Thread: "color graphs of MagicTiles"

From: "Eduard" <baumann@mcnet.ch>
Date: Sat, 02 Jun 2012 11:37:22 -0000
Subject: color graphs of MagicTiles



--1-8157260164-2887103078=:2
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable


I think "hyp G4GX 6 color non orientable" is also a "bad guy".

Here are color graphs:

color graph ell sph 3,5 8.PNG=20
IKZ6FqLl1uT3MlMNAdZUqQnXfMSX84f2pkRYN-Se0SHbEZXgsVg9_CgzNACU4/Eduard/col\
or%20graph%20ell%20sph%203%2C5%208.PNG>

color graph hyp 10,4 6 no.PNG=20
ffrUmQMte5sRTCWMajX2wFFDWuQP2x-Kqkir3j8ClMNUJAKh8j4M8BWQF_kU8/Eduard/col\
or%20graph%20hyp%2010%2C4%206%20no.PNG>

color graph hyp 8,4 5.PNG
eKsJF-nzdvXWO1Dd8N4lru-Ch_vUH-7pckDSLGdSRgi324ZykkjX80zl9HAf8/Eduard/col\
or%20graph%20hyp%208%2C4%205.PNG>

color graph hyp 8,4 9.PNG
FsEPgNq_mKzT4Qnn6k3gacTgJxLo16cQI9jmpqZoXpi4AzEOchSHuso6hIm5M/Eduard/col\
or%20graph%20hyp%208%2C4%209.PNG>

color graph hyp 8,4 10.PNG
svf5L_B1LJYq4qszlASw_w-NvFTV2U-O-SGik5Q4ff310S493B38B72Qcj0Y0/Eduard/col\
or%20graph%20hyp%208%2C4%2010.PNG>




--1-8157260164-2887103078=:2
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I think "hyp G4GX 6 color non orientable" is also a "bad guy".


Here are color graphs:


ouECAkZ03XIKZ6FqLl1uT3MlMNAdZUqQnXfMSX84f2pkRYN-Se0SHbEZXgsVg9_CgzNACU4/Edu=
ard/color%20graph%20ell%20sph%203%2C5%208.PNG">color graph ell sph 3,5 8.PN=
 


NzjxLeMs9kffrUmQMte5sRTCWMajX2wFFDWuQP2x-Kqkir3j8ClMNUJAKh8j4M8BWQF_kU8/Edu=
ard/color%20graph%20hyp%2010%2C4%206%20no.PNG">color graph hyp 10,4 6 no.PN=
 


L1QK-JgKOKeKsJF-nzdvXWO1Dd8N4lru-Ch_vUH-7pckDSLGdSRgi324ZykkjX80zl9HAf8/Edu=
ard/color%20graph%20hyp%208%2C4%205.PNG">color graph hyp 8,4 5.PNG
 =
;


YD4FKOyXbCFsEPgNq_mKzT4Qnn6k3gacTgJxLo16cQI9jmpqZoXpi4AzEOchSHuso6hIm5M/Edu=
ard/color%20graph%20hyp%208%2C4%209.PNG">color graph hyp 8,4 9.PNG
 =
;


NQAoXHsLMEsvf5L_B1LJYq4qszlASw_w-NvFTV2U-O-SGik5Q4ff310S493B38B72Qcj0Y0/Edu=
ard/color%20graph%20hyp%208%2C4%2010.PNG">color graph hyp 8,4 10.PNG
&nb=
sp;


 



--1-8157260164-2887103078=:2--




From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Sat, 2 Jun 2012 14:11:14 +0200
Subject: Re: color graphs of MagicTiles



------=_NextPart_000_002C_01CD40C9.921F9580
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

The links are not working in e-mail (why?).=20
Goto to the group to be able to see the links.
Ed
------=_NextPart_000_002C_01CD40C9.921F9580
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>




The links are not working in e-mail (why?)=
.=20

Goto to the group to be able to see the=20
links.

Ed


------=_NextPart_000_002C_01CD40C9.921F9580--




From: Roice Nelson <roice3@gmail.com>
Date: Sat, 2 Jun 2012 12:23:39 -0500
Subject: Re: [MC4D] Re: color graphs of MagicTiles



--e89a8f22c34fcb492704c1808fdd
Content-Type: text/plain; charset=ISO-8859-1

Cool, thanks Ed.

People have had trouble with the file links before. I'm not sure why, but
there must be some common path that results in broken links. Hopefully the
following links to your graphs will work.

- color graph ell sph 3,5
8.PNG

- color graph hyp 10,4 6
no.PNG
- color graph hyp 8,4
5.PNG

- color graph hyp 8,4
9.PNG

- color graph hyp 8,4
10.PNG


It looks like you are working on dual graphs. By that I mean you made the
faces on the puzzles vertices in the graphs. The {8,4} graphs all makes
sense to me from that perspective, and they definitely help in studying the
structure. Here's something interesting: turn the 5C graph on its side,
and check out how it relates to the 10C graph. The {10,4} graph is
intriguing too.

Looking at the {3,5} 8C graph, and comparing it to the one I
made,
I
think I'm following your graph, but did you make this one when looking at
the puzzle with the default colors? What does n stand for?

Roice


On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann wrote:

> **
>
>
> The links are not working in e-mail (why?).
> Goto to the group to be able to see the links.
> Ed
>
>
>

--e89a8f22c34fcb492704c1808fdd
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

Cool, thanks Ed.


People have had trouble with the file l=
inks before. =A0I'm not sure why, but there must be some common path th=
at results in broken links. =A0Hopefully the following links to your graphs=
will work.



