Thread: "Making a puzzle based on 11-cell"

These thoughts can apply to the 11-cell as well.=A0 May=
be the t=3D"_blank">icosahedral honeycomb be used with identification of eleme=
nts (?)=A0 The "graph with small colored ribbons" approach seems =
like it would work better in this case because the graph=A0embedding is les=
s complex.

For the wiki image you link to, if the puzzle represent=
ation were based on this, I think it would be nice if the pristine state sh=
owed solid colored hemi-icosahedra rather than multicolored ones.=A0 They l=
ook to be trying to show all the connections between cells in the wiki imag=
e, but having them multi-colored makes it feel like a 2D puzzle, when it is=
so far from that :)

Although any representation would be an achievement, I&=
#39;m heavily biased towards those which are connected myself.=A0 Even if c=
onnected versions are messy looking on the screen, I find the dissected var=
iants less elegant.=A0 (With MC5D, I was never willing to approach it by sh=
owing the hyperfaces laid out side by side.=A0 I wanted it all connected up=
.)

Anyway, those are some quick thoughts, but I'm inte=
rested to discuss and spec more on these abstract puzzles!

div>



--bcaec554da9c8dcb5c04c009104c--

---

From: "schuma" <mananself@gmail.com>
Date: Wed, 23 May 2012 02:50:37 -0000
Subject: Re: Making a puzzle based on 11-cell

Hi guys,

In the last week I've been working on the 11-cell. Although not completed, =
it's a playable puzzle now. I'll keep refining it. But I want to let you gu=
ys see the current version of the applet:

http://people.bu.edu/nanma/ElevenCell/ElevenCell.html

When you open it, you can see eleven hemi-icosahedral cells. The color sche=
me is exactly identical to the one here: [http://en.wikipedia.org/wiki/File=
:Hemi-icosahedron_coloured.svg]. But in that figure, the faces are colored =
to be identical to the opposite cell, whereas in my illustration, the faces=
are colored to be identical to the cell it belongs to. I also changed the =
layout of the cells to make it more intuitive.

There are 11 cells. I consider each cell has a core that never moves. The c=
ore is represented by a colored disk as the background of a cell. Just like=
the centers of the Rubik's cube, the cores should be used as references du=
ring a solve. There are 2-color face pieces, 3-color edge pieces, and 6-col=
or vertex pieces. When you move the cursor on a cell, the turning region wi=
ll be highlighted. The region includes all the pieces that have stickers on=
the hemi-icosahedron.=20

Left or right clicking the mouse will twist the puzzle. I'm allowing twists=
around vertices and face centers. When the cursor is on top of a vertex, a=
ll the stickers on the vertex piece will be circled. When the cursor is on =
top of a triangular face, the two stickers on the face piece will be circle=
d. These features can help you see the connectivity of 11-cell, to some ext=
end. Please try click on the red cell, which is considered by myself as the=
"central cell". Twists around that cell are more symmetrical and thus unde=
rstandable.=20

Holding shift and clicking mouse will re-orient the whole puzzle. Currently=
this is the only way to re-orient.=20

The checkboxes "F", "E", and "V" controls the visibility of the faces, edge=
s and vertices. The percentages of stickers in the correct position are als=
o shown. When all are solved, the background turns light blue.

The meaning of the buttons "reset" "scramble" and "undo" are self-explainin=
g. I put a "1-move scramble" button for testing purpose. But I found it was=
already a nontrivial challenge. Let me know if you can solve it!

In the future I will fix bugs, and add macros. I haven't seriously thought =
about how to solve it. But it looks like a pretty deep cut puzzle: each tur=
n affects six out of eleven vertices, and it should be hard to solve. So I =
think macros should be necessary.

Nan

--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> Hi Nan,
>=20
> I have devoted a little thought to the idea of making puzzles out of the
> 11-cell and 57-cell, mainly the latter. I also would love to see a
> realization of these abstract polytopes as puzzles.
>=20
> For the 57-cell, it turns out you can consider it derived from the {5,3,5=
}
> hyperbolic honeycombneycomb>with
> identification of certain elements (wiki says this anyway). Because
> the cells themselves are abstract, it may be more complex than just
> identification of cells like in Andrey's MHT633. But there could be a ni=
ce
> representation achievable by taking the approach of showing the object
> unrolled on the {5,3,5} honeycomb.
>=20
> As far as showing the object rolled up, my best mental image so far has
> been to display an embedding the graph with some kind of coloring attache=
d
> to the edges. There would be no solid 3D stickers, just edges with small
> ribbons of colors coming off of them (like Sequin's images of the 11-cell
> in the paper you link to). For the 57-cell, each edge would have 5
> attached colors. Twisting would break some edges apart and connect them
> back together to others at the twist end. If animated, the movements wou=
ld
> involve all kinds of distortions. I hope I'm painting the mental picture
> well enough.
>=20
> Toward that end, I've played around with embedding the graph of the 57-ce=
ll
> in 3D space, in the attempt to find nice ones. Since the object lives
> in such a high dimensional space, I've had little success. But I can tel=
l
> you how to connect up the graph (and can share code on this if anyone was
> interested). There is an open
> challengee-made-in-vzome-without-strut-crossings>on
> the
> vzome group to find a 57-cell skeleton model in zo=
me
> using a limited set of directions and without intersection of graph edges=
.
> We don't know if it is possible, but after my attempts I'm confident sayi=
ng
> it will look pretty ugly if such a model is found! We've found many nice
> zome embeddings of the hemi-dodec though. And without the restrictions o=
f
> zome, there are probably some reasonable looking embeddings that could be
> used for a puzzle.
>=20
> These thoughts can apply to the 11-cell as well. Maybe the icosahedral
> honeycomb be used wi=
th
> identification of elements (?) The "graph with small colored ribbons"
> approach seems like it would work better in this case because the
> graph embedding is less complex.
>=20
> For the wiki image you link to, if the puzzle representation were based o=
n
> this, I think it would be nice if the pristine state showed solid colored
> hemi-icosahedra rather than multicolored ones. They look to be trying to
> show all the connections between cells in the wiki image, but having them
> multi-colored makes it feel like a 2D puzzle, when it is so far from that=
:)
>=20
> Although any representation would be an achievement, I'm heavily biased
> towards those which are connected myself. Even if connected versions are
> messy looking on the screen, I find the dissected variants less elegant.
> (With MC5D, I was never willing to approach it by showing the hyperfaces
> laid out side by side. I wanted it all connected up.)
>=20
> Anyway, those are some quick thoughts, but I'm interested to discuss and
> spec more on these abstract puzzles!
>=20
> Cheers,
> Roice
>=20
> P.S. I was able to visit with Carlo a little at the Gathering as well, a=
nd
> really enjoyed the brief time I got to talk with him. He thinks about
> really amazing things, and I just love hearing what he has to say. His
> talk was on the 11-cell. Here's a short
> paper
> he
> wrote on the 57-cell. It's cool you have access to his office hours.
>=20
>=20
> On Mon, May 14, 2012 at 3:06 PM, schuma wrote:
>=20
> > Hi everyone,
> >
> > Last night I was surfing the internet looking for some potential shapes=
to
> > make puzzles. Then I looked at the 11-cell <
> > http://en.wikipedia.org/wiki/11-cell>. I found that this shape, togethe=
r
> > with the more complicated 57-cell, was mentioned once in our group in t=
his
> > post and
> > Andrey's reply. But there's no follow up discussion about them.
> >
> > 11-cell is an abstract regular four-dimensional polytope, where each ce=
ll
> > is a hemi-icosahedron. It can be illustrated nicely in this way <
> > http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg> by
> > drawing eleven half icosahedra, with many vertices, edges and faces
> > identified.
> >
> > I feel that we can use this illustration as the interface of the "Magic
> > 11-cell" simulator. We can define the following pieces: eleven 6-color
> > vertices, fifty-five 3-color edges, fifty-five 2-color faces, and eleve=
n
> > 1-color cell centers (never move). We ignore other tiny pieces that wou=
ld
> > come if we define a proper geometry in a high dimensional space and
> > properly cut the puzzle by hyperplanes (think of the small pieces in th=
e
> > 16-cell puzzle).
> >
> > After defining the pieces, we can consider a twist of a hemi-icosahedra=
l
> > cell as a permutation of the vertices, edges and faces related to that
> > cell. After that, a cell-turning 11-cell will be well-defined.
> >
> > Through the wikipedia page, I found some recent presentations by Prof.
> > Carlo Sequin at UC Berkeley about visualizing the 11-cell and the 57-ce=
ll.
> > Since I'm also at Berkeley and there's his office hour this morning, I
> > stopped by his office, introduced myself and discussed happily about th=
e
> > possibility of combining a twisty puzzle with the 11-cell. He confirmed
> > this possibility and was happy to see it coming out someday.
> >
> > About the puzzle based on a single hemi-icosahedron, which has been
> > implemented in Magic Tile v2, he suggested a 3D visualization based on =
this
> > octahedral shape: see Fig. 4(c) in this paper: <
> > http://www.cs.berkeley.edu/~sequin/PAPERS/2007_ISAMA_11Cell.pdf>. He
> > likes this shape a lot. While it's a good visualization for one
> > hemi-icosahedron, it's hard to imagine combining eleven of them to form=
a
> > 11-cell. So he said the illustration <
> > http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg> would =
be
> > better for the 11-cell.
> >
> > It turns out he knew Melinda Green through the Gathering for Gardner
> > meeting. And he said that he had some thoughts about using the 11-cell =
as a
> > building block of IRP, and he needs to write to Melinda about it.
> >
> > His office is filled by tons of different Math models, paper-made or 3D
> > printed. It's like a toy store.
> >
> > Any thoughts for this 11-cell thing?
> >
> > Nan
> >
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>

