Thread: "Another {7,3} puzzle"

--0015175dd9cedde94104b3d99646
Content-Type: text/plain; charset=ISO-8859-1

I added a fun version of the {7,3} which has all three types of twisting.
The cuts are shallow, so the puzzle is relatively easy. The
vertex-centered and face-centered circles are all tangent to each other.
If the puzzle only had these two types of twists, there would only be
trivial tips to solve, and face turning twists would scramble nothing.
Adding edge-centered twisting makes things much more interesting.

With all the tangencies and mutual intersections, the pattern of cuts is
quite nice. A picture is
here
.

Cheers,
Roice

--0015175dd9cedde94104b3d99646
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

I added a fun version of the {7,3} which has all three types of twisting. =
=A0The cuts are shallow, so the puzzle is relatively easy. =A0The vertex-ce=
ntered and face-centered circles are all tangent to each other. =A0If the p=
uzzle only had these two types of twists, there would only be trivial tips =
to solve, and face turning twists would scramble nothing. =A0Adding edge-ce=
ntered twisting makes things much more interesting.


With all the tangencies and mutual intersections, the pattern of cuts i=
s quite nice. =A0A picture is ubing/photos/album/1694853720/pic/2077514421/view?picmode=3Doriginal&mo=
de=3Dtn&order=3Dordinal&start=3D1&dir=3Dasc">here.

--------------000403020408030907000007
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit

Wow! That's amazing, Roice!!

Here's the link to the puzzle, just to make it easier for everyone to get:

http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip
Note that there isn't even an install involved. Just unpack the zip file
and run the executable. The new puzzle is found in the menus here:
Puzzle > Hyperbolic > Klein's Quartic > {7,3} FEV Turning.

You know it's funny but I don't think I had even considered the idea of
a hyperbolic puzzle with more than one type of twist. I have to say that
I *really* like the way they work together. It's funny that the edge
pieces can't be moved, they can only be flipped. Of course the face
centers can't move either but all the other types can freely roam the
whole surface.

Looking closely I now see that you already support a {6,3} with two
types of twists. I didn't recall discussing it on the list. Looking at
it now, it seems like such a frightening crazy-quilt. Somehow this new
{7,3} with many more colors and three types of twists seems much more
tractable to me and much more elegant. Might there be other similarly
{6,3} or perhaps even {5,3} puzzles that are as elegant as this new gem?

Some minor suggestions:
* Even with the maximum scramble of 5,000 twists it still doesn't look
quite fully scrambled. You might consider adding a "Full" scramble item
for all of your puzzles and use David's Goldilocks function at least as
a starting point to select a good number. One nice thing about a "Full"
option is that the solver is then assured that that it counts as fully
solved it they manage to solve it.
* It seems to need different twisting speeds for the different element
types.
* It seems to want a more fitting name. I can't think what though so
maybe someone else on the list can suggest one.

This thing is really huge! I'm noticing that when I twist something it
is hard to see other copies also twisting. So will this be much harder
than the other KQ puzzles? What do you think, Nan?

Tremendous job, Roice! I love it.
-Melinda

On 12/11/2011 3:43 PM, Roice Nelson wrote:
>
>
> I added a fun version of the {7,3} which has all three types of
> twisting. The cuts are shallow, so the puzzle is relatively easy.
> The vertex-centered and face-centered circles are all tangent to each
> other. If the puzzle only had these two types of twists, there would
> only be trivial tips to solve, and face turning twists would scramble
> nothing. Adding edge-centered twisting makes things much more
> interesting.
>
> With all the tangencies and mutual intersections, the pattern of cuts
> is quite nice. A picture is here
> .



--------------000403020408030907000007
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit



http-equiv="Content-Type">


Wow! That's amazing, Roice!!



Here's the link to the puzzle, just to make it easier for everyone
to get:

   
http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip

Note that there isn't even an install involved. Just unpack the zip
file and run the executable. The new puzzle is  found in the menus
here:

    Puzzle > Hyperbolic > Klein's Quartic > {7,3} FEV
Turning.



You know it's funny but I don't think I had even considered the idea
of a hyperbolic puzzle with more than one type of twist. I have to
say that I *really* like the way they work together. It's funny that
the edge pieces can't be moved, they can only be flipped. Of course
the face centers can't move either but all the other types can
freely roam the whole surface.