It looks like you are working on dual graphs. =A0By that I mean y=
ou made the faces on the puzzles vertices in the graphs. =A0The {8,4} graph=
s all makes sense to me from that perspective, and they definitely help in =
studying the structure. =A0Here's something interesting: turn the 5C gr=
aph on its side, and check out how it relates to the 10C graph. =A0The {10,=
4} graph is intriguing too.



Looking at the {3,5} 8C graph, and comparing it to ref=3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/=
1602345595/view?picmode=3D&mode=3Dtn&order=3Dordinal&start=3D1&=
amp;count=3D20&dir=3Dasc" target=3D"_blank">the one I made
,=A0I thi=
nk I'm following your graph, but did you make this one when looking at =
the puzzle with the default colors? =A0What does n stand for?




Roice


On S=
at, Jun 2, 2012 at 7:11 AM, Eduard Baumann <"mailto:baumann@mcnet.ch" target=3D"_blank">baumann@mcnet.ch>=
wrote:



x #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20



















The links are not working in e-mail (why?).=20

Goto to the group to be able to see the=20
links.

Ed










--e89a8f22c34fcb492704c1808fdd--




From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Sat, 2 Jun 2012 19:45:34 +0200
Subject: Re: [MC4D] Re: color graphs of MagicTiles



------=_NextPart_000_000C_01CD40F8.46C3B330
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Thanks.
n as neutral, s as silver, ...


----- Original Message -----=20
From: Roice Nelson=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, June 02, 2012 7:23 PM
Subject: Re: [MC4D] Re: color graphs of MagicTiles


=20=20=20=20
Cool, thanks Ed.



People have had trouble with the file links before. I'm not sure why, bu=
t there must be some common path that results in broken links. Hopefully t=
he following links to your graphs will work.
a.. color graph ell sph 3,5 8.PNG=20=20=20
b.. color graph hyp 10,4 6 no.PNG=20=20=20
c.. color graph hyp 8,4 5.PNG=20=20
d.. color graph hyp 8,4 9.PNG=20=20
e.. color graph hyp 8,4 10.PNG=20=20
It looks like you are working on dual graphs. By that I mean you made th=
e faces on the puzzles vertices in the graphs. The {8,4} graphs all makes =
sense to me from that perspective, and they definitely help in studying the=
structure. Here's something interesting: turn the 5C graph on its side, a=
nd check out how it relates to the 10C graph. The {10,4} graph is intrigui=
ng too.


Looking at the {3,5} 8C graph, and comparing it to the one I made, I thin=
k I'm following your graph, but did you make this one when looking at the p=
uzzle with the default colors? What does n stand for?


Roice



On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann wrote:




The links are not working in e-mail (why?).=20
Goto to the group to be able to see the links.
Ed




=20=20
------=_NextPart_000_000C_01CD40F8.46C3B330
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>


Thanks.

n as neutral, s as silver, ...>
 

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
Roice Nelson=
=20

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Saturday, June 02, 2012 7:23=
=20
PM

Subject: Re: [MC4D] Re: color grap=
hs of=20
MagicTiles


 =20

Cool, thanks Ed.



People have had trouble with the file links before.  I'm not su=
re=20
why, but there must be some common path that results in broken links.=20
 Hopefully the following links to your graphs will work.


It looks like you are working on dual graphs.  By that I mean y=
ou=20
made the faces on the puzzles vertices in the graphs.  The {8,4} gra=
phs=20
all makes sense to me from that perspective, and they definitely help in=
=20
studying the structure.  Here's something interesting: turn the 5C g=
raph=20
on its side, and check out how it relates to the 10C graph.  The {10=
,4}=20
graph is intriguing too.



Looking at the {3,5} 8C graph, and comparing it to href=3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/p=
ic/1602345595/view?picmode=3D&mode=3Dtn&order=3Dordinal&start=
=3D1&count=3D20&dir=3Dasc"=20
target=3D_blank>the one I made, I think I'm following your graph=
, but=20
did you make this one when looking at the puzzle with the default colors?=
=20
 What does n stand for?



Roice




On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann <=
SPAN=20
dir=3Dltr>< target=3D_blank>baumann@mcnet.ch> wrote:

=




The links are not working in e-mail (why?).=20

Goto to the group to be able to see the=20
links.

Ed


>



------=_NextPart_000_000C_01CD40F8.46C3B330--




From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Sat, 2 Jun 2012 19:55:16 +0200
Subject: Re: [MC4D] Re: color graphs of MagicTiles



------=_NextPart_000_000E_01CD40F9.A14AA330
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Sadly the links in your e-mail don't work too.

----- Original Message -----=20
From: Roice Nelson=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, June 02, 2012 7:23 PM
Subject: Re: [MC4D] Re: color graphs of MagicTiles


=20=20=20=20
Cool, thanks Ed.



People have had trouble with the file links before. I'm not sure why, bu=
t there must be some common path that results in broken links. Hopefully t=
he following links to your graphs will work.
a.. color graph ell sph 3,5 8.PNG=20=20=20
b.. color graph hyp 10,4 6 no.PNG=20=20=20
c.. color graph hyp 8,4 5.PNG=20=20
d.. color graph hyp 8,4 9.PNG=20=20
e.. color graph hyp 8,4 10.PNG=20=20
It looks like you are working on dual graphs. By that I mean you made th=
e faces on the puzzles vertices in the graphs. The {8,4} graphs all makes =
sense to me from that perspective, and they definitely help in studying the=
structure. Here's something interesting: turn the 5C graph on its side, a=
nd check out how it relates to the 10C graph. The {10,4} graph is intrigui=
ng too.


Looking at the {3,5} 8C graph, and comparing it to the one I made, I thin=
k I'm following your graph, but did you make this one when looking at the p=
uzzle with the default colors? What does n stand for?


