Thread: "some stained glass"

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Here's another puzzle quiz to throw out there, and shouldn't be too hard :)
Can you tell what it is?

http://www.gravitation3d.com/magictile/pics/stained_glass.png

Cheers,
Roice

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Here's another puzzle quiz to throw out there, and shouldn't be too=
hard :) =A0Can you tell what it is?

Is it the dual of Klein's quartic?=20

--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> Here's another puzzle quiz to throw out there, and shouldn't be too hard =
:)
> Can you tell what it is?
>=20
> http://www.gravitation3d.com/magictile/pics/stained_glass.png
>=20
> Cheers,
> Roice
>

That's my guess too. Here is an undistorted model I built a long time
ago, and in cross-eyed stereo to boot:

http://superliminal.com/geometry/3_7st.jpg

I would sure love to solve it in this form. It may not even be that hard
to implement using a single dynamic texture mapped onto this surface.

-Melinda

On 5/2/2011 7:43 PM, schuma wrote:
> Is it the dual of Klein's quartic?
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>> Here's another puzzle quiz to throw out there, and shouldn't be too hard :)
>> Can you tell what it is?
>>
>> http://www.gravitation3d.com/magictile/pics/stained_glass.png

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Yep, it is based on the {3,7} tiling, and has 56 faces. It is also
noteworthy because the picture is of a vertex-turning puzzle rather than a
face-turning one (the centers of the slicing circles coincide with the
vertices). So I suppose this could be considered a hyperbolic analogue to
gelatinbrain's 2.2.2. It should be a much more pleasant puzzle to solve
than the face-turning {3,7} will be.

Melinda, the texture approach in my recent MagicTile v2 coding has been
working out fantastically, and one great thing about that is I should be
able to map it to an IRP representation at some point without a great deal
of effort :D

seeya,
Roice

On Mon, May 2, 2011 at 9:51 PM, Melinda Green wrote:

> That's my guess too. Here is an undistorted model I built a long time
> ago, and in cross-eyed stereo to boot:
>
> http://superliminal.com/geometry/3_7st.jpg
>
> I would sure love to solve it in this form. It may not even be that hard
> to implement using a single dynamic texture mapped onto this surface.
>
> -Melinda
>
> On 5/2/2011 7:43 PM, schuma wrote:
> > Is it the dual of Klein's quartic?
> >
> > --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> >> Here's another puzzle quiz to throw out there, and shouldn't be too hard
> :)
> >> Can you tell what it is?
> >>
> >> http://www.gravitation3d.com/magictile/pics/stained_glass.png
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

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Yep, it is based on the {3,7} tiling, and has 56 faces. =A0It is also notew=
orthy because the picture is of a vertex-turning puzzle rather than a face-=
turning one (the centers of the slicing circles coincide with the vertices)=
. =A0So I suppose this could be considered a hyperbolic analogue to gelatin=
brain's 2.2.2. =A0It should be a much more pleasant puzzle to solve tha=
n the face-turning {3,7} will be.

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That will be fantastical! There are dozens of other models for which I
have worked out the 3D vertex, face, and tiling data. All you should
need are contined in the xxx_cell.wrl files here:
http://superliminal.com/geometry/infinite/ which describe the repeat
units and their tiling vectors.

I haven't touched that data for a very long time. Now that VRML has long
fallen out of favor, I have been hoping to resurrect it in some more
accessible way, and this sounds like it. What fun!

-Melinda

On 5/2/2011 8:03 PM, Roice Nelson wrote:
>
> Melinda, the texture approach in my recent MagicTile v2 coding has
> been working out fantastically, and one great thing about that is I
> should be able to map it to an IRP representation at some point
> without a great deal of effort :D


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That will be fantastical! There are dozens of other models for which
I have worked out the 3D vertex, face, and tiling data. All you
should need are contined in the xxx_cell.wrl files here:
http://superliminal.com/geometry/infinite/ which describe the repeat
units and their tiling vectors.



I haven't touched that data for a very long time. Now that VRML has
long fallen out of favor, I have been hoping to resurrect it in some
more accessible way, and this sounds like it. What fun!



