That was about all that Roice said about these three puzzles and nobody
seems to have noticed them. That's understandable because he was
dropping hundreds of new puzzles on us at the same time and the {8,4}s
were at the very end. Well I stumbled into them a couple of days ago and
can say "Mighty strange indeed!" As you know, I've been focusing on
edge-turning puzzles that I can solve intuitively and found the 5-color
and 10-color versions to be a lot of fun. They start out easy enough and
finish with enough of a brain stretch to be quite rewarding to solve. I
had tried and failed with with the 9-color version after a couple of
half-hearted attempts, but since I had solved the other two I figured it
was time to make a serious attempt to collect all three, and all I can
say is "OH................................, MY GOD!" Roice mentioned
that they have some interesting topological properties that would be fun
to study and I completely agree. The best single word I can find to
describe tthe 9-color version is "perverse". Rather than try to
describe what I found, I want to invite Ed and Nan and any other serious
puzzlers to give these a shot. Then please let us know what you think.
Do they yield easily to your standard methods? Do the face and vertex
turning version behave as oddly as the edge-turning? I definitely want
to learn more about these bad boys!
-Melinda
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I can't help in the solution department, but here is some basic info about
the topologies :)
*{8,4} 5-Color*
Faces 5
Edges 8
Vertices 4
Euler Characteristic 1
*{8,4} 9-Color*
Faces 9
Edges 16
Vertices 8
Euler Characteristic 1
*{8,4} 10-Color*
Faces 10
Edges 16
Vertices 8
Euler Characteristic 2
So the first two have the topology of the projective plane
(non-orientable), and the last of the sphere.
Anyone want to figure out counts and kinds (henagons, digons, etc.) of the
particular faces? The 10C should have a nice, planar graph representation.
Roice
On Fri, Jun 1, 2012 at 5:23 AM, Melinda Green
> That was about all that Roice said about these three puzzles and nobody
> seems to have noticed them. That's understandable because he was
> dropping hundreds of new puzzles on us at the same time and the {8,4}s
> were at the very end. Well I stumbled into them a couple of days ago and
> can say "Mighty strange indeed!" As you know, I've been focusing on
> edge-turning puzzles that I can solve intuitively and found the 5-color
> and 10-color versions to be a lot of fun. They start out easy enough and
> finish with enough of a brain stretch to be quite rewarding to solve. I
> had tried and failed with with the 9-color version after a couple of
> half-hearted attempts, but since I had solved the other two I figured it
> was time to make a serious attempt to collect all three, and all I can
> say is "OH................................, MY GOD!" Roice mentioned
> that they have some interesting topological properties that would be fun
> to study and I completely agree. The best single word I can find to
> describe tthe 9-color version is "perverse". Rather than try to
> describe what I found, I want to invite Ed and Nan and any other serious
> puzzlers to give these a shot. Then please let us know what you think.
> Do they yield easily to your standard methods? Do the face and vertex
> turning version behave as oddly as the edge-turning? I definitely want
> to learn more about these bad boys!
>
> -Melinda
>
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fo about the topologies :)
racteristic 1
Edges 16
=A0
es 16
the first two have the topology of the projective plane (non-orientable), =
and the last of the sphere.
to figure out counts and kinds (henagons, digons, etc.) of the particular =
faces?=A0 The 10C should have a nice, planar graph representation.
=A0
Jun 1, 2012 at 5:23 AM, Melinda Green <to:melinda@superliminal.com" target=3D"_blank">melinda@superliminal.com=
> wrote:color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class=
=3D"gmail_quote">That was about all that Roice said about these three puzzl=
es and nobody
seems to have noticed them. That's understandable because he was
dropping hundreds of new puzzles on us at the same time and the {8,4}s
were at the very end. Well I stumbled into them a couple of days ago and
can say "Mighty strange indeed!" As you know, I've been focus=
ing on
edge-turning puzzles that I can solve intuitively and found the 5-color
and 10-color versions to be a lot of fun. They start out easy enough and
finish with enough of a brain stretch to be quite rewarding to solve. I
had tried and failed with with the 9-color version after a couple of
half-hearted attempts, but since I had solved the other two I figured it
was time to make a serious attempt to collect all three, and all I can
say is "OH................................, MY GOD!" Roice mentio=
ned
that they have some interesting topological properties that would be fun
to study and I completely agree. The best single word I can find to
describe tthe 9-color version is "perverse". =A0Rather than try t=
o
describe what I found, I want to invite Ed and Nan and any other serious
puzzlers to give these a shot. Then please let us know what you think.
Do they yield easily to your standard methods? Do the face and vertex
turning version behave as oddly as the edge-turning? I definitely want
to learn more about these bad boys!
-Melinda
--e89a8f22c34f388bff04c16ac030--
From: Roice Nelson <roice3@gmail.com>
Date: Sat, 2 Jun 2012 09:58:53 -0500
Subject: Re: [MC4D] "Three strange {8,4} colorings"
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Melinda asked if I could add FEV versions for the {8,4} puzzles, so they
are available now
.