Roice



On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann wrote:




The links are not working in e-mail (why?).=20
Goto to the group to be able to see the links.
Ed




=20=20
------=_NextPart_000_000E_01CD40F9.A14AA330
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>


Sadly the links in your e-mail don't work=
=20
too.

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
Roice Nelson=
=20

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Saturday, June 02, 2012 7:23=
=20
PM

Subject: Re: [MC4D] Re: color grap=
hs of=20
MagicTiles


 =20

Cool, thanks Ed.



People have had trouble with the file links before.  I'm not su=
re=20
why, but there must be some common path that results in broken links.=20
 Hopefully the following links to your graphs will work.


  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT_T82JY8g6js55yIbhEnvUOvlogyhh=
    XTCFwDwiHWlgok-3r83OCddxHOqF3WkIhIdKgwkx6dZN_-a7dnxA/Eduard/color%20graph%2=
    0ell%20sph%203%2C5%208.PNG"=20
    target=3D_blank>color graph ell sph 3,5 8.PNG  =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT32hHYs8g6jsrVsu1iB6G1U4WK-e08=
    hSKNcgcZOvO4wgQio68uIhEqetbY2RtSvm5yyV9A4IJqFEyZ8bhA/Eduard/color%20graph%2=
    0hyp%2010%2C4%206%20no.PNG"=20
    target=3D_blank>color graph hyp 10,4 6 no.PNG  =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT4scdqo8g6jsXm2reMiFtoRw5-uSvc=
    pddy5jsaXRn0C-WiNcewKMHho77977FgmRShHJ4In6Bxc7v-HVOA/Eduard/color%20graph%2=
    0hyp%208%2C4%205.PNG"=20
    target=3D_blank>color graph hyp 8,4 5.PNG =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT59Yo048g6jsSG-hyVLHa2-WOv1Zw2=
    55nryBZoaEa0qQ9W3eUxdResF9XKd0lf4VF6KKk07Ob5mDo_gj6g/Eduard/color%20graph%2=
    0hyp%208%2C4%209.PNG"=20
    target=3D_blank>color graph hyp 8,4 9.PNG =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKTzEn5F48g6jslyN_rYIT2HYMvPK-Rd=
    FDlpUVG2_-MgUobEUK4CCDq72ZovnoyDAHIhIhlCrncR6-eM1WOw/Eduard/color%20graph%2=
    0hyp%208%2C4%2010.PNG"=20
    target=3D_blank>color graph hyp 8,4 10.PNG 

It looks like you are working on dual graphs.  By that I mean y=
ou=20
made the faces on the puzzles vertices in the graphs.  The {8,4} gra=
phs=20
all makes sense to me from that perspective, and they definitely help in=
=20
studying the structure.  Here's something interesting: turn the 5C g=
raph=20
on its side, and check out how it relates to the 10C graph.  The {10=
,4}=20
graph is intriguing too.



Looking at the {3,5} 8C graph, and comparing it to href=3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/p=
ic/1602345595/view?picmode=3D&mode=3Dtn&order=3Dordinal&start=
=3D1&count=3D20&dir=3Dasc"=20
target=3D_blank>the one I made, I think I'm following your graph=
, but=20
did you make this one when looking at the puzzle with the default colors?=
=20
 What does n stand for?



Roice




On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann <=
SPAN=20
dir=3Dltr>< target=3D_blank>baumann@mcnet.ch> wrote:

=




The links are not working in e-mail (why?).=20

Goto to the group to be able to see the=20
links.

Ed


>



------=_NextPart_000_000E_01CD40F9.A14AA330--




From: Roice Nelson <roice3@gmail.com>
Date: Sat, 2 Jun 2012 16:48:30 -0500
Subject: Re: [MC4D] Re: color graphs of MagicTiles



--f46d040838d3f6464c04c18442b0
Content-Type: text/plain; charset=ISO-8859-1

Bummer, Yahoo doesn't make this easy. When you click on items in the
'Files' section, it seems to produce links that are only valid for the
current logged in session. Links to items in the 'Photos' section seem to
work. How about the following?

- color graph ell sph 3,5
8.PNG
- color graph hyp 10,4 6
no.PNG
- color graph hyp 8,4
5.PNG

- color graph hyp 8,4
9.PNG

- color graph hyp 8,4
10.PNG


Roice


On Sat, Jun 2, 2012 at 12:55 PM, Eduard Baumann wrote:

> **
>
>
> Sadly the links in your e-mail don't work too.
>
>
> ----- Original Message -----
> *From:* Roice Nelson
> *To:* 4D_Cubing@yahoogroups.com
> *Sent:* Saturday, June 02, 2012 7:23 PM
> *Subject:* Re: [MC4D] Re: color graphs of MagicTiles
>
>
>
> Cool, thanks Ed.
>
> People have had trouble with the file links before. I'm not sure why, but
> there must be some common path that results in broken links. Hopefully the
> following links to your graphs will work.
>
> - color graph ell sph 3,5 8.PNG
>
> - color graph hyp 10,4 6 no.PNG
> - color graph hyp 8,4 5.PNG
>
> - color graph hyp 8,4 9.PNG
>
> - color graph hyp 8,4 10.PNG
>
>
> It looks like you are working on dual graphs. By that I mean you made the
> faces on the puzzles vertices in the graphs. The {8,4} graphs all makes
> sense to me from that perspective, and they definitely help in studying the
> structure. Here's something interesting: turn the 5C graph on its side,
> and check out how it relates to the 10C graph. The {10,4} graph is
> intriguing too.
>
> Looking at the {3,5} 8C graph, and comparing it to the one I made, I
> think I'm following your graph, but did you make this one when looking at
> the puzzle with the default colors? What does n stand for?
>
> Roice
>
>
> On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann wrote:
>
>> **
>>
>>
>> The links are not working in e-mail (why?).
>> Goto to the group to be able to see the links.
>> Ed
>>
>>
>>
>
>
>

--f46d040838d3f6464c04c18442b0
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

Bummer, Yahoo doesn't make this easy. =A0When you click on items in the=
'Files' section, it seems to produce links that are only valid for=
the current logged in session. =A0Links to items in the 'Photos' s=
ection seem to work. =A0How about the following?