---

From: Roice Nelson <roice3@gmail.com>
Date: Wed, 23 May 2012 15:29:29 -0500
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell

--f46d04088ef503dc9104c0b9fe89
Content-Type: text/plain; charset=ISO-8859-1

This is fantastic Nan!

I really like your design choice for displaying the core colors. It is
especially lovely how clean the pristine state looks.

It looks fair to say this is a "cell turning" 11-Cell. For twisting a
cell, would it be difficult to also include twisting the cell around an
edge? In addition to giving full cell-turning functionality, this would be
helpful to see how the 3C edges connect up.

On the 3^4, you can do 3C/4C twists, then solve them with 2C twists. The
situation here is analogous. You can do a single 6C twist, then solve it
with three 2C twists. It's a good bite-sized challenge to try! I don't
know yet if you can do a single 2C, then solve with 6C twists. That will
be a fun question to reason through.

I realize the slicing is abstract (topological vs. geometric). I think
it'd be nice to make the size of the 3C/6C pieces bigger, maybe even
controllable with a slider or something. This would make the puzzle feel a
little more like a classic Rubik's Cube.

Not a big deal, but I think it'd be better if puzzle reorientations did
not increment the move count.

My brief experience with this makes me wonder about a "vertex turning"
11-cell as well. Overcoming the hurdle of how to make twists on a VT
puzzle seems especially difficult (even more so than it was for the
polychora puzzles).

Great work! It's awesome to see permutation puzzles enter the domain of
abstract polytopes, and I look forward to studying this more :D

Cheers,
Roice


On Tue, May 22, 2012 at 9:50 PM, schuma wrote:

> Hi guys,
>
> In the last week I've been working on the 11-cell. Although not completed,
> it's a playable puzzle now. I'll keep refining it. But I want to let you
> guys see the current version of the applet:
>
> http://people.bu.edu/nanma/ElevenCell/ElevenCell.html
>
> When you open it, you can see eleven hemi-icosahedral cells. The color
> scheme is exactly identical to the one here: [
> http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg]. But in
> that figure, the faces are colored to be identical to the opposite cell,
> whereas in my illustration, the faces are colored to be identical to the
> cell it belongs to. I also changed the layout of the cells to make it more
> intuitive.
>
> There are 11 cells. I consider each cell has a core that never moves. The
> core is represented by a colored disk as the background of a cell. Just
> like the centers of the Rubik's cube, the cores should be used as
> references during a solve. There are 2-color face pieces, 3-color edge
> pieces, and 6-color vertex pieces. When you move the cursor on a cell, the
> turning region will be highlighted. The region includes all the pieces that
> have stickers on the hemi-icosahedron.
>
> Left or right clicking the mouse will twist the puzzle. I'm allowing
> twists around vertices and face centers. When the cursor is on top of a
> vertex, all the stickers on the vertex piece will be circled. When the
> cursor is on top of a triangular face, the two stickers on the face piece
> will be circled. These features can help you see the connectivity of
> 11-cell, to some extend. Please try click on the red cell, which is
> considered by myself as the "central cell". Twists around that cell are
> more symmetrical and thus understandable.
>
> Holding shift and clicking mouse will re-orient the whole puzzle.
> Currently this is the only way to re-orient.
>
> The checkboxes "F", "E", and "V" controls the visibility of the faces,
> edges and vertices. The percentages of stickers in the correct position are
> also shown. When all are solved, the background turns light blue.
>
> The meaning of the buttons "reset" "scramble" and "undo" are
> self-explaining. I put a "1-move scramble" button for testing purpose. But
> I found it was already a nontrivial challenge. Let me know if you can solve
> it!
>
> In the future I will fix bugs, and add macros. I haven't seriously thought
> about how to solve it. But it looks like a pretty deep cut puzzle: each
> turn affects six out of eleven vertices, and it should be hard to solve. So
> I think macros should be necessary.
>
> Nan
>

--f46d04088ef503dc9104c0b9fe89
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

>My brief experience with this makes me wonder about a "vertex turning=
" 11-cell as well.=A0 Overcoming the hurdle of how to make twists on a=
VT puzzle seems especially difficult (even more so than it was for the pol=
ychora puzzles).