Looking closely I now see that you already support a {6,3} with two
types of twists. I didn't recall discussing it on the list. Looking
at it now, it seems like such a frightening crazy-quilt. Somehow
this new {7,3} with many more colors and three types of twists seems
much more tractable to me and much more elegant. Might there be
other similarly {6,3} or perhaps even {5,3} puzzles that are as
elegant as this new gem?



Some minor suggestions:

* Even with the maximum scramble of 5,000 twists it still doesn't
look quite fully scrambled. You might consider adding a "Full"
scramble item for all of your puzzles and use David's Goldilocks
function at least as a starting point to select a good number. One
nice thing about a "Full" option is that the solver is then assured
that that it counts as fully solved it they manage to solve it.

* It seems to need different twisting speeds for the different
element types.

* It seems to want a more fitting name. I can't think what though so
maybe someone else on the list can suggest one.



This thing is really huge! I'm noticing that when I twist something
it is hard to see other copies also twisting. So will this be much
harder than the other KQ puzzles? What do you think, Nan?



Tremendous job, Roice! I love it.

-Melinda



On 12/11/2011 3:43 PM, Roice Nelson wrote:
cite="mid:CAEMuGXqXFi_C+LCp84-RbiujSUkakq6xOVqfDNQ17UYFnGmDzA@mail.gmail.com"
type="cite">


I added a fun version of the {7,3} which has all three types of
twisting.  The cuts are shallow, so the puzzle is relatively easy.
 The vertex-centered and face-centered circles are all tangent to
each other.  If the puzzle only had these two types of twists,
there would only be trivial tips to solve, and face turning twists
would scramble nothing.  Adding edge-centered twisting makes
things much more interesting.



With all the tangencies and mutual intersections, the pattern of
cuts is quite nice.  A picture is href="http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/2077514421/view?picmode=original&mode=tn&order=ordinal&start=1&dir=asc">here.







--------------000403020408030907000007--

Hi Melinda,

This puzzle ({7,3} FEV turning) is indeed huge. It has 612 pieces, certainl=
y much larger than the {7,3} FT, its dual {3,7} VT, {7,3} ET and {7,3} VT. =
These simpler puzzles have 100~200 pieces. But {7,3} FEV is smaller than {3=
,7} ET and {3,7} FT, which have 800~900 pieces. Solving {7,3} FEV is easier=
than {3,7} ET and FT in several ways:=20
(1) Fewer pieces.
(2) Shorter algorithms to do pure 3-cycles. All 3-cycle algorithms here are=
4-move [1,1] commutators. Easy to remember.
(3) Fewer colors: 24 colors vs 56 colors: easier to find a piece.

I've started solving it for a while. Although I'm still in the early stage =
of this solution, I'll say it's a bit tedious. Just too many pieces.

It's an interesting observation that you can't see the other copies of the =
moving circle. The default view is as same as the classic KQ. where you can=
see the other copies. I think the reason is simple the circles here are sm=
aller than in the classic KQ.

Nan

--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Wow! That's amazing, Roice!!
>=20
> Here's the link to the puzzle, just to make it easier for everyone to get=
:
>=20=20=20=20=20=20
> http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip
> Note that there isn't even an install involved. Just unpack the zip file=
=20
> and run the executable. The new puzzle is found in the menus here:
> Puzzle > Hyperbolic > Klein's Quartic > {7,3} FEV Turning.
>=20
> You know it's funny but I don't think I had even considered the idea of=20
> a hyperbolic puzzle with more than one type of twist. I have to say that=
=20
> I *really* like the way they work together. It's funny that the edge=20
> pieces can't be moved, they can only be flipped. Of course the face=20
> centers can't move either but all the other types can freely roam the=20
> whole surface.
>=20
> Looking closely I now see that you already support a {6,3} with two=20
> types of twists. I didn't recall discussing it on the list. Looking at=20
> it now, it seems like such a frightening crazy-quilt. Somehow this new=20
> {7,3} with many more colors and three types of twists seems much more=20
> tractable to me and much more elegant. Might there be other similarly=20
> {6,3} or perhaps even {5,3} puzzles that are as elegant as this new gem?
>=20
> Some minor suggestions:
> * Even with the maximum scramble of 5,000 twists it still doesn't look=20
> quite fully scrambled. You might consider adding a "Full" scramble item=20
> for all of your puzzles and use David's Goldilocks function at least as=20
> a starting point to select a good number. One nice thing about a "Full"=20
> option is that the solver is then assured that that it counts as fully=20
> solved it they manage to solve it.
> * It seems to need different twisting speeds for the different element=20
> types.
> * It seems to want a more fitting name. I can't think what though so=20
> maybe someone else on the list can suggest one.
>=20
> This thing is really huge! I'm noticing that when I twist something it=20
> is hard to see other copies also twisting. So will this be much harder=20
> than the other KQ puzzles? What do you think, Nan?
>=20
> Tremendous job, Roice! I love it.
> -Melinda
>=20
> On 12/11/2011 3:43 PM, Roice Nelson wrote:
> >
> >
> > I added a fun version of the {7,3} which has all three types of=20
> > twisting. The cuts are shallow, so the puzzle is relatively easy.=20
> > The vertex-centered and face-centered circles are all tangent to each=
=20
> > other. If the puzzle only had these two types of twists, there would=20
> > only be trivial tips to solve, and face turning twists would scramble=20
> > nothing. Adding edge-centered twisting makes things much more=20
> > interesting.
> >
> > With all the tangencies and mutual intersections, the pattern of cuts=20
> > is quite nice. A picture is here=20
> > 77514421/view?picmode=3Doriginal&mode=3Dtn&order=3Dordinal&start=3D1&dir=3D=
asc>.
>