Roice


On =
Sat, Jun 2, 2012 at 12:55 PM, Eduard Baumann <=3D"mailto:baumann@mcnet.ch" target=3D"_blank">baumann@mcnet.ch>an> wrote:

x #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20

















Sadly the links in your e-mail don't work=20
too.

=A0

-RIGHT:0px;MARGIN-LEFT:5px;MARGIN-RIGHT:0px">

----- Original Message -----



Sent: Saturday, June 02, 2012 7:23=
=20
PM

Subject: Re: [MC4D] Re: color graph=
s of=20
MagicTiles


=A0=20

Cool, thanks Ed.



People have had trouble with the file links before. =A0I'm not s=
ure=20
why, but there must be some common path that results in broken links.=20
=A0Hopefully the following links to your graphs will work.


It looks like you are working on dual graphs. =A0By that I mean you=
=20
made the faces on the puzzles vertices in the graphs. =A0The {8,4} graphs=
=20
all makes sense to me from that perspective, and they definitely help in=
=20
studying the structure. =A0Here's something interesting: turn the 5C =
graph=20
on its side, and check out how it relates to the 10C graph. =A0The {10,4}=
=20
graph is intriguing too.



Looking at the {3,5} 8C graph, and comparing it to /groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/1602345595/vi=
ew?picmode=3D&mode=3Dtn&order=3Dordinal&start=3D1&count=3D2=
0&dir=3Dasc" target=3D"_blank">the one I made
,=A0I think I'm fo=
llowing your graph, but=20
did you make this one when looking at the puzzle with the default colors?=
=20
=A0What does n stand for?



Roice




On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann=
<">baumann@mcnet.ch> wrote:

>



The links are not working in e-mail (why?).=20

Goto to the group to be able to see the=20
links.

Ed


iv>










=20=20=20=20
=20=20=20=20











--f46d040838d3f6464c04c18442b0--




From: Melinda Green <melinda@superliminal.com>
Date: Sat, 02 Jun 2012 16:29:06 -0700
Subject: Re: [MC4D] Re: color graphs of MagicTiles



--------------000308070805070604070505
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit

These work. I guess we just need to remember to use the photos folder.
Looking at the graphs the 9-color only looks slightly more complicated
than its sister's. Is the difference really a proxy for difficulty? If
so, the spherical 8-color FE graph looks complex though Nan solved it in
just 59 twists. Of course we shouldn't be misled by the shortness of his
solutions, but it suggests that an edge-only version can't be very hard.
I'm also just comparing against my experience with the {8,4}s and that
is not much of a guide either but for the opposite reason that I'm a
beginner with these puzzles.

Nan & Ed, can we get your opinions on the {8,4}s?

And Roice, how about a pure edge-turning 8-color {3,5} so that I can
compare against the similar {8,4}s?

Oh, and everyone be sure to notice Roice's new "gliding" setting. It
allows you to "fling" the left-drag rotations of all puzzles. A value of
0 gives the previous behavior in case you don't like it. A value of 1
rotates forever, and values between the two control the damping speed
which controls how quickly to slow the rotation to zero. Thanks, Roice!

-Melinda

On 6/2/2012 2:48 PM, Roice Nelson wrote:
>
>
> Bummer, Yahoo doesn't make this easy. When you click on items in the
> 'Files' section, it seems to produce links that are only valid for the
> current logged in session. Links to items in the 'Photos' section
> seem to work. How about the following?
>
> * color graph ell sph 3,5 8.PNG
>
> * color graph hyp 10,4 6 no.PNG
>
>
> * color graph hyp 8,4 5.PNG
>
>
> * color graph hyp 8,4 9.PNG
>
>
> * color graph hyp 8,4 10.PNG
>
>
>
> Roice
>
>
> On Sat, Jun 2, 2012 at 12:55 PM, Eduard Baumann > > wrote:
>
>
>
> Sadly the links in your e-mail don't work too.
>
> ----- Original Message -----
> *From:* Roice Nelson
> *To:* 4D_Cubing@yahoogroups.com
>
> *Sent:* Saturday, June 02, 2012 7:23 PM
> *Subject:* Re: [MC4D] Re: color graphs of MagicTiles
>
> Cool, thanks Ed.
>
>
> People have had trouble with the file links before. I'm not
> sure why, but there must be some common path that results in
> broken links. Hopefully the following links to your graphs
> will work.
>
> * color graph ell sph 3,5 8.PNG
>
>
> * color graph hyp 10,4 6 no.PNG
>
>
> * color graph hyp 8,4 5.PNG
>
>
> * color graph hyp 8,4 9.PNG
>
>
> * color graph hyp 8,4 10.PNG
>
>
>
> It looks like you are working on dual graphs. By that I mean
> you made the faces on the puzzles vertices in the graphs. The
> {8,4} graphs all makes sense to me from that perspective, and
> they definitely help in studying the structure. Here's
> something interesting: turn the 5C graph on its side, and
> check out how it relates to the 10C graph. The {10,4} graph
> is intriguing too.
>
> Looking at the {3,5} 8C graph, and comparing it to the one I
> made
> , I
> think I'm following your graph, but did you make this one when
> looking at the puzzle with the default colors? What does n
> stand for?
>
> Roice
>
>
> On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann
> > wrote:
>
>
>
> The links are not working in e-mail (why?).
> Goto to the group to be able to see the links.
> Ed
>
>
>
>
>
>
>
>

--------------000308070805070604070505
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit



http-equiv="Content-Type">


These work. I guess we just need to remember to use the photos
folder.

