Thread: "{7,3} vertex and edge turning puzzles"

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Hi Nan,

If you download the
latest,
you'll now see vertex and edge turning versions of the {7,3}. They are quite
beautifulwhen
scrambled.

I picked depths that felt like a nice balance, but they can be changed. I
made the ET slightly deeper than I did for the {3,7}. It seemed better to
do so in this case. I wonder if the {7,3} ET will also have some
intriguing piece orbits, like you observed on the {3,7}.

If you are interested in a more detailed write up on how to edit slicing
circles and their depths, let me know. It requires hand editing the puzzle
config files, but the format is pretty simple. It is based on discussion
we had in the past - you can enter depths as multiples of
incircles/circumcircles/edge lengths, or you can enter them as an absolute
distance.

In any case, I am happy to configure files for any puzzles you describe,
assuming MagicTile can support them.

Roice

P.S. This version also removes the duplicate color you found in the
default settings. Thanks for noticing that :)



On Mon, Nov 7, 2011 at 2:56 AM, Nan Ma wrote:

>
>
> Hi Roice,
>
> About the Klein quartic, I'm curious if the vertex turning and edge
> turning {7,3} can be made. They have less colors than the {3,7}
> counterparts. So it should be easier to find pieces on them. Thanks.
>
> Nan
>

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That's a really creative idea. When I first saw your suggestion, I had the
same question as Nan.

MagicTile can't support this with only via configuration at the moment. It
will take some code work, but I like the thought of trying to handle it in
the future.

Like the {3,7} puzzles, my bet is this IRP puzzle will not have the same
connection pattern between heptagonal faces that the current KQ puzzle has.

A further speculation is that although there might not be a {7,3} IRP that
fits into *R**3*, maybe there is one that fits into *R**4 *or something
else. In any case, I wouldn't be surprised if there is a different set of
2-dimensional IRPs that can work in 4-dimensional space, in a similar way
to the ones Melinda has enumerated for 3 dimensions.

Roice


P.S. Short implementation thoughts, probably just for me...

A longer term goal is to support truncated tilings (giving puzzles based on
uniform tilings, etc.). I'm not sure how it is going to evolve exactly, but
one approach would be to still have one texture mapped to each polygon in
the underlying regular tiling. It'd just be that the texture now contained
portions from multiple tiles instead of just one (e.g., a soccer ball
puzzle would have 32 faces, but only 20 textures). The {7,3} IRP could
potentially fit well into that piece of work. What I'm thinking is that the
code would handle this as a {3,7} tiling that is truncated all the way to
its dual.

Maybe the right solution for truncated tilings is still one texture per
face though, in which case this IRP could be harder to do...


On Tue, Nov 8, 2011 at 1:03 AM, Melinda Green wrote:

> No, I was inquiring into the possibility of such a puzzle. I meant to
> send privately to Roice because I didn't want to pressure him but I
> screwed up.
>
> I'm pretty sure there isn't a true {7,3} IRP though I hope that I am
> wrong. I could however imagine a MagicTile version in which a {7,3}
> texture could be mapped onto the VT {3,7} IRP surface to approximate
> one. Seems doable though the real way to do this sort of thing might be
> to map it onto a minimal curvature surface with the same topology. The
> IRPs are interesting because they can be constructed using flat
> polygonal faces but there are all sorts of crazy puzzles that become
> possible without that constraint.
>
> -Melinda
>
> On 11/7/2011 10:50 PM, schuma wrote:
> > Is there a {7,3} IRP?
> >
> > --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
> >> How about a FT {7,3} IRP?
>

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Maybe another possibility is to use ceased heptagons, just like this one:



This photo is from a long webpage by Gerard Westendorp. If you go to //westy31.home.xs4all.nl/Geometry/Geometry.html#constant> and scroll UPWARD=
a little bit, you can find the discussion about it where he considered dif=
ferent ways to "glue" the cardboard model. One way results in Klein Quartic=
. Another way results in the dual of the {3,7} IRP that we have in MagicTil=
e. There are even more ways resulting in other {7,3} with other connectivit=
y. I need to catch up on math but it looks interesting.