=A0

Great work!=A0 It's awesome to see permutation puzzl=
es enter the domain of abstract polytopes, and I look forward to=A0studying=
this more=A0:D

=A0

Cheers,

Roice

<=
br>=A0

I'm proud. I did the 1-scramble!IV>





------=_NextPart_000_0014_01CD394B.3A7551B0--

---

From: Melinda Green <melinda@superliminal.com>
Date: Wed, 23 May 2012 16:22:35 -0700
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell

--------------060006060606000001090203
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit

Congratulations, Ed!
That's pretty funny when solving a single twist of any puzzle can be
tricky. So has anybody worked out any algorithms? Who will be the first
to solve this beast? I'm looking at you, Andrey! :-)

On 5/23/2012 4:19 PM, Eduard Baumann wrote:
>
>
> I'm proud. I did the 1-scramble!
> 17 moves, 00:04:33
> ;-)
> Ed

--------------060006060606000001090203
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Content-Transfer-Encoding: 7bit



http-equiv="Content-Type">


Congratulations, Ed!

That's pretty funny when solving a single twist of any puzzle can be
tricky. So has anybody worked out any algorithms? Who will be the
first to solve this beast? I'm looking at you, Andrey!  :-)



On 5/23/2012 4:19 PM, Eduard Baumann wrote:

type="cite">

http-equiv="Content-Type">

I'm proud. I did the 1-scramble!

17 moves, 00:04:33

 

;-)

Ed

 

--------------060006060606000001090203--

---

From: "Matthew" <damienturtle@hotmail.co.uk>
Date: Wed, 23 May 2012 23:29:17 -0000
Subject: [MC4D] Re: Making a puzzle based on 11-cell

My first attempt was 16 moves. It's crazy how difficult it is! I've littl=
e idea how this geometry works, but I'm planning to try and figure it out. =
Might not be able to solve this beast, but I'll at least have some proper =
way of understanding what I'm looking at.

Matt

--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Congratulations, Ed!
> That's pretty funny when solving a single twist of any puzzle can be=20
> tricky. So has anybody worked out any algorithms? Who will be the first=20
> to solve this beast? I'm looking at you, Andrey! :-)
>=20
> On 5/23/2012 4:19 PM, Eduard Baumann wrote:
> >
> >
> > I'm proud. I did the 1-scramble!
> > 17 moves, 00:04:33
> > ;-)
> > Ed
>

---

From: "Eduard" <baumann@mcnet.ch>
Date: Wed, 23 May 2012 23:36:15 -0000
Subject: Re: Making a puzzle based on 11-cell

Wonderful! Awesome! Thanks.
You show he connection of the 6C pieces and of the 2C pieces because those =
turning axis are active. How about showing he connection for the 3C pieces?
For me it would be very helpful if all stickers are labeled. This would har=
m the very clean and beautyful puzzle. But what about showing the label of =
the sticker where the mouse pointer is on in a small window?
Kind regards
Ed