Looking at the graphs the 9-color only looks slightly more
complicated than its sister's. Is the difference really a proxy for
difficulty? If so, the spherical 8-color FE graph looks complex
though Nan solved it in just 59 twists. Of course we shouldn't be
misled by the shortness of his solutions, but it suggests that an
edge-only version can't be very hard. I'm also just comparing
against my experience with the {8,4}s and that is not much of a
guide either but for the opposite reason that I'm a beginner with
these puzzles.



Nan & Ed, can we get your opinions on the {8,4}s?



And Roice, how about a pure edge-turning 8-color {3,5} so that I can
compare against the similar {8,4}s?



Oh, and everyone be sure to notice Roice's new "gliding" setting. It
allows you to "fling" the left-drag rotations of all puzzles. A
value of 0 gives the previous behavior in case you don't like it. A
value of 1 rotates forever, and values between the two control the
damping speed which controls how quickly to slow the rotation to
zero. Thanks, Roice!



-Melinda



On 6/2/2012 2:48 PM, Roice Nelson wrote:
cite="mid:CAEMuGXooYzj3XWFT5hAPMkMN+smRG=+z6KNwHSw1sxCigBHHXw@mail.gmail.com"
type="cite">


Bummer, Yahoo doesn't make this easy.  When you click on items in
the 'Files' section, it seems to produce links that are only valid
for the current logged in session.  Links to items in the 'Photos'
section seem to work.  How about the following?



Roice






On Sat, Jun 2, 2012 at 12:55 PM,
Eduard Baumann < moz-do-not-send="true" href="mailto:baumann@mcnet.ch"
target="_blank">baumann@mcnet.ch>
wrote:







Sadly the links in your e-mail
don't work too.

 



----- Original Message
-----


To: moz-do-not-send="true"
title="4D_Cubing@yahoogroups.com"
href="mailto:4D_Cubing@yahoogroups.com"
target="_blank">4D_Cubing@yahoogroups.com

Sent: Saturday,
June 02, 2012 7:23 PM

Subject: Re:
[MC4D] Re: color graphs of MagicTiles




 


Cool, thanks Ed.







People have had trouble with the file links
before.  I'm not sure why, but there must be
some common path that results in broken links.
 Hopefully the following links to your graphs
will work.


It looks like you are working on dual
graphs.  By that I mean you made the faces on
the puzzles vertices in the graphs.  The {8,4}
graphs all makes sense to me from that
perspective, and they definitely help in
studying the structure.  Here's something
interesting: turn the 5C graph on its side,
and check out how it relates to the 10C graph.
 The {10,4} graph is intriguing too.




Looking at the {3,5} 8C graph, and
comparing it to href="http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/1602345595/view?picmode=&mode=tn&order=ordinal&start=1&count=20&dir=asc"
target="_blank">the one I made
, I think
I'm following your graph, but did you make
this one when looking at the puzzle with the
default colors?  What does n stand for?




Roice





On Sat, Jun 2, 2012
at 7:11 AM, Eduard Baumann < moz-do-not-send="true"
href="mailto:baumann@mcnet.ch"
target="_blank">baumann@mcnet.ch>

wrote:






The links are
not working in e-mail (why?).

Goto to the
group to be able to see the links.

Ed






























--------------000308070805070604070505--




From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Sun, 3 Jun 2012 02:37:20 +0200
Subject: Re: [MC4D] Re: color graphs of MagicTiles



------=_NextPart_000_0014_01CD4131.CCC7C6E0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Melinda: I tried one {8,4} and saw the difficulties. I have not yet continu=
ed my effort.

Roice: photos folder okay.

----- Original Message -----=20
From: Melinda Green=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Sunday, June 03, 2012 1:29 AM
Subject: Re: [MC4D] Re: color graphs of MagicTiles


=20=20=20=20
These work. I guess we just need to remember to use the photos folder.
Looking at the graphs the 9-color only looks slightly more complicated th=
an its sister's. Is the difference really a proxy for difficulty? If so, th=
e spherical 8-color FE graph looks complex though Nan solved it in just 59 =
twists. Of course we shouldn't be misled by the shortness of his solutions,=
but it suggests that an edge-only version can't be very hard. I'm also jus=
t comparing against my experience with the {8,4}s and that is not much of a=
guide either but for the opposite reason that I'm a beginner with these pu=
zzles.

Nan & Ed, can we get your opinions on the {8,4}s?

And Roice, how about a pure edge-turning 8-color {3,5} so that I can comp=
are against the similar {8,4}s?

Oh, and everyone be sure to notice Roice's new "gliding" setting. It allo=
ws you to "fling" the left-drag rotations of all puzzles. A value of 0 give=
s the previous behavior in case you don't like it. A value of 1 rotates for=
ever, and values between the two control the damping speed which controls h=
ow quickly to slow the rotation to zero. Thanks, Roice!

-Melinda

On 6/2/2012 2:48 PM, Roice Nelson wrote:=20

Bummer, Yahoo doesn't make this easy. When you click on items in the '=
Files' section, it seems to produce links that are only valid for the curre=
nt logged in session. Links to items in the 'Photos' section seem to work.=
How about the following?=20
a.. color graph ell sph 3,5 8.PNG=20
b.. color graph hyp 10,4 6 no.PNG=20=20=20
c.. color graph hyp 8,4 5.PNG=20=20
d.. color graph hyp 8,4 9.PNG=20=20
e.. color graph hyp 8,4 10.PNG=20=20
Roice




On Sat, Jun 2, 2012 at 12:55 PM, Eduard Baumann wrot=
e:




Sadly the links in your e-mail don't work too.