-Melinda



On 5/2/2011 8:03 PM, Roice Nelson wrote:
cite="mid:BANLkTi=apGMKX5QXpeKU3SrV1myvf+87xg@mail.gmail.com"
type="cite">

The {3,4} counterpart (Gelatinbrain 4.2.1) is more well known, usually call=
ed Trajber's Octahedron. It is now a mass produced cheap puzzle. It's just =
a shape mod and color variation of the common 3x3x3. In my opinion, it's ev=
en easier than 3x3x3 because you don't have to worry about the orientation =
of corners. The 4x4x4 analog is also mass produced. .html?_from=3DR40&_trksid=3Dm570&_nkw=3Dtrajber&_sacat=3DSee-All-Categories=
>

So I believe this vertex turning {3,7} is easier than the current Klein's q=
uartic. (certainly much easier than the face turning {3,7})

Nan

--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> Yep, it is based on the {3,7} tiling, and has 56 faces. It is also
> noteworthy because the picture is of a vertex-turning puzzle rather than =
a
> face-turning one (the centers of the slicing circles coincide with the
> vertices). So I suppose this could be considered a hyperbolic analogue t=
o
> gelatinbrain's 2.2.2. It should be a much more pleasant puzzle to solve
> than the face-turning {3,7} will be.
>=20
> Melinda, the texture approach in my recent MagicTile v2 coding has been
> working out fantastically, and one great thing about that is I should be
> able to map it to an IRP representation at some point without a great dea=
l
> of effort :D
>=20
> seeya,
> Roice
>=20
> On Mon, May 2, 2011 at 9:51 PM, Melinda Green wrote:
>=20
> > That's my guess too. Here is an undistorted model I built a long time
> > ago, and in cross-eyed stereo to boot:
> >
> > http://superliminal.com/geometry/3_7st.jpg
> >
> > I would sure love to solve it in this form. It may not even be that har=
d
> > to implement using a single dynamic texture mapped onto this surface.
> >
> > -Melinda
> >
> > On 5/2/2011 7:43 PM, schuma wrote:
> > > Is it the dual of Klein's quartic?
> > >
> > > --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> > >> Here's another puzzle quiz to throw out there, and shouldn't be too =
hard
> > :)
> > >> Can you tell what it is?
> > >>
> > >> http://www.gravitation3d.com/magictile/pics/stained_glass.png
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>

Yes, in vertex turning {3,n} you don't care about "corners" orientation, bu=
t "centers" orientation is significant there. So you just trade one problem=
to another. Orientation of centers is not a problem for commutator-based a=
lgorithms (in 2D puzzles), but if you solve this puzzle by growing of solve=
d area, you should select center orientation before you "attach" the first =
2C piece to it.=20
So I'm not sure that {3,7} is more easy than {7,3} - they are almost the =
same. But there are too many colors in {3,7} - piece search may be a proble=
m.

Andrey

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> The {3,4} counterpart (Gelatinbrain 4.2.1) is more well known, usually ca=
lled Trajber's Octahedron. It is now a mass produced cheap puzzle. It's jus=
t a shape mod and color variation of the common 3x3x3. In my opinion, it's =
even easier than 3x3x3 because you don't have to worry about the orientatio=
n of corners. The 4x4x4 analog is also mass produced. /i.html?_from=3DR40&_trksid=3Dm570&_nkw=3Dtrajber&_sacat=3DSee-All-Categori=
es>
>=20
> So I believe this vertex turning {3,7} is easier than the current Klein's=
quartic. (certainly much easier than the face turning {3,7})
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> >
> > Yep, it is based on the {3,7} tiling, and has 56 faces. It is also
> > noteworthy because the picture is of a vertex-turning puzzle rather tha=
n a
> > face-turning one (the centers of the slicing circles coincide with the
> > vertices). So I suppose this could be considered a hyperbolic analogue=
to
> > gelatinbrain's 2.2.2. It should be a much more pleasant puzzle to solv=
e
> > than the face-turning {3,7} will be.
> >=20
> > Melinda, the texture approach in my recent MagicTile v2 coding has been
> > working out fantastically, and one great thing about that is I should b=
e
> > able to map it to an IRP representation at some point without a great d=
eal
> > of effort :D
> >=20
> > seeya,
> > Roice
> >=20
> > On Mon, May 2, 2011 at 9:51 PM, Melinda Green wrote:
> >=20
> > > That's my guess too. Here is an undistorted model I built a long time
> > > ago, and in cross-eyed stereo to boot:
> > >
> > > http://superliminal.com/geometry/3_7st.jpg
> > >
> > > I would sure love to solve it in this form. It may not even be that h=
ard
> > > to implement using a single dynamic texture mapped onto this surface.
> > >
> > > -Melinda
> > >
> > > On 5/2/2011 7:43 PM, schuma wrote:
> > > > Is it the dual of Klein's quartic?
> > > >
> > > > --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> > > >> Here's another puzzle quiz to throw out there, and shouldn't be to=
o hard
> > > :)
> > > >> Can you tell what it is?
> > > >>
> > > >> http://www.gravitation3d.com/magictile/pics/stained_glass.png
> > >
> > >
> > > ------------------------------------
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>