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Hi guys,
>=20
> In the last week I've been working on the 11-cell. Although not completed=
, it's a playable puzzle now. I'll keep refining it. But I want to let you =
guys see the current version of the applet:
>=20
> http://people.bu.edu/nanma/ElevenCell/ElevenCell.html
>=20
> When you open it, you can see eleven hemi-icosahedral cells. The color sc=
heme is exactly identical to the one here: [http://en.wikipedia.org/wiki/Fi=
le:Hemi-icosahedron_coloured.svg]. But in that figure, the faces are colore=
d to be identical to the opposite cell, whereas in my illustration, the fac=
es are colored to be identical to the cell it belongs to. I also changed th=
e layout of the cells to make it more intuitive.
>=20
> There are 11 cells. I consider each cell has a core that never moves. The=
core is represented by a colored disk as the background of a cell. Just li=
ke the centers of the Rubik's cube, the cores should be used as references =
during a solve. There are 2-color face pieces, 3-color edge pieces, and 6-c=
olor vertex pieces. When you move the cursor on a cell, the turning region =
will be highlighted. The region includes all the pieces that have stickers =
on the hemi-icosahedron.=20
>=20
> Left or right clicking the mouse will twist the puzzle. I'm allowing twis=
ts around vertices and face centers. When the cursor is on top of a vertex,=
all the stickers on the vertex piece will be circled. When the cursor is o=
n top of a triangular face, the two stickers on the face piece will be circ=
led. These features can help you see the connectivity of 11-cell, to some e=
xtend. Please try click on the red cell, which is considered by myself as t=
he "central cell". Twists around that cell are more symmetrical and thus un=
derstandable.=20
>=20
> Holding shift and clicking mouse will re-orient the whole puzzle. Current=
ly this is the only way to re-orient.=20
>=20
> The checkboxes "F", "E", and "V" controls the visibility of the faces, ed=
ges and vertices. The percentages of stickers in the correct position are a=
lso shown. When all are solved, the background turns light blue.
>=20
> The meaning of the buttons "reset" "scramble" and "undo" are self-explain=
ing. I put a "1-move scramble" button for testing purpose. But I found it w=
as already a nontrivial challenge. Let me know if you can solve it!
>=20
> In the future I will fix bugs, and add macros. I haven't seriously though=
t about how to solve it. But it looks like a pretty deep cut puzzle: each t=
urn affects six out of eleven vertices, and it should be hard to solve. So =
I think macros should be necessary.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> >
> > Hi Nan,
> >=20
> > I have devoted a little thought to the idea of making puzzles out of th=
e
> > 11-cell and 57-cell, mainly the latter. I also would love to see a
> > realization of these abstract polytopes as puzzles.
> >=20
> > For the 57-cell, it turns out you can consider it derived from the {5,3=
,5}
> > hyperbolic honeycombhoneycomb>with
> > identification of certain elements (wiki says this anyway). Because
> > the cells themselves are abstract, it may be more complex than just
> > identification of cells like in Andrey's MHT633. But there could be a =
nice
> > representation achievable by taking the approach of showing the object
> > unrolled on the {5,3,5} honeycomb.
> >=20
> > As far as showing the object rolled up, my best mental image so far has
> > been to display an embedding the graph with some kind of coloring attac=
hed
> > to the edges. There would be no solid 3D stickers, just edges with sma=
ll
> > ribbons of colors coming off of them (like Sequin's images of the 11-ce=
ll
> > in the paper you link to). For the 57-cell, each edge would have 5
> > attached colors. Twisting would break some edges apart and connect the=
m
> > back together to others at the twist end. If animated, the movements w=
ould
> > involve all kinds of distortions. I hope I'm painting the mental pictu=
re
> > well enough.
> >=20
> > Toward that end, I've played around with embedding the graph of the 57-=
cell
> > in 3D space, in the attempt to find nice ones. Since the object lives
> > in such a high dimensional space, I've had little success. But I can t=
ell
> > you how to connect up the graph (and can share code on this if anyone w=
as
> > interested). There is an open
> > challenge-be-made-in-vzome-without-strut-crossings>on
> > the
> > vzome group to find a 57-cell skeleton model in =
zome
> > using a limited set of directions and without intersection of graph edg=
es.
> > We don't know if it is possible, but after my attempts I'm confident sa=
ying
> > it will look pretty ugly if such a model is found! We've found many ni=
ce
> > zome embeddings of the hemi-dodec though. And without the restrictions=
of
> > zome, there are probably some reasonable looking embeddings that could =
be
> > used for a puzzle.
> >=20
> > These thoughts can apply to the 11-cell as well. Maybe the icosahedral
> > honeycomb be used =
with
> > identification of elements (?) The "graph with small colored ribbons"
> > approach seems like it would work better in this case because the
> > graph embedding is less complex.
> >=20
> > For the wiki image you link to, if the puzzle representation were based=
on
> > this, I think it would be nice if the pristine state showed solid color=
ed
> > hemi-icosahedra rather than multicolored ones. They look to be trying =
to
> > show all the connections between cells in the wiki image, but having th=
em
> > multi-colored makes it feel like a 2D puzzle, when it is so far from th=
at :)
> >=20
> > Although any representation would be an achievement, I'm heavily biased
> > towards those which are connected myself. Even if connected versions a=
re
> > messy looking on the screen, I find the dissected variants less elegant=
.
> > (With MC5D, I was never willing to approach it by showing the hyperface=
s
> > laid out side by side. I wanted it all connected up.)
> >=20
> > Anyway, those are some quick thoughts, but I'm interested to discuss an=
d
> > spec more on these abstract puzzles!
> >=20
> > Cheers,
> > Roice
> >=20
> > P.S. I was able to visit with Carlo a little at the Gathering as well,=
and
> > really enjoyed the brief time I got to talk with him. He thinks about
> > really amazing things, and I just love hearing what he has to say. His
> > talk was on the 11-cell. Here's a short
> > paperf>
> > he
> > wrote on the 57-cell. It's cool you have access to his office hours.
> >=20
> >=20
> > On Mon, May 14, 2012 at 3:06 PM, schuma wrote:
> >=20
> > > Hi everyone,
> > >
> > > Last night I was surfing the internet looking for some potential shap=
es to
> > > make puzzles. Then I looked at the 11-cell <
> > > http://en.wikipedia.org/wiki/11-cell>. I found that this shape, toget=
her
> > > with the more complicated 57-cell, was mentioned once in our group in=
this
> > > post and
> > > Andrey's reply. But there's no follow up discussion about them.
> > >
> > > 11-cell is an abstract regular four-dimensional polytope, where each =
cell
> > > is a hemi-icosahedron. It can be illustrated nicely in this way <
> > > http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg> by
> > > drawing eleven half icosahedra, with many vertices, edges and faces
> > > identified.
> > >
> > > I feel that we can use this illustration as the interface of the "Mag=
ic
> > > 11-cell" simulator. We can define the following pieces: eleven 6-colo=
r
> > > vertices, fifty-five 3-color edges, fifty-five 2-color faces, and ele=
ven
> > > 1-color cell centers (never move). We ignore other tiny pieces that w=
ould
> > > come if we define a proper geometry in a high dimensional space and
> > > properly cut the puzzle by hyperplanes (think of the small pieces in =
the
> > > 16-cell puzzle).
> > >
> > > After defining the pieces, we can consider a twist of a hemi-icosahed=
ral
> > > cell as a permutation of the vertices, edges and faces related to tha=
t
> > > cell. After that, a cell-turning 11-cell will be well-defined.
> > >
> > > Through the wikipedia page, I found some recent presentations by Prof=
.
> > > Carlo Sequin at UC Berkeley about visualizing the 11-cell and the 57-=
cell.
> > > Since I'm also at Berkeley and there's his office hour this morning, =
I
> > > stopped by his office, introduced myself and discussed happily about =
the
> > > possibility of combining a twisty puzzle with the 11-cell. He confirm=
ed
> > > this possibility and was happy to see it coming out someday.
> > >
> > > About the puzzle based on a single hemi-icosahedron, which has been
> > > implemented in Magic Tile v2, he suggested a 3D visualization based o=
n this
> > > octahedral shape: see Fig. 4(c) in this paper: <
> > > http://www.cs.berkeley.edu/~sequin/PAPERS/2007_ISAMA_11Cell.pdf>. He
> > > likes this shape a lot. While it's a good visualization for one
> > > hemi-icosahedron, it's hard to imagine combining eleven of them to fo=
rm a
> > > 11-cell. So he said the illustration <
> > > http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg> woul=
d be
> > > better for the 11-cell.
> > >
> > > It turns out he knew Melinda Green through the Gathering for Gardner
> > > meeting. And he said that he had some thoughts about using the 11-cel=
l as a
> > > building block of IRP, and he needs to write to Melinda about it.
> > >
> > > His office is filled by tons of different Math models, paper-made or =
3D
> > > printed. It's like a toy store.
> > >
> > > Any thoughts for this 11-cell thing?
> > >
> > > Nan
> > >
> > >
> > >
> > > ------------------------------------
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>

---

From: "schuma" <mananself@gmail.com>
Date: Wed, 23 May 2012 23:45:29 -0000
Subject: Re: Making a puzzle based on 11-cell

Great job, Ed!

Because the pattern in a hemi-icosahedron is nonorientable (like on a Mobiu=
s strip). Sometimes you will see that you need to mirror a cell. I wonder i=
f you met the tricky situation at this end of your solve.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>
> I'm proud. I did the 1-scramble!
> 17 moves, 00:04:33
>=20
> ;-)
> Ed
>

---

From: "schuma" <mananself@gmail.com>
Date: Wed, 23 May 2012 23:52:01 -0000
Subject: Re: Making a puzzle based on 11-cell

Roice also asked about the 3C pieces. As I replied earlier, I plan to show =
the connectivity of 3C's and turn around the edges if you hold the ctrl but=
ton. I'll implement this in a day or two.

Can you elaborate the meaning of "label"? In my terminology, there are seve=
ral "stickers" on each "piece". Should the "labels" distinct for different =
pieces, or different stickers?=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> Wonderful! Awesome! Thanks.
> You show he connection of the 6C pieces and of the 2C pieces because thos=
e turning axis are active. How about showing he connection for the 3C piece=
s?
> For me it would be very helpful if all stickers are labeled. This would h=
arm the very clean and beautyful puzzle. But what about showing the label o=
f the sticker where the mouse pointer is on in a small window?
> Kind regards
> Ed

---

From: "Eduard" <baumann@mcnet.ch>
Date: Thu, 24 May 2012 01:28:08 -0000
Subject: Re: Making a puzzle based on 11-cell

The "labels" should be distinct for different stickers!

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Roice also asked about the 3C pieces. As I replied earlier, I plan to sho=
w the connectivity of 3C's and turn around the edges if you hold the ctrl b=
utton. I'll implement this in a day or two.
>=20
> Can you elaborate the meaning of "label"? In my terminology, there are se=
veral "stickers" on each "piece". Should the "labels" distinct for differen=
t pieces, or different stickers?=20
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> >
> > Wonderful! Awesome! Thanks.
> > You show he connection of the 6C pieces and of the 2C pieces because th=
ose turning axis are active. How about showing he connection for the 3C pie=
ces?
> > For me it would be very helpful if all stickers are labeled. This would=
harm the very clean and beautyful puzzle. But what about showing the label=
of the sticker where the mouse pointer is on in a small window?
> > Kind regards
> > Ed
>

---

From: "Eduard" <baumann@mcnet.ch>
Date: Thu, 24 May 2012 01:32:14 -0000
Subject: Re: Making a puzzle based on 11-cell

Not the sticker color number but an individual label for each sticker.