----- Original Message -----=20
From: Roice Nelson=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, June 02, 2012 7:23 PM
Subject: Re: [MC4D] Re: color graphs of MagicTiles


=20=20=20=20=20=20=20=20=20=20
Cool, thanks Ed.=20



People have had trouble with the file links before. I'm not sure w=
hy, but there must be some common path that results in broken links. Hopef=
ully the following links to your graphs will work.
a.. color graph ell sph 3,5 8.PNG=20=20=20
b.. color graph hyp 10,4 6 no.PNG=20=20=20
c.. color graph hyp 8,4 5.PNG=20=20
d.. color graph hyp 8,4 9.PNG=20=20
e.. color graph hyp 8,4 10.PNG=20=20
It looks like you are working on dual graphs. By that I mean you m=
ade the faces on the puzzles vertices in the graphs. The {8,4} graphs all =
makes sense to me from that perspective, and they definitely help in studyi=
ng the structure. Here's something interesting: turn the 5C graph on its s=
ide, and check out how it relates to the 10C graph. The {10,4} graph is in=
triguing too.


Looking at the {3,5} 8C graph, and comparing it to the one I made, =
I think I'm following your graph, but did you make this one when looking at=
the puzzle with the default colors? What does n stand for?


Roice



On Sat, Jun 2, 2012 at 7:11 AM, Eduard Baumann w=
rote:




The links are not working in e-mail (why?).=20
Goto to the group to be able to see the links.
Ed









=20=20
------=_NextPart_000_0014_01CD4131.CCC7C6E0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>


Melinda: I tried one {8,4} and saw the=20
difficulties. I have not yet continued my effort.

 

Roice: photos folder okay.

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
href=3D"mailto:melinda@superliminal.com">Melinda Green

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Sunday, June 03, 2012 1:29 A=
M

Subject: Re: [MC4D] Re: color grap=
hs of=20
MagicTiles


 =20

These work. I guess we just need to remember to use the photos=20
folder.
Looking at the graphs the 9-color only looks slightly more=20
complicated than its sister's. Is the difference really a proxy for=20
difficulty? If so, the spherical 8-color FE graph looks complex though Na=
n=20
solved it in just 59 twists. Of course we shouldn't be misled by the shor=
tness=20
of his solutions, but it suggests that an edge-only version can't be very=
=20
hard. I'm also just comparing against my experience with the {8,4}s and t=
hat=20
is not much of a guide either but for the opposite reason that I'm a begi=
nner=20
with these puzzles.

Nan & Ed, can we get your opinions on the=
=20
{8,4}s?

And Roice, how about a pure edge-turning 8-color {3,5} so =
that=20
I can compare against the similar {8,4}s?

Oh, and everyone be sure=
to=20
notice Roice's new "gliding" setting. It allows you to "fling" the left-d=
rag=20
rotations of all puzzles. A value of 0 gives the previous behavior in cas=
e you=20
don't like it. A value of 1 rotates forever, and values between the two=20
control the damping speed which controls how quickly to slow the rotation=
to=20
zero. Thanks, Roice!

-Melinda

On 6/2/2012 2:48 PM, Roice Ne=
lson=20
wrote:=20
cite=3Dmid:CAEMuGXooYzj3XWFT5hAPMkMN+smRG=3D+z6KNwHSw1sxCigBHHXw@mail.gma=
il.com=20
type=3D"cite">Bummer, Yahoo doesn't make this easy.  When you click =
on=20
items in the 'Files' section, it seems to produce links that are only v=
alid=20
for the current logged in session.  Links to items in the 'Photos'=
=20
section seem to work.  How about the following?=20



  • href=3D"http://games.groups.yahoo.com/group/4D_Cubing/files/Eduard/co=
    lor%20graph%20ell%20sph%203%2C5%208.PNG"=20
    moz=3D"true">color graph ell sph 3,5 8.PNG=20
  • href=3D"http://games.groups.yahoo.com/group/4D_Cubing/files/Eduard/co=
    lor%20graph%20hyp%2010%2C4%206%20no.PNG"=20
    moz=3D"true">color graph hyp 10,4 6 no.PNG  =20
  • href=3D"http://games.groups.yahoo.com/group/4D_Cubing/files/Eduard/co=
    lor%20graph%20hyp%208%2C4%205.PNG"=20
    moz=3D"true">color graph hyp 8,4 5.PNG =20
  • href=3D"http://games.groups.yahoo.com/group/4D_Cubing/files/Eduard/co=
    lor%20graph%20hyp%208%2C4%209.PNG"=20
    moz=3D"true">color graph hyp 8,4 9.PNG =20
  • href=3D"http://games.groups.yahoo.com/group/4D_Cubing/files/Eduard/co=
    lor%20graph%20hyp%208%2C4%2010.PNG"=20
    moz=3D"true">color graph hyp 8,4 10.PNG 

Roice





On Sat, Jun 2, 2012 at 12:55 PM, Eduard Bauman=
n dir=3Dltr>< moz=3D"true">baumann@mcnet.ch> wrote:





Sadly the links in your e-mail don't work=20
too.

 



----- Original Message -----

From: <=
A=20
title=3Droice3@gmail.com href=3D"mailto:roice3@gmail.com" target=3D=
_blank=20
moz=3D"true">Roice Nelson

To: title=3D4D_Cubing@yahoogroups.com href=3D"mailto:4D_Cubing@yahoogro=
ups.com"=20
target=3D_blank moz=3D"true">4D_Cubing@yahoogroups.com

Sent: Saturday, June 02, 201=
2 7:23=20
PM

Subject: Re: [MC4D] Re: colo=
r=20
graphs of MagicTiles


 


Cool, thanks Ed.