Some experience about solving IRP puzzles:

I've solved three simple IRP puzzles. For each of them, I solved it in two =
ways: the "show as IRP" option true and false. I found solving in the IRP v=
iew more challenging than in the Poincare disk (PD) view, because (1) in PD=
I can see everything but in IRP I can only see about half; (2) in IRP the =
pieces with best visibility are on boundary, but some of them are truncated=
; (3) when I'm making a turn sometimes the face that I need to click on is =
facing the other direction. Sometimes I have to carefully adjust the viewpo=
int and click on some inside faces. Because of the above reasons, I always =
first look at the puzzle with the IRP view off to study it, before turning =
on the IRP.=20

Nan


--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> That's a really creative idea. When I first saw your suggestion, I had t=
he
> same question as Nan.
>=20
> MagicTile can't support this with only via configuration at the moment. =
It
> will take some code work, but I like the thought of trying to handle it i=
n
> the future.
>=20
> Like the {3,7} puzzles, my bet is this IRP puzzle will not have the same
> connection pattern between heptagonal faces that the current KQ puzzle ha=
s.
>=20
> A further speculation is that although there might not be a {7,3} IRP tha=
t
> fits into *R**3*, maybe there is one that fits into *R**4 *or something
> else. In any case, I wouldn't be surprised if there is a different set o=
f
> 2-dimensional IRPs that can work in 4-dimensional space, in a similar way
> to the ones Melinda has enumerated for 3 dimensions.
>=20
> Roice
>=20
>=20
> P.S. Short implementation thoughts, probably just for me...
>=20
> A longer term goal is to support truncated tilings (giving puzzles based =
on
> uniform tilings, etc.). I'm not sure how it is going to evolve exactly, b=
ut
> one approach would be to still have one texture mapped to each polygon in
> the underlying regular tiling. It'd just be that the texture now contain=
ed
> portions from multiple tiles instead of just one (e.g., a soccer ball
> puzzle would have 32 faces, but only 20 textures). The {7,3} IRP could
> potentially fit well into that piece of work. What I'm thinking is that t=
he
> code would handle this as a {3,7} tiling that is truncated all the way to
> its dual.
>=20
> Maybe the right solution for truncated tilings is still one texture per
> face though, in which case this IRP could be harder to do...
>=20
>=20
> On Tue, Nov 8, 2011 at 1:03 AM, Melinda Green wrote:
>=20
> > No, I was inquiring into the possibility of such a puzzle. I meant to
> > send privately to Roice because I didn't want to pressure him but I
> > screwed up.
> >
> > I'm pretty sure there isn't a true {7,3} IRP though I hope that I am
> > wrong. I could however imagine a MagicTile version in which a {7,3}
> > texture could be mapped onto the VT {3,7} IRP surface to approximate
> > one. Seems doable though the real way to do this sort of thing might be
> > to map it onto a minimal curvature surface with the same topology. The
> > IRPs are interesting because they can be constructed using flat
> > polygonal faces but there are all sorts of crazy puzzles that become
> > possible without that constraint.
> >
> > -Melinda
> >
> > On 11/7/2011 10:50 PM, schuma wrote:
> > > Is there a {7,3} IRP?
> > >
> > > --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
> > >> How about a FT {7,3} IRP?
> >
>

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Today I visited MSRI to see this sculpture of the Klein Quartic
5084071/view> . The base is a {7,3} in the Poincare Disk view just like
in Magic Tile. The main part of the sculpture is a folded version of it,
which has 24 curved heptagons.