I've just solved {7,3} FEVT. Since turning FT doesn't scramble the puzzle, =
one has a lot of freedom to move the inner small 1C pieces around. Thus the=
"freestyle" setup moves of this kind of pieces are pretty easy to find.

Given that you have enough patience and a couple of hours, it's a relativel=
y easy puzzle to solve.

Nan

--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
>
> Hi Melinda,
>=20
> This puzzle ({7,3} FEV turning) is indeed huge. It has 612 pieces, certai=
nly much larger than the {7,3} FT, its dual {3,7} VT, {7,3} ET and {7,3} VT=
. These simpler puzzles have 100~200 pieces. But {7,3} FEV is smaller than =
{3,7} ET and {3,7} FT, which have 800~900 pieces. Solving {7,3} FEV is easi=
er than {3,7} ET and FT in several ways:=20
> (1) Fewer pieces.
> (2) Shorter algorithms to do pure 3-cycles. All 3-cycle algorithms here a=
re 4-move [1,1] commutators. Easy to remember.
> (3) Fewer colors: 24 colors vs 56 colors: easier to find a piece.
>=20
> I've started solving it for a while. Although I'm still in the early stag=
e of this solution, I'll say it's a bit tedious. Just too many pieces.
>=20
> It's an interesting observation that you can't see the other copies of th=
e moving circle. The default view is as same as the classic KQ. where you c=
an see the other copies. I think the reason is simple the circles here are =
smaller than in the classic KQ.
>=20
> Nan
>=20
> --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
> >
> > Wow! That's amazing, Roice!!
> >=20
> > Here's the link to the puzzle, just to make it easier for everyone to g=
et:
> >=20=20=20=20=20=20
> > http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.z=
ip
> > Note that there isn't even an install involved. Just unpack the zip fil=
e=20
> > and run the executable. The new puzzle is found in the menus here:
> > Puzzle > Hyperbolic > Klein's Quartic > {7,3} FEV Turning.
> >=20
> > You know it's funny but I don't think I had even considered the idea of=
=20
> > a hyperbolic puzzle with more than one type of twist. I have to say tha=
t=20
> > I *really* like the way they work together. It's funny that the edge=20
> > pieces can't be moved, they can only be flipped. Of course the face=20
> > centers can't move either but all the other types can freely roam the=20
> > whole surface.
> >=20
> > Looking closely I now see that you already support a {6,3} with two=20
> > types of twists. I didn't recall discussing it on the list. Looking at=
=20
> > it now, it seems like such a frightening crazy-quilt. Somehow this new=
=20
> > {7,3} with many more colors and three types of twists seems much more=20
> > tractable to me and much more elegant. Might there be other similarly=20
> > {6,3} or perhaps even {5,3} puzzles that are as elegant as this new gem=
?
> >=20
> > Some minor suggestions:
> > * Even with the maximum scramble of 5,000 twists it still doesn't look=
=20
> > quite fully scrambled. You might consider adding a "Full" scramble item=
=20
> > for all of your puzzles and use David's Goldilocks function at least as=
=20
> > a starting point to select a good number. One nice thing about a "Full"=
=20
> > option is that the solver is then assured that that it counts as fully=
=20
> > solved it they manage to solve it.
> > * It seems to need different twisting speeds for the different element=
=20
> > types.
> > * It seems to want a more fitting name. I can't think what though so=20
> > maybe someone else on the list can suggest one.
> >=20
> > This thing is really huge! I'm noticing that when I twist something it=
=20
> > is hard to see other copies also twisting. So will this be much harder=
=20
> > than the other KQ puzzles? What do you think, Nan?
> >=20
> > Tremendous job, Roice! I love it.
> > -Melinda
> >=20
> > On 12/11/2011 3:43 PM, Roice Nelson wrote:
> > >
> > >
> > > I added a fun version of the {7,3} which has all three types of=20
> > > twisting. The cuts are shallow, so the puzzle is relatively easy.=20
> > > The vertex-centered and face-centered circles are all tangent to eac=
h=20
> > > other. If the puzzle only had these two types of twists, there would=
=20
> > > only be trivial tips to solve, and face turning twists would scramble=
=20
> > > nothing. Adding edge-centered twisting makes things much more=20
> > > interesting.
> > >
> > > With all the tangencies and mutual intersections, the pattern of cuts=
=20
> > > is quite nice. A picture is here=20
> > > 2077514421/view?picmode=3Doriginal&mode=3Dtn&order=3Dordinal&start=3D1&dir=
=3Dasc>.
> >
>