People have had trouble with the file links before.  I'm =
not=20
sure why, but there must be some common path that results in broken=
=20
links.  Hopefully the following links to your graphs will=20
work.


  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT_T82JY8g6js55yIbhEnvUOv=
    logyhhXTCFwDwiHWlgok-3r83OCddxHOqF3WkIhIdKgwkx6dZN_-a7dnxA/Eduard/color%20g=
    raph%20ell%20sph%203%2C5%208.PNG"=20
    target=3D_blank moz=3D"true">color graph ell sph 3,5 8.PNG&nb=
    sp; =20

  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT32hHYs8g6jsrVsu1iB6G1U4=
    WK-e08hSKNcgcZOvO4wgQio68uIhEqetbY2RtSvm5yyV9A4IJqFEyZ8bhA/Eduard/color%20g=
    raph%20hyp%2010%2C4%206%20no.PNG"=20
    target=3D_blank moz=3D"true">color graph hyp 10,4 6 no.PNG &n=
    bsp;=20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT4scdqo8g6jsXm2reMiFtoRw=
    5-uSvcpddy5jsaXRn0C-WiNcewKMHho77977FgmRShHJ4In6Bxc7v-HVOA/Eduard/color%20g=
    raph%20hyp%208%2C4%205.PNG"=20
    target=3D_blank moz=3D"true">color graph hyp 8,4 5.PNG =
    =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKT59Yo048g6jsSG-hyVLHa2-W=
    Ov1Zw255nryBZoaEa0qQ9W3eUxdResF9XKd0lf4VF6KKk07Ob5mDo_gj6g/Eduard/color%20g=
    raph%20hyp%208%2C4%209.PNG"=20
    target=3D_blank moz=3D"true">color graph hyp 8,4 9.PNG =
    =20
  • href=3D"http://f1.grp.yahoofs.com/v1/cCrKTzEn5F48g6jslyN_rYIT2HYM=
    vPK-RdFDlpUVG2_-MgUobEUK4CCDq72ZovnoyDAHIhIhlCrncR6-eM1WOw/Eduard/color%20g=
    raph%20hyp%208%2C4%2010.PNG"=20
    target=3D_blank moz=3D"true">color graph hyp 8,4 10.PNG =

It looks like you are working on dual graphs.  By that I =
mean=20
you made the faces on the puzzles vertices in the graphs.  The=
=20
{8,4} graphs all makes sense to me from that perspective, and they=
=20
definitely help in studying the structure.  Here's something=20
interesting: turn the 5C graph on its side, and check out how it re=
lates=20
to the 10C graph.  The {10,4} graph is intriguing too.



Looking at the {3,5} 8C graph, and comparing it to href=3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/169485=
3720/pic/1602345595/view?picmode=3D&mode=3Dtn&order=3Dordinal&s=
tart=3D1&count=3D20&dir=3Dasc"=20
target=3D_blank moz=3D"true">the one I made, I think I'm f=
ollowing=20
your graph, but did you make this one when looking at the puzzle wi=
th=20
the default colors?  What does n stand for?



Roice




On Sat, Jun 2, 2012 at 7:11 AM, Eduard Bau=
mann=20
<lank=20
moz=3D"true">baumann@mcnet.ch
>
wrote:

te>



The links are not working in e-mail (why?=
).=20

Goto to the group to be able to see the=20
links.

face=3DArial>Ed


=



<=
/DIV>



------=_NextPart_000_0014_01CD4131.CCC7C6E0--




From: "schuma" <mananself@gmail.com>
Date: Sun, 03 Jun 2012 02:26:20 -0000
Subject: Re: color graphs of MagicTiles



I just got time to solve these {8,4} puzzles. I directly faced them before =
I looked at Ed's drawing.=20

Take the 9-color version for example.=20

I first noticed that some octagons (gray, purple, orange, and cyan) have on=
ly two distinct edges, therefore the commutator of turning these two edges =
is not a 3-cycle. I solved these octagons first, and then avoided using the=
se commutators. This is also what I did in the {3,5} 8C: to solve the speci=
al faces first.

The second thing is, of course, the long long orbits, which surprised me. I=
haven't found out the structure of the orbits yet. But it seems I don't re=
ally need to know the structure to move pieces along them.=20

Nan

--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
> Nan & Ed, can we get your opinions on the {8,4}s?
> -Melinda
>=20




From: Melinda Green <melinda@superliminal.com>
Date: Sat, 02 Jun 2012 20:16:21 -0700
Subject: Re: [MC4D] Re: color graphs of MagicTiles



On 6/2/2012 7:26 PM, schuma wrote:
> I just got time to solve these {8,4} puzzles. I directly faced them before I looked at Ed's drawing.
>
> Take the 9-color version for example.
>
> I first noticed that some octagons (gray, purple, orange, and cyan) have only two distinct edges, therefore the commutator of turning these two edges is not a 3-cycle. I solved these octagons first, and then avoided using these commutators. This is also what I did in the {3,5} 8C: to solve the special faces first.

Well this must be the secret that eluded me. I'll try again using your
method and see what a difference that makes. I had the puzzle nearly
solved by move 125 and then I flailed badly until it came together.

>
> The second thing is, of course, the long long orbits, which surprised me. I haven't found out the structure of the orbits yet. But it seems I don't really need to know the structure to move pieces along them.

Yes, most of the orbits are 16 steps long and intersects with itself
several times in different ways, but as you can that can be largely ignored.