Nan

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Maybe another possibility is to use ceased heptagons, just like this
one:
>
>
>
> This photo is from a long webpage by Gerard Westendorp. If you go to
and
scroll UPWARD a little bit, you can find the discussion about it where
he considered different ways to "glue" the cardboard model. One way
results in Klein Quartic. Another way results in the dual of the {3,7}
IRP that we have in MagicTile. There are even more ways resulting in
other {7,3} with other connectivity. I need to catch up on math but it
looks interesting.
>
> Some experience about solving IRP puzzles:
>
> I've solved three simple IRP puzzles. For each of them, I solved it in
two ways: the "show as IRP" option true and false. I found solving in
the IRP view more challenging than in the Poincare disk (PD) view,
because (1) in PD I can see everything but in IRP I can only see about
half; (2) in IRP the pieces with best visibility are on boundary, but
some of them are truncated; (3) when I'm making a turn sometimes the
face that I need to click on is facing the other direction. Sometimes I
have to carefully adjust the viewpoint and click on some inside faces.
Because of the above reasons, I always first look at the puzzle with the
IRP view off to study it, before turning on the IRP.
>
> Nan
>
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson roice3@ wrote:
> >
> > That's a really creative idea. When I first saw your suggestion, I
had the
> > same question as Nan.
> >
> > MagicTile can't support this with only via configuration at the
moment. It
> > will take some code work, but I like the thought of trying to handle
it in
> > the future.
> >
> > Like the {3,7} puzzles, my bet is this IRP puzzle will not have the
same
> > connection pattern between heptagonal faces that the current KQ
puzzle has.
> >
> > A further speculation is that although there might not be a {7,3}
IRP that
> > fits into *R**3*, maybe there is one that fits into *R**4 *or
something
> > else. In any case, I wouldn't be surprised if there is a different
set of
> > 2-dimensional IRPs that can work in 4-dimensional space, in a
similar way
> > to the ones Melinda has enumerated for 3 dimensions.
> >
> > Roice
> >
> >
> > P.S. Short implementation thoughts, probably just for me...
> >
> > A longer term goal is to support truncated tilings (giving puzzles
based on
> > uniform tilings, etc.). I'm not sure how it is going to evolve
exactly, but
> > one approach would be to still have one texture mapped to each
polygon in
> > the underlying regular tiling. It'd just be that the texture now
contained
> > portions from multiple tiles instead of just one (e.g., a soccer
ball
> > puzzle would have 32 faces, but only 20 textures). The {7,3} IRP
could
> > potentially fit well into that piece of work. What I'm thinking is
that the
> > code would handle this as a {3,7} tiling that is truncated all the
way to
> > its dual.
> >
> > Maybe the right solution for truncated tilings is still one texture
per
> > face though, in which case this IRP could be harder to do...
> >
> >
> > On Tue, Nov 8, 2011 at 1:03 AM, Melinda Green melinda@wrote:
> >
> > > No, I was inquiring into the possibility of such a puzzle. I meant
to
> > > send privately to Roice because I didn't want to pressure him but
I
> > > screwed up.
> > >
> > > I'm pretty sure there isn't a true {7,3} IRP though I hope that I
am
> > > wrong. I could however imagine a MagicTile version in which a
{7,3}
> > > texture could be mapped onto the VT {3,7} IRP surface to
approximate
> > > one. Seems doable though the real way to do this sort of thing
might be
> > > to map it onto a minimal curvature surface with the same topology.
The
> > > IRPs are interesting because they can be constructed using flat
> > > polygonal faces but there are all sorts of crazy puzzles that
become
> > > possible without that constraint.
> > >
> > > -Melinda
> > >
> > > On 11/7/2011 10:50 PM, schuma wrote:
> > > > Is there a {7,3} IRP?
> > > >
> > > > --- In 4D_Cubing@yahoogroups.com, Melinda Green=20
wrote:
> > > >> How about a FT {7,3} IRP?
> > >
> >
>


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Today I visited MSRI to see ing/photos/album/1962624577/pic/1675084071/view">this sculpture of the Klei=
n Quartic. The base is a {7,3} in the Poincare Disk view just like in M=
agic Tile. The main part of the sculpture is a folded version of it, which =
has 24 curved heptagons.