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> The "labels" should be distinct for different stickers!
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> >
> > Roice also asked about the 3C pieces. As I replied earlier, I plan to s=
how the connectivity of 3C's and turn around the edges if you hold the ctrl=
button. I'll implement this in a day or two.
> >=20
> > Can you elaborate the meaning of "label"? In my terminology, there are =
several "stickers" on each "piece". Should the "labels" distinct for differ=
ent pieces, or different stickers?=20
> >=20
> > Nan
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > >
> > > Wonderful! Awesome! Thanks.
> > > You show he connection of the 6C pieces and of the 2C pieces because =
those turning axis are active. How about showing he connection for the 3C p=
ieces?
> > > For me it would be very helpful if all stickers are labeled. This wou=
ld harm the very clean and beautyful puzzle. But what about showing the lab=
el of the sticker where the mouse pointer is on in a small window?
> > > Kind regards
> > > Ed
> >
>

---

From: "Eduard" <baumann@mcnet.ch>
Date: Thu, 24 May 2012 01:42:26 -0000
Subject: Re: Making a puzzle based on 11-cell

I fear you retain only the color of each sticker in your program and not an=
individual label. I know that "puzzle solved" is declared when the colors =
are "homogeneous" and NOT when each sticker is at home. But to see where th=
e stickers go when I'm studying sequences the color of the sticker is not s=
ufficient.

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> Not the sticker color number but an individual label for each sticker.
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> >
> > The "labels" should be distinct for different stickers!
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > >
> > > Roice also asked about the 3C pieces. As I replied earlier, I plan to=
show the connectivity of 3C's and turn around the edges if you hold the ct=
rl button. I'll implement this in a day or two.
> > >=20
> > > Can you elaborate the meaning of "label"? In my terminology, there ar=
e several "stickers" on each "piece". Should the "labels" distinct for diff=
erent pieces, or different stickers?=20
> > >=20
> > > Nan
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > > >
> > > > Wonderful! Awesome! Thanks.
> > > > You show he connection of the 6C pieces and of the 2C pieces becaus=
e those turning axis are active. How about showing he connection for the 3C=
pieces?
> > > > For me it would be very helpful if all stickers are labeled. This w=
ould harm the very clean and beautyful puzzle. But what about showing the l=
abel of the sticker where the mouse pointer is on in a small window?
> > > > Kind regards
> > > > Ed
> > >
> >
>

---

From: "schuma" <mananself@gmail.com>
Date: Thu, 24 May 2012 03:23:19 -0000
Subject: Re: Making a puzzle based on 11-cell

Ed,

You are right on that for each sticker I only keep the color but not an ID.=
When the puzzle is rotated, the only colors are changed. I will figure out=
a way to highlight or label a sticker and "trace" its movement. I think th=
at would be great for you to use.

The "modified way of move counting" and "control button for selecting edges=
" are online now. When you use the control button, please make sure the puz=
zle get focus. The focus may be on other windows or in the input/output tex=
t boxes. The simplest way to focus on the puzzle is to click somewhere betw=
een the disks.=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> I fear you retain only the color of each sticker in your program and not =
an individual label. I know that "puzzle solved" is declared when the color=
s are "homogeneous" and NOT when each sticker is at home. But to see where =
the stickers go when I'm studying sequences the color of the sticker is not=
sufficient.
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> >
> > Not the sticker color number but an individual label for each sticker.
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > >
> > > The "labels" should be distinct for different stickers!
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > > >
> > > > Roice also asked about the 3C pieces. As I replied earlier, I plan =
to show the connectivity of 3C's and turn around the edges if you hold the =
ctrl button. I'll implement this in a day or two.
> > > >=20
> > > > Can you elaborate the meaning of "label"? In my terminology, there =
are several "stickers" on each "piece". Should the "labels" distinct for di=
fferent pieces, or different stickers?=20
> > > >=20
> > > > Nan
> > > >=20
> > > > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > > > >
> > > > > Wonderful! Awesome! Thanks.
> > > > > You show he connection of the 6C pieces and of the 2C pieces beca=
use those turning axis are active. How about showing he connection for the =
3C pieces?
> > > > > For me it would be very helpful if all stickers are labeled. This=
would harm the very clean and beautyful puzzle. But what about showing the=
label of the sticker where the mouse pointer is on in a small window?
> > > > > Kind regards
> > > > > Ed
> > > >
> > >
> >
>

---

From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Thu, 24 May 2012 11:41:58 +0200
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell

------=_NextPart_000_000A_01CD39A2.3A5226C0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Has anybody of you seen the DaYan Bermuda Star.
Interesting cutting!

----- Original Message -----=20
From: schuma=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Thursday, May 24, 2012 5:23 AM
Subject: [MC4D] Re: Making a puzzle based on 11-cell


=20=20=20=20
Ed,

You are right on that for each sticker I only keep the color but not an I=
D. When the puzzle is rotated, the only colors are changed. I will figure o=
ut a way to highlight or label a sticker and "trace" its movement. I think =
that would be great for you to use.

The "modified way of move counting" and "control button for selecting edg=
es" are online now. When you use the control button, please make sure the p=
uzzle get focus. The focus may be on other windows or in the input/output t=
ext boxes. The simplest way to focus on the puzzle is to click somewhere be=
tween the disks.=20

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> I fear you retain only the color of each sticker in your program and no=
t an individual label. I know that "puzzle solved" is declared when the col=
ors are "homogeneous" and NOT when each sticker is at home. But to see wher=
e the stickers go when I'm studying sequences the color of the sticker is n=
ot sufficient.
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> >
> > Not the sticker color number but an individual label for each sticker=
.
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > >
> > > The "labels" should be distinct for different stickers!
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
> > > >
> > > > Roice also asked about the 3C pieces. As I replied earlier, I pla=
n to show the connectivity of 3C's and turn around the edges if you hold th=
e ctrl button. I'll implement this in a day or two.
> > > >=20
> > > > Can you elaborate the meaning of "label"? In my terminology, ther=
e are several "stickers" on each "piece". Should the "labels" distinct for =
different pieces, or different stickers?=20
> > > >=20
> > > > Nan
> > > >=20
> > > > --- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
> > > > >
> > > > > Wonderful! Awesome! Thanks.
> > > > > You show he connection of the 6C pieces and of the 2C pieces be=
cause those turning axis are active. How about showing he connection for th=
e 3C pieces?
> > > > > For me it would be very helpful if all stickers are labeled. Th=
is would harm the very clean and beautyful puzzle. But what about showing t=
he label of the sticker where the mouse pointer is on in a small window?
> > > > > Kind regards
> > > > > Ed
> > > >
> > >
> >
>



=20=20
------=_NextPart_000_000A_01CD39A2.3A5226C0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>

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
schuma=
=20

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>


 =20


------=_NextPart_000_000A_01CD39A2.3A5226C0--

---

From: "Andrey" <andreyastrelin@yahoo.com>
Date: Thu, 24 May 2012 14:21:47 -0000
Subject: [MC4D] Re: Making a puzzle based on 11-cell