Thanks for taking them on and reporting back.
-Melinda




From: Roice Nelson <roice3@gmail.com>
Date: Sun, 3 Jun 2012 12:07:09 -0500
Subject: Re: [MC4D] Re: color graphs of MagicTiles



--f46d0401fab1a6259304c19472ad
Content-Type: text/plain; charset=ISO-8859-1

On Sat, Jun 2, 2012 at 6:29 PM, Melinda Green wrote:

>
> And Roice, how about a pure edge-turning 8-color {3,5} so that I can
> compare against the similar {8,4}s?
>
>
An edge-only puzzle for that tiling turns out to be impossible. To see
why, pull up the FE version and highlight the edge cuts on the cyan face
(or the purple one). Now imagine increasing the size of these cuts. If we
configure an edge-only version, we can't make the cuts big enough to lead
to non-trivial scrambling without also causing identified cuts to intersect
themselves.

On the positive side, the FE puzzle is quite similar in feel to other
edge-only puzzles, and I bet it could be solved with only [1,1]
commutators. I went ahead and configured similar FE versions for the
{8,4}s, in case that would be helpful for comparisons. These FE puzzles
make me think of bubbles, which might be a nice name for them :)

seeya,
Roice

--f46d0401fab1a6259304c19472ad
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable


On Sat, Jun 2, 2012 at 6:29 PM, Melinda Gree=
n=A0wrote:
border-left:1px #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20

=20=20
=20=20=20=20
=20=20


And Roice, how about a pure edge-turning 8-color {3,5} so that I can
compare against the similar {8,4}s?


=
An edge-only puzzle for that tiling turns out to be impossible. =
=A0To see why, pull up the FE version and highlight the edge cuts on the cy=
an face (or the purple one). =A0Now imagine increasing the size of these cu=
ts. =A0If we configure an edge-only version, we can't make the cuts big=
enough to lead to non-trivial scrambling without also causing identified c=
uts to intersect themselves.



On the positive side, the FE puzzle is quite similar in=
feel to other edge-only puzzles, and I bet it could be solved with only [1=
,1] commutators. =A0I went ahead and configured similar FE versions for the=
{8,4}s, in case that would be helpful for comparisons. =A0These FE puzzles=
make me think of bubbles, which might be a nice name for them :)


seeya,
Roice


--f46d0401fab1a6259304c19472ad--




From: Melinda Green <melinda@superliminal.com>
Date: Sun, 03 Jun 2012 12:40:02 -0700
Subject: Re: [MC4D] Re: color graphs of MagicTiles



--------------090203040604020909010408
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit

Ah ha! I should have thought about that for a few more seconds before
asking because the whole point was because this was another screwy
topology and I forgot to look for the screwiness.

I did briefly look at the sorts of paths that the petals can take and
they are quite interesting. Alternating LLRRLL, etc. can create a
straightish ziz-zag path that miraculously involves all faces except
those two odd ones, whereas if you start with one of those odd faces you
hit a dead-end at the other one! Fascinating.

And yes, they do look a lot like streams of bubbles filling the air. I
like it!
-Melinda

On 6/3/2012 10:07 AM, Roice Nelson wrote:
>
>
>
> On Sat, Jun 2, 2012 at 6:29 PM, Melinda Green wrote:
>
>
> And Roice, how about a pure edge-turning 8-color {3,5} so that I
> can compare against the similar {8,4}s?
>
>
> An edge-only puzzle for that tiling turns out to be impossible. To
> see why, pull up the FE version and highlight the edge cuts on the
> cyan face (or the purple one). Now imagine increasing the size of
> these cuts. If we configure an edge-only version, we can't make the
> cuts big enough to lead to non-trivial scrambling without also causing
> identified cuts to intersect themselves.
>
> On the positive side, the FE puzzle is quite similar in feel to other
> edge-only puzzles, and I bet it could be solved with only [1,1]
> commutators. I went ahead and configured similar FE versions for the
> {8,4}s, in case that would be helpful for comparisons. These FE
> puzzles make me think of bubbles, which might be a nice name for them :)
>
> seeya,
> Roice
>
>
>

--------------090203040604020909010408
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit



http-equiv="Content-Type">


Ah ha! I should have thought about that for a few more seconds
before asking because the whole point was because this was another
screwy topology and I forgot to look for the screwiness.



I did briefly look at the sorts of paths that the petals can take
and they are quite interesting. Alternating LLRRLL, etc. can create
a straightish ziz-zag path that miraculously involves all faces
except those two odd ones, whereas if you start with one of those
odd faces you hit a dead-end at the other one! Fascinating.



And yes, they do look a lot like streams of bubbles filling the air.
I like it!

-Melinda



On 6/3/2012 10:07 AM, Roice Nelson wrote:
cite="mid:CAEMuGXosX4kdWbiFr-RWT5jNxqO0OB+f0EzR=3tQqr5r2yWoAw@mail.gmail.com"
type="cite">




On Sat, Jun 2, 2012 at 6:29 PM, Melinda
Green wrote:




And Roice, how about a pure edge-turning 8-color {3,5} so
that I can compare against the similar {8,4}s?








An edge-only puzzle for that tiling turns out to be
impossible.  To see why, pull up the FE version and highlight
the edge cuts on the cyan face (or the purple one).  Now
imagine increasing the size of these cuts.  If we configure an
edge-only version, we can't make the cuts big enough to lead
to non-trivial scrambling without also causing identified cuts
to intersect themselves.




On the positive side, the FE puzzle is quite similar in
feel to other edge-only puzzles, and I bet it could be solved
with only [1,1] commutators.  I went ahead and configured
similar FE versions for the {8,4}s, in case that would be
helpful for comparisons.  These FE puzzles make me think of
bubbles, which might be a nice name for them :)




seeya,

Roice








--------------090203040604020909010408--





Return to MagicCube4D main page
Return to the Superliminal home page