Nan

--- In 4D_Cubing@yahoogroups.com=
, "schuma" <mananself@...> wrote:
>
> Maybe another possi=
bility is to use ceased heptagons, just like this one:
>
> <=
;http://westy31.home.xs4all.nl/Geometry/KleinHoles.jpg>
>
>=
This photo is from a long webpage by Gerard Westendorp. If you go to <h=
ttp://westy31.home.xs4all.nl/Geometry/Geometry.html#constant> and scroll=
UPWARD a little bit, you can find the discussion about it where he conside=
red different ways to "glue" the cardboard model. One way results in Klein =
Quartic. Another way results in the dual of the {3,7} IRP that we have in M=
agicTile. There are even more ways resulting in other {7,3} with other conn=
ectivity. I need to catch up on math but it looks interesting.
>
=
> Some experience about solving IRP puzzles:
>
> I've solve=
d three simple IRP puzzles. For each of them, I solved it in two ways: the =
"show as IRP" option true and false. I found solving in the IRP view more c=
hallenging than in the Poincare disk (PD) view, because (1) in PD I can see=
everything but in IRP I can only see about half; (2) in IRP the pieces wit=
h best visibility are on boundary, but some of them are truncated; (3) when=
I'm making a turn sometimes the face that I need to click on is facing the=
other direction. Sometimes I have to carefully adjust the viewpoint and cl=
ick on some inside faces. Because of the above reasons, I always first look=
at the puzzle with the IRP view off to study it, before turning on the IRP=
.
>
> Nan
>
>
> --- In 4D_Cubing@yahoogro=
ups.com, Roice Nelson roice3@ wrote:
> >
> > That's a rea=
lly creative idea. When I first saw your suggestion, I had the
> >=
; same question as Nan.
> >
> > MagicTile can't support =
this with only via configuration at the moment. It
> > will take =
some code work, but I like the thought of trying to handle it in
> &g=
t; the future.
> >
> > Like the {3,7} puzzles, my bet is=
this IRP puzzle will not have the same
> > connection pattern bet=
ween heptagonal faces that the current KQ puzzle has.
> >
>=
> A further speculation is that although there might not be a {7,3} IRP=
that
> > fits into *R**3*, maybe there is one that fits into *R**=
4 *or something
> > else. In any case, I wouldn't be surprised if=
there is a different set of
> > 2-dimensional IRPs that can work =
in 4-dimensional space, in a similar way
> > to the ones Melinda h=
as enumerated for 3 dimensions.
> >
> > Roice
> &g=
t;
> >
> > P.S. Short implementation thoughts, probably=
just for me...
> >
> > A longer term goal is to support=
truncated tilings (giving puzzles based on
> > uniform tilings, e=
tc.). I'm not sure how it is going to evolve exactly, but
> > one =
approach would be to still have one texture mapped to each polygon in
&g=
t; > the underlying regular tiling. It'd just be that the texture now c=
ontained
> > portions from multiple tiles instead of just one (e.g=
., a soccer ball
> > puzzle would have 32 faces, but only 20 textu=
res). The {7,3} IRP could
> > potentially fit well into that piec=
e of work. What I'm thinking is that the
> > code would handle thi=
s as a {3,7} tiling that is truncated all the way to
> > its dual.=

> >
> > Maybe the right solution for truncated tilings =
is still one texture per
> > face though, in which case this IRP c=
ould be harder to do...
> >
> >
> > On Tue, No=
v 8, 2011 at 1:03 AM, Melinda Green melinda@wrote:
> >
> &g=
t; > No, I was inquiring into the possibility of such a puzzle. I meant =
to
> > > send privately to Roice because I didn't want to press=
ure him but I
> > > screwed up.
> > >
> > =
> I'm pretty sure there isn't a true {7,3} IRP though I hope that I amr>> > > wrong. I could however imagine a MagicTile version in whic=
h a {7,3}
> > > texture could be mapped onto the VT {3,7} IRP s=
urface to approximate
> > > one. Seems doable though the real w=
ay to do this sort of thing might be
> > > to map it onto a min=
imal curvature surface with the same topology. The
> > > IRPs a=
re interesting because they can be constructed using flat
> > >=
polygonal faces but there are all sorts of crazy puzzles that become
&g=
t; > > possible without that constraint.
> > >
> &g=
t; > -Melinda
> > >
> > > On 11/7/2011 10:50 PM,=
schuma wrote:
> > > > Is there a {7,3} IRP?
> > &g=
t; >
> > > > --- In 4D_Cubing@yahoogroups.com, Melinda Gr=
een<melinda@> wrote:
> > > >> How about a FT {7,3}=
IRP?
> > >
> >
>



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Cool!
Wherever did you find it?!

On 11/9/2011 3:16 PM, schuma wrote:
>
>
> Today I visited MSRI to see this sculpture of the Klein Quartic
> .
> The base is a {7,3} in the Poincare Disk view just like in Magic Tile.
> The main part of the sculpture is a folded version of it, which has 24
> curved heptagons.

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Cool!

Wherever did you find it?!



On 11/9/2011 3:16 PM, schuma wrote:

Today I visited MSRI to see href="http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/1675084071/view">this
sculpture of the Klein Quartic. The base is a {7,3} in the
Poincare Disk view just like in Magic Tile. The main part of the
sculpture is a folded version of it, which has 24 curved
heptagons.

I heard about it in many different places where people talked about Klein Q=
uartic. Its location is in a patio of Mathematical Sciences Research Instit=
ute(MSRI), which is located on the hill overlooking Berkeley.=20

--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Cool!
> Wherever did you find it?!
>=20
> On 11/9/2011 3:16 PM, schuma wrote:
> >
> >
> > Today I visited MSRI to see this sculpture of the Klein Quartic=20
> > 75084071/view>.=20
> > The base is a {7,3} in the Poincare Disk view just like in Magic Tile.=
=20
> > The main part of the sculpture is a folded version of it, which has 24=
=20
> > curved heptagons.
>