My first result for 1-scramble was 4 twists :)


--- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>
> I'm proud. I did the 1-scramble!
> 17 moves, 00:04:33
>=20
> ;-)
> Ed
>

---

From: "Andrey" <andreyastrelin@yahoo.com>
Date: Thu, 24 May 2012 14:23:28 -0000
Subject: [MC4D] Re: Making a puzzle based on 11-cell

I'll do it faster if I'll implement 3D version first :D



--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Congratulations, Ed!
> That's pretty funny when solving a single twist of any puzzle can be=20
> tricky. So has anybody worked out any algorithms? Who will be the first=20
> to solve this beast? I'm looking at you, Andrey! :-)
>=20
> On 5/23/2012 4:19 PM, Eduard Baumann wrote:
> >
> >
> > I'm proud. I did the 1-scramble!
> > 17 moves, 00:04:33
> > ;-)
> > Ed
>

---

From: "schuma" <mananself@gmail.com>
Date: Thu, 24 May 2012 18:58:22 -0000
Subject: [MC4D] Re: Making a puzzle based on 11-cell

I think it would be unfair to compare your move count with Ed's, because af=
ter Ed solved it for the first time, I changed the way moves are counted: w=
hole puzzle re-orientation doesn't count any more.

It's interesting that you mention implementing it in "3D". A natural way to=
represent this puzzle is to make a {3,5,3} hyperbolic honeycomb, then iden=
tify opposite faces of each icosahedron, then, to make it consistent, ident=
ify the icosahedra to which the opposite faces attach. Given your experienc=
e making the {6,3,3} honeycomb, I think you'll be good at making an interfa=
ce this way. I seriously thought about this approach, but I really don't kn=
ow how to draw the 3D hyperbolic space, especially like your {6,3,3}, where=
the view is "what you see from inside of the space". By the way I think th=
at would be the only way to code the 57-cell.=20

In my applet, I do have a 3D model but in an Euclidean space, basically try=
ing to simulate the hyperbolic space locally. I put a red icosahedron at th=
e origin. Then for each of its ten visible faces, I place an icosahedron on=
top of it. Then I have to move the surrounding icosahedra outside for a di=
stance, just because in Euclidean space, they don't fit in. This is my 3D m=
odel of the 11 cells. And in this model, all the rotations on the central c=
ell are implemented as a normal 3D rotation. Rotation on other cells are ha=
rd. I first somehow move the cell-to-twist to the central position and rota=
te it, then move it back to its original position. My code for this part is=
dirty and not elegant at all. If you simulate a hyperbolic space, all the =
rotations on all the cells will be well defined hyperbolic rotation. That's=
what a mathematician likes.

My 2D painting of the puzzle is related to my 3D model. The central red cel=
l is just what an icosahedron looks like normally. The cyan cell is the one=
in front of the red cell, attaching it on the front triangular face. In th=
e 2D painting I just place it under the red cell so that we can see the red=
one. I'm drawing the BACK side of the cyan cell, rather than the front sid=
e. The reason is that in this way, both face-stickers have a vertex on top =
and an edge at the bottom, so they look like together. If I draw the front =
side of cyan cell as usual, the result is like this:

http://people.bu.edu/nanma/ElevenCell/ElevenCell2.html

the face on the cyan cell that directly faces the red cell would be invisib=
le, the identified face that's visible is upside down. I don't feel that's =
intuitive.=20

All the other cells are treated similarly. The orientation of them are just=
as in the 3D model, and I'm drawing the back sides. The green, magenta and=
brown cells look more symmetrical because they attach the red cell on the =
three neighboring faces of the center one, which are more symmetrical than =
the other six farther faces. I use perspective drawing for all the cells to=
distort them a little bit so that the faces close to the boundaries of the=
icosahedra looks larger.=20

So this is how I made it. Please feel free to make the 11-cell in your favo=
rite way or even the 57-cell!

Nan

--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>
> My first result for 1-scramble was 4 twists :)
>=20
>=20
> --- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
> >
> > I'm proud. I did the 1-scramble!
> > 17 moves, 00:04:33
> >=20
> > ;-)
> > Ed
> >
>

---

From: "Andrey" <andreyastrelin@yahoo.com>
Date: Thu, 24 May 2012 19:15:59 -0000
Subject: [MC4D] Re: Making a puzzle based on 11-cell

Nan,
I didn't use puzzle reorientation because I don't know how to do it. And =
at the time of solving I didn't find edge-centered rotation :)
Yes, for 11- and 57-cells I'm going to use hyperbolic view (probably with=
two layers of cells around the central one). But at first I have to comput=
e parameters of {5,3,5} and {3,5,3} honeycombs in the algebraic form, and I=
feel that it will be not easy :) But after that I can find painting patter=
n by computing H3 transformations in Z_11 for 11-cell and in Z_19 for 57-ce=
ll (and may be find some more patterns).
It's strange that there is no information about periodic patterns based o=
n {4,3,5} or {5,3,4} - there should be some of them with not large number o=
f colors...=20=20

Andrey


--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> I think it would be unfair to compare your move count with Ed's, because =
after Ed solved it for the first time, I changed the way moves are counted:=
whole puzzle re-orientation doesn't count any more.
>=20
> It's interesting that you mention implementing it in "3D". A natural way =
to represent this puzzle is to make a {3,5,3} hyperbolic honeycomb, then id=
entify opposite faces of each icosahedron, then, to make it consistent, ide=
ntify the icosahedra to which the opposite faces attach. Given your experie=
nce making the {6,3,3} honeycomb, I think you'll be good at making an inter=
face this way. I seriously thought about this approach, but I really don't =
know how to draw the 3D hyperbolic space, especially like your {6,3,3}, whe=
re the view is "what you see from inside of the space". By the way I think =
that would be the only way to code the 57-cell.=20
>=20
> In my applet, I do have a 3D model but in an Euclidean space, basically t=
rying to simulate the hyperbolic space locally. I put a red icosahedron at =
the origin. Then for each of its ten visible faces, I place an icosahedron =
on top of it. Then I have to move the surrounding icosahedra outside for a =
distance, just because in Euclidean space, they don't fit in. This is my 3D=
model of the 11 cells. And in this model, all the rotations on the central=
cell are implemented as a normal 3D rotation. Rotation on other cells are =
hard. I first somehow move the cell-to-twist to the central position and ro=
tate it, then move it back to its original position. My code for this part =
is dirty and not elegant at all. If you simulate a hyperbolic space, all th=
e rotations on all the cells will be well defined hyperbolic rotation. That=
's what a mathematician likes.
>=20
> My 2D painting of the puzzle is related to my 3D model. The central red c=
ell is just what an icosahedron looks like normally. The cyan cell is the o=
ne in front of the red cell, attaching it on the front triangular face. In =
the 2D painting I just place it under the red cell so that we can see the r=
ed one. I'm drawing the BACK side of the cyan cell, rather than the front s=
ide. The reason is that in this way, both face-stickers have a vertex on to=
p and an edge at the bottom, so they look like together. If I draw the fron=
t side of cyan cell as usual, the result is like this:
>=20
> http://people.bu.edu/nanma/ElevenCell/ElevenCell2.html
>=20
> the face on the cyan cell that directly faces the red cell would be invis=
ible, the identified face that's visible is upside down. I don't feel that'=
s intuitive.=20
>=20
> All the other cells are treated similarly. The orientation of them are ju=
st as in the 3D model, and I'm drawing the back sides. The green, magenta a=
nd brown cells look more symmetrical because they attach the red cell on th=
e three neighboring faces of the center one, which are more symmetrical tha=
n the other six farther faces. I use perspective drawing for all the cells =
to distort them a little bit so that the faces close to the boundaries of t=
he icosahedra looks larger.=20
>=20
> So this is how I made it. Please feel free to make the 11-cell in your fa=
vorite way or even the 57-cell!
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
> >
> > My first result for 1-scramble was 4 twists :)
> >=20
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
> > >
> > > I'm proud. I did the 1-scramble!
> > > 17 moves, 00:04:33
> > >=20
> > > ;-)
> > > Ed
> > >
> >
>

