around centers, then corners) was smooth en=
ough, and then simple 4-twist commutators were all I need to resolve edges.=
I even haven't needed special operation for re-orientation of edges :)
> > > With 9 colors first stage was equally easy, but edges are too much =
connected. The best thing that I could develop was 22-twist commutators for=
3-cycle of edges and 10-twist for re-orientation of the couple of edges. A=
nd I had to remember them in normal and mirrored forms in all orientations =
of the plane. Terrible...
> > > Anyway, results are 1254 twist for 16 colors and 1630 for 9 colors.
> > > Nice puzzles!
> > >=20
> > > Andrey
> > >
> >
>
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Very valuable info's I would like to see in wiki.=20
Fill the two Hexagonal pages (9c and 16c) and add link "Hx Documents".
For future simple solvers (not first and not shortest) ;-)
Thanks.
Ed
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