For the other FEV puzzles we've discussed, I set the E and V cut diameters
to the tiling edge length, then made the F cuts tangent to the V cuts. On
the {8,4} tilings, you get some tiny pieces with this approach, so I made
the {8,4} FEV puzzles slightly different. The V cut is still equal to the
tile edge length and the F cut is still tangent to it (on this tiling, they
turn out to have the same radius), but I configured the E cut slightly
smaller. It is set to intersect where the F and V cuts are tangent. I
like the result
49 stickers per face.
Cheers,
Roice
On Fri, Jun 1, 2012 at 10:22 AM, Roice Nelson
> I can't help in the solution department, but here is some basic info about
> the topologies :)
>
> *{8,4} 5-Color*
> Faces 5
> Edges 8
> Vertices 4
> Euler Characteristic 1
>
> *{8,4} 9-Color*
> Faces 9
> Edges 16
> Vertices 8
> Euler Characteristic 1
>
> *{8,4} 10-Color*
> Faces 10
> Edges 16
> Vertices 8
> Euler Characteristic 2
>
> So the first two have the topology of the projective plane
> (non-orientable), and the last of the sphere.
>
> Anyone want to figure out counts and kinds (henagons, digons, etc.) of the
> particular faces? The 10C should have a nice, planar graph representation.
> Roice
>
>
> On Fri, Jun 1, 2012 at 5:23 AM, Melinda Green
>
>> That was about all that Roice said about these three puzzles and nobody
>> seems to have noticed them. That's understandable because he was
>> dropping hundreds of new puzzles on us at the same time and the {8,4}s
>> were at the very end. Well I stumbled into them a couple of days ago and
>> can say "Mighty strange indeed!" As you know, I've been focusing on
>> edge-turning puzzles that I can solve intuitively and found the 5-color
>> and 10-color versions to be a lot of fun. They start out easy enough and
>> finish with enough of a brain stretch to be quite rewarding to solve. I
>> had tried and failed with with the 9-color version after a couple of
>> half-hearted attempts, but since I had solved the other two I figured it
>> was time to make a serious attempt to collect all three, and all I can
>> say is "OH................................, MY GOD!" Roice mentioned
>> that they have some interesting topological properties that would be fun
>> to study and I completely agree. The best single word I can find to
>> describe tthe 9-color version is "perverse". Rather than try to
>> describe what I found, I want to invite Ed and Nan and any other serious
>> puzzlers to give these a shot. Then please let us know what you think.
>> Do they yield easily to your standard methods? Do the face and vertex
>> turning version behave as oddly as the edge-turning? I definitely want
>> to learn more about these bad boys!
>>
>> -Melinda
>>
>
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Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
ey are e_v2.zip">available now.
zles we've discussed, I set the E and V cut diameters to the tiling edg=
e length, then made the F cuts tangent to the V cuts.=A0 On the {8,4} tilin=
gs, you get some tiny pieces with this approach, so I=A0made the {8,4} FEV =
puzzles=A0slightly different.=A0 The V cut is still equal to the tile edge =
length and the F cut is still tangent to it (on this tiling, they turn out =
to have the same radius), but I configured the E cut slightly smaller.=A0 I=
t is set to intersect where the F and V cuts are tangent.=A0 I like =3D"http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/189=
3562896/view?picmode=3Dlarge">the result.=A0 49 stickers per face.>
mail.com> wrote:color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class=
=3D"gmail_quote">
is some basic info about the topologies :)
8
Edges 16
=A0
es 16
the first two have the topology of the projective plane (non-orientable), =
and the last of the sphere.
to figure out counts and kinds (henagons, digons, etc.) of the particular =
faces?=A0 The 10C should have a nice, planar graph representation.
=A0
2012 at 5:23 AM, Melinda Green <nda@superliminal.com" target=3D"_blank">melinda@superliminal.com>pan> wrote:color:rgb(204,204,204);border-left-width:1px;border-left-style:solid" class=
=3D"gmail_quote">That was about all that Roice said about these three puzzl=
es and nobody
seems to have noticed them. That's understandable because he was
dropping hundreds of new puzzles on us at the same time and the {8,4}s
were at the very end. Well I stumbled into them a couple of days ago and
can say "Mighty strange indeed!" As you know, I've been focus=
ing on
edge-turning puzzles that I can solve intuitively and found the 5-color
and 10-color versions to be a lot of fun. They start out easy enough and
finish with enough of a brain stretch to be quite rewarding to solve. I
had tried and failed with with the 9-color version after a couple of
half-hearted attempts, but since I had solved the other two I figured it
was time to make a serious attempt to collect all three, and all I can
say is "OH................................, MY GOD!" Roice mentio=
ned
that they have some interesting topological properties that would be fun
to study and I completely agree. The best single word I can find to
describe tthe 9-color version is "perverse". =A0Rather than try t=
o
describe what I found, I want to invite Ed and Nan and any other serious
puzzlers to give these a shot. Then please let us know what you think.
Do they yield easily to your standard methods? Do the face and vertex
turning version behave as oddly as the edge-turning? I definitely want
to learn more about these bad boys!
-Melinda
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