---

From: "schuma" <mananself@gmail.com>
Date: Thu, 24 May 2012 19:56:28 -0000
Subject: Re: Making a puzzle based on 11-cell

As requested by Ed, I added a function to customize a label for a sticker. =
Just place the mouse on top of a vertex or a face, then press any number be=
tween 1~9 to put a label on that sticker. To label an edge sticker, hold ct=
rl to select it, then press any number. After that, this label will move fo=
rever with the sticker. To remove a label, press 0 (label "0" means no labe=
l) on that sticker. Resetting or scrambling also remove all labels.

Note that numbers don't have to be unique. For example, you may manually la=
bel all the connected stickers on a piece as the same number.

I hope this feature will help you find algorithms.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> I fear you retain only the color of each sticker in your program and not =
an individual label. I know that "puzzle solved" is declared when the color=
s are "homogeneous" and NOT when each sticker is at home. But to see where =
the stickers go when I'm studying sequences the color of the sticker is not=
sufficient.
>=20

---

From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Thu, 24 May 2012 23:04:49 +0200
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell

------=_NextPart_000_0012_01CD3A01.9E7B6E40
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Perfect. Thanks.

----- Original Message -----=20
From: schuma=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Thursday, May 24, 2012 9:56 PM
Subject: [MC4D] Re: Making a puzzle based on 11-cell


=20=20=20=20
As requested by Ed, I added a function to customize a label for a sticker=
. Just place the mouse on top of a vertex or a face, then press any number =
between 1~9 to put a label on that sticker. To label an edge sticker, hold =
ctrl to select it, then press any number. After that, this label will move =
forever with the sticker. To remove a label, press 0 (label "0" means no la=
bel) on that sticker. Resetting or scrambling also remove all labels.

Note that numbers don't have to be unique. For example, you may manually =
label all the connected stickers on a piece as the same number.

I hope this feature will help you find algorithms.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard" wrote:
>
> I fear you retain only the color of each sticker in your program and no=
t an individual label. I know that "puzzle solved" is declared when the col=
ors are "homogeneous" and NOT when each sticker is at home. But to see wher=
e the stickers go when I'm studying sequences the color of the sticker is n=
ot sufficient.
>=20



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

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com <=
/DIV>


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From: "schuma" <mananself@gmail.com>
Date: Fri, 25 May 2012 08:25:02 -0000
Subject: Re: Making a puzzle based on 11-cell

I've solved the puzzle from a full scrambled state. It took me 3 hours and =
9600 moves.

I found both suggestions of selecting edges, and labeling stickers are very=
good. They are pretty useful in a solve. I've also found some other things=
to improve.

Nan

--- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>
> Perfect. Thanks.
>=20

---

From: "schuma" <mananself@gmail.com>
Date: Fri, 25 May 2012 10:01:38 -0700
Subject: Re: Making a puzzle based on 11-cell

Congratulations, Nan!
Please tell us the story of your solve? Most of us will never attempt a
solution so we must take our enjoyment vicariously from the descriptions
of others. In particular, I wonder how it compares with solving puzzles
that make more sense visually. Or should we expect it to be as
inconceivable as an 11 dimensional puzzle? Inquiring minds wish to know.
-Melinda

On 5/25/2012 1:25 AM, schuma wrote:
> I've solved the puzzle from a full scrambled state. It took me 3 hours and 9600 moves.
>
> I found both suggestions of selecting edges, and labeling stickers are very good. They are pretty useful in a solve. I've also found some other things to improve.
>
> Nan
>
> --- In 4D_Cubing@yahoogroups.com, "Eduard Baumann" wrote:
>> Perfect. Thanks.

---

From: "schuma" <mananself@gmail.com>
Date: Fri, 25 May 2012 19:24:12 -0000
Subject: Re: Making a puzzle based on 11-cell

I haven't explained how the text input/output function works yet. Let me do=
it now.

When you make some turns, you'll notice some characters are generated in th=
e text output box. You can ctrl-A and ctrl-C to copy them out. When you ctr=
l-P them into the input box and press the "input" button, this sequence wil=
l be executed again. You can also edit them in any editor.

Here's the meaning of the sequence: each twist is represented by three char=
acters. The first character may be A~K or a~k, representing which cell is t=
urned. An uppercase letter means it's a normal twist. A lowercase letter me=
ans it's a whole-puzzle twist. The second character may be V, v, F, f, E, e=
. It means the axis passes through a vertex, or a face, or an edge. Upperca=
se =3D CCW (left click), lowercase =3D CW (right click). The third characte=
r can be 0~9 or A~E. It's an internal ID for a vertex/face/edge on each cel=
l. Even I don't remember which number stands for which object. You may put =
any separator between the three-character triplets, "," ";" "(" space newl=
ine etc. All of them will be ignored.=20

For example, "AV0" means turning around cell-A (the red cell), on vertex nu=
mber 0, CCW. Inverting a move can always be done by changing between upper =
case and lower case of the second character.=20

--------- here comes the story of solution -----------

Using this text input method, I studied the algorithms.=20

2C face pieces: permutation is always even, and two 2C pieces can be flippe=
d at the same time. There's [1,1] commutator. So solving the permutation is=
intuitive.

The orientation of 3C edge pieces behave like in MC4D: two edges can be fli=
pped, each like (a,b,c)->(b,a,c), and a single edge can be rotated like (a,=
b,c)->(b,c,a). I conjecture that single-edge flipping like (a,b,c)->(b,a,c)=
is impossible, but I just haven't got a proof yet. I need to count the par=
ity of edge stickers of a twist to prove it.

For the 6C vertex pieces, each can be rotated in place in many ways. The si=
x stickers are always in even permutation. I've seen a 5-cycle, or two 3-cy=
cles, or two 2-cycles. But the group A6 is simple, so there should be an al=
gorithm to do a 3-cycle. But I haven't found it yet.=20

After the preparation, I started to solve it. 2C pieces are mostly solved i=
ntuitively (I consider [1,1] commutators are intuitive). 3C is the most ted=
ious step. When solving 3C pieces, for example, I have a cyan-blue-yellow p=
iece, then I need to find the destination of it. To do that I hold ctrl and=
hover the cursor around the the cyan cell, and look at the blue and yellow=
cells and check when there's a circle in each of those two cells. Once I f=
ound the destination, it doesn't take more than two or three setup moves to=
bring it to the 3-cycle working spot.=20

There's an episode here. I had a cyan-yellow-brown piece. When I looked for=
its destination, I found there shouldn't be such an edge of this color com=
bination. I was nervous because there must be a tricky bug in my code creat=
ing the "invalid piece". It would be very hard to repeat this bug. I was th=
inking about how to validate the moves to catch this bug. I thought a lot, =
then I realized "brown" is actually purple. It was just the edges are so na=
rrow that it was hard to distinguish a foreground colors with the presence =
of a colorful background. Roice warned me about it, but I haven't changed i=
t yet. After the solution I made the edge wider.=20

6C pieces are not that tedious. There are only 11 of them. For permutation,=
I have a 3-cycle algorithm. For orientation, I have an algorithm to do two=
3-cycles for the six stickers on one piece. I just use that orientation al=
gorithm again and again to solve all the cases.=20

That's the end of the solution. I'm going to add a dialog to warn the solve=
r because clicking reset during a formal solution. Currently if I misclick =
the reset button in a solution everything will be lost. This is something I=
noticed in my solve.

Nan


--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Congratulations, Nan!
> Please tell us the story of your solve? Most of us will never attempt a=20
> solution so we must take our enjoyment vicariously from the descriptions=
=20
> of others. In particular, I wonder how it compares with solving puzzles=20
> that make more sense visually. Or should we expect it to be as=20
> inconceivable as an 11 dimensional puzzle? Inquiring minds wish to know.
> -Melinda

---

From: Melinda Green <melinda@superliminal.com>
Date: Sat, 26 May 2012 19:20:02 -0700
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell

Thanks for your solution story, Nan. I always appreciate learning about
the experience of solving each crazy new puzzle we get. Oh, and
congratulations on both your puzzle and first solve. Both are *very*
impressive.
-Melinda

On 5/25/2012 12:24 PM, schuma wrote:
> I haven't explained how the text input/output function works yet. Let me do it now.
>
> When you make some turns, you'll notice some characters are generated in the text output box. You can ctrl-A and ctrl-C to copy them out. When you ctrl-P them into the input box and press the "input" button, this sequence will be executed again. You can also edit them in any editor.
>
> Here's the meaning of the sequence: each twist is represented by three characters. The first character may be A~K or a~k, representing which cell is turned. An uppercase letter means it's a normal twist. A lowercase letter means it's a whole-puzzle twist. The second character may be V, v, F, f, E, e. It means the axis passes through a vertex, or a face, or an edge. Uppercase = CCW (left click), lowercase = CW (right click). The third character can be 0~9 or A~E. It's an internal ID for a vertex/face/edge on each cell. Even I don't remember which number stands for which object. You may put any separator between the three-character triplets, "," ";" "(" space newline etc. All of them will be ignored.
>
> For example, "AV0" means turning around cell-A (the red cell), on vertex number 0, CCW. Inverting a move can always be done by changing between upper case and lower case of the second character.
>
> --------- here comes the story of solution -----------
>
> Using this text input method, I studied the algorithms.
>
> 2C face pieces: permutation is always even, and two 2C pieces can be flipped at the same time. There's [1,1] commutator. So solving the permutation is intuitive.
>
> The orientation of 3C edge pieces behave like in MC4D: two edges can be flipped, each like (a,b,c)->(b,a,c), and a single edge can be rotated like (a,b,c)->(b,c,a). I conjecture that single-edge flipping like (a,b,c)->(b,a,c) is impossible, but I just haven't got a proof yet. I need to count the parity of edge stickers of a twist to prove it.
>
> For the 6C vertex pieces, each can be rotated in place in many ways. The six stickers are always in even permutation. I've seen a 5-cycle, or two 3-cycles, or two 2-cycles. But the group A6 is simple, so there should be an algorithm to do a 3-cycle. But I haven't found it yet.
>
> After the preparation, I started to solve it. 2C pieces are mostly solved intuitively (I consider [1,1] commutators are intuitive). 3C is the most tedious step. When solving 3C pieces, for example, I have a cyan-blue-yellow piece, then I need to find the destination of it. To do that I hold ctrl and hover the cursor around the the cyan cell, and look at the blue and yellow cells and check when there's a circle in each of those two cells. Once I found the destination, it doesn't take more than two or three setup moves to bring it to the 3-cycle working spot.
>
> There's an episode here. I had a cyan-yellow-brown piece. When I looked for its destination, I found there shouldn't be such an edge of this color combination. I was nervous because there must be a tricky bug in my code creating the "invalid piece". It would be very hard to repeat this bug. I was thinking about how to validate the moves to catch this bug. I thought a lot, then I realized "brown" is actually purple. It was just the edges are so narrow that it was hard to distinguish a foreground colors with the presence of a colorful background. Roice warned me about it, but I haven't changed it yet. After the solution I made the edge wider.
>
> 6C pieces are not that tedious. There are only 11 of them. For permutation, I have a 3-cycle algorithm. For orientation, I have an algorithm to do two 3-cycles for the six stickers on one piece. I just use that orientation algorithm again and again to solve all the cases.
>
> That's the end of the solution. I'm going to add a dialog to warn the solver because clicking reset during a formal solution. Currently if I misclick the reset button in a solution everything will be lost. This is something I noticed in my solve.
>
> Nan
>
>
> --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>> Congratulations, Nan!
>> Please tell us the story of your solve? Most of us will never attempt a
>> solution so we must take our enjoyment vicariously from the descriptions
>> of others. In particular, I wonder how it compares with solving puzzles
>> that make more sense visually. Or should we expect it to be as
>> inconceivable as an 11 dimensional puzzle? Inquiring minds wish to know.
>> -Melinda
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

---

From: "schuma" <mananself@gmail.com>
Date: Sun, 27 May 2012 22:55:01 -0000
Subject: Re: Making a puzzle based on 11-cell

Hi Andrey,

I'm reading Coxeter's paper "Ten toroids and fifty-seven hemi-dodecahedra",=
In section 5, he mentioned:

Grunbaum [1976, p. 197] went on to consider the possibility of using a non-=
orientable cell such as the hemi-dodecahedron {5, 3}/2 =3D {5, 3}5 or the h=
emi-icosahedron {3, 5}/2 =3D {3, 5}5. He found that 32 hemi-dodecahedra can=
be fitted together to make a polystroma of type {5, 3, 4}, and 11 hemi-ico=
sahedra to make one of type {3, 5, 3}.

He's referring to=20

Grunbaum, Branko: 1976, 'Regularity of Graphs, Complexes and Designs'. Coll=
oque CNRS, Problemes Combinatoires et Theorie des Graphes, Orsay.

I can't find Grunbaum's book/paper. But I wonder if the shape with 32 hemi-=
dodecahedra is what you've been looking for.

Nan



--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
> It's strange that there is no information about periodic patterns based=
on {4,3,5} or {5,3,4} - there should be some of them with not large number=
of colors...=20=20

---