I've just finished solving of {7,3} FEVT. It took about 6 hours, and I used=
only one macro (3-cycle of radial 1C). Puzzle is easy enough. What is unus=
ual - you can't move large set of pieces by FT rotation, so you have to bui=
ld long sequence of twists for setups.

6779 twists. Could be less with different solving strategy.

Roice, thank you for the puzzle!

Andrey


--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>
> I added a fun version of the {7,3} which has all three types of twisting.
> The cuts are shallow, so the puzzle is relatively easy. The
> vertex-centered and face-centered circles are all tangent to each other.
> If the puzzle only had these two types of twists, there would only be
> trivial tips to solve, and face turning twists would scramble nothing.
> Adding edge-centered twisting makes things much more interesting.
>=20
> With all the tangencies and mutual intersections, the pattern of cuts is
> quite nice. A picture is
> here2077514421/view?picmode=3Doriginal&mode=3Dtn&order=3Dordinal&start=3D1&dir=
=3Dasc>
> .
>=20
> Cheers,
> Roice
>

--0015175cfd7e4f23f604b3ef64e8
Content-Type: text/plain; charset=ISO-8859-1

On Sun, Dec 11, 2011 at 9:41 PM, Melinda Green wrote:

> Wow! That's amazing, Roice!!
>

Thanks! I didn't know this one was going to get such a good reaction :D


> Looking closely I now see that you already support a {6,3} with two
> types of twists. I didn't recall discussing it on the list. Looking at it
> now, it seems like such a frightening crazy-quilt. Somehow this new {7,3}
> with many more colors and three types of twists seems much more tractable
> to me and much more elegant. Might there be other similarly {6,3} or
> perhaps even {5,3} puzzles that are as elegant as this new gem?
>

Yep, this cut pattern works for other tilings. I went ahead and added
{5,3} and {6,3} variants (and uploaded pictures
here
and
here).


A disclaimer though... This {5,3} is the first spherical puzzle I've put
into MagicTile V2, and it's not really ready. Twisting of inverted slices
misbehaves (affects one inverted slice in this puzzle), plus the drawing is
undeveloped (stickers aren't filled in, and twists aren't animated). The
spherical world needs some love.


> * It seems to need different twisting speeds for the different element
> types.
>

Right now, I have the different twist types animating so they will complete
in the same time interval. Because of the varying angles they rotate
through, this makes some twist types appear to move faster than others. I
liked this better than having all twist types rotate through the same angle
at each animation step. Edge twists felt like they took too long to
complete that way.


> * It seems to want a more fitting name. I can't think what though so maybe
> someone else on the list can suggest one.
>

I agree completely. FEV isn't really descriptive enough, as there are a
huge number of potential FEV puzzles, and this particular pattern would
benefit from having a special name for sure. A couple ideas are to name
them "Braid" puzzles or "Doily" puzzles. Maybe something else which evoked
the image of all the tangent circles would be good...

Roice

--0015175cfd7e4f23f604b3ef64e8
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable