Hi guys,
Recently I made a puzzle simulator called RefleCube:
http://nanma80.github.com/
The idea is, instead of twisting a layer by 90 degrees like on the Rubik's =
Cube, we can mirror a layer. For example, the top layer (U) can be mirrored=
with respect to the plane bisecting the cube into left and right halves. T=
he result of the reflection is swapping UFR with UFL, UBR with UBL, UR with=
UL.=20
We can also think of reflecting a layer with respect to a diagonal plane so=
that UFR<->UBL, UF<->UL, UR<->UB.
I call the first transform "mirror +", and the second transform "mirror X".=
=20
You can choose to play a puzzle with only one type of mirroring moves, or b=
oth of them (which implies the Rubik's Cube's twisting moves).
I also included the common Rubik's cube and a half-turn cube (only allows 1=
80 degree turns) because they are related.
This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/cube/=
mc2d.html) and the discussion about it. I also emulated this puzzle using M=
C4D and MPUlt before implementing it. You know, we can use 4D rotation to e=
mulate 3D reflection.
I'm not going to tell you what can happen or cannot happen on RefleCube. Fi=
nd out by yourself!
Nan
------=_NextPart_000_0022_01CDDC61.4D189ED0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Awesome!
Very cool, your RefleCube !
Ed
----- Original Message -----=20
From: schuma=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Monday, December 17, 2012 7:40 AM
Subject: [MC4D] RefleCube: a reflection on the Rubik's Cube
=20=20=20=20
Hi guys,
Recently I made a puzzle simulator called RefleCube:
http://nanma80.github.com/
The idea is, instead of twisting a layer by 90 degrees like on the Rubik'=
s Cube, we can mirror a layer. For example, the top layer (U) can be mirror=
ed with respect to the plane bisecting the cube into left and right halves.=
The result of the reflection is swapping UFR with UFL, UBR with UBL, UR wi=
th UL.=20
We can also think of reflecting a layer with respect to a diagonal plane =
so that UFR<->UBL, UF<->UL, UR<->UB.
I call the first transform "mirror +", and the second transform "mirror X=
".=20
You can choose to play a puzzle with only one type of mirroring moves, or=
both of them (which implies the Rubik's Cube's twisting moves).
I also included the common Rubik's cube and a half-turn cube (only allows=
180 degree turns) because they are related.
This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/cub=
e/mc2d.html) and the discussion about it. I also emulated this puzzle using=
MC4D and MPUlt before implementing it. You know, we can use 4D rotation to=
emulate 3D reflection.
I'm not going to tell you what can happen or cannot happen on RefleCube. =
Find out by yourself!
Nan
=20=20
------=_NextPart_000_0022_01CDDC61.4D189ED0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
Hi guys,
Recently I made a puzzle simulator called=20
RefleCube:
idea is, instead of twisting a layer by 90 degrees like on the Rubik's Cu=
be,=20
we can mirror a layer. For example, the top layer (U) can be mirrored wit=
h=20
respect to the plane bisecting the cube into left and right halves. The r=
esult=20
of the reflection is swapping UFR with UFL, UBR with UBL, UR with UL.=20
We can also think of reflecting a layer with respect to a diagona=
l=20
plane so that UFR<->UBL, UF<->UL, UR<->UB.
I cal=
l the=20
first transform "mirror +", and the second transform "mirror X".
=
You=20
can choose to play a puzzle with only one type of mirroring moves, or bot=
h of=20
them (which implies the Rubik's Cube's twisting moves).
I also inc=
luded=20
the common Rubik's cube and a half-turn cube (only allows 180 degree turn=
s)=20
because they are related.
This puzzle is inspired by Magic Cube 2D=
(
al.com/cube/mc2d.html)=20
and the discussion about it. I also emulated this puzzle using MC4D and M=
PUlt=20
before implementing it. You know, we can use 4D rotation to emulate 3D=20
reflection.
I'm not going to tell you what can happen or cannot ha=
ppen=20
on RefleCube. Find out by yourself!
Nan
Nice puzzle!
Mirror+ and mirrorX solved, no special operations required :) Now trying =
mixed puzzle...
Andrey
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Hi guys,
>=20
> Recently I made a puzzle simulator called RefleCube:
>=20
> http://nanma80.github.com/
>=20
> The idea is, instead of twisting a layer by 90 degrees like on the Rubik'=
s Cube, we can mirror a layer. For example, the top layer (U) can be mirror=
ed with respect to the plane bisecting the cube into left and right halves.=
The result of the reflection is swapping UFR with UFL, UBR with UBL, UR wi=
th UL.=20
>=20
> We can also think of reflecting a layer with respect to a diagonal plane =
so that UFR<->UBL, UF<->UL, UR<->UB.
>=20
> I call the first transform "mirror +", and the second transform "mirror X=
".=20
>=20
> You can choose to play a puzzle with only one type of mirroring moves, or=
both of them (which implies the Rubik's Cube's twisting moves).
>=20
> I also included the common Rubik's cube and a half-turn cube (only allows=
180 degree turns) because they are related.
>=20
> This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/cub=
e/mc2d.html) and the discussion about it. I also emulated this puzzle using=
MC4D and MPUlt before implementing it. You know, we can use 4D rotation to=
emulate 3D reflection.
>=20
> I'm not going to tell you what can happen or cannot happen on RefleCube. =
Find out by yourself!
>=20
> Nan
>
Mixed cube solved... Very funny thing :)
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Nice puzzle!
> Mirror+ and mirrorX solved, no special operations required :) Now tryin=
g mixed puzzle...
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Hi guys,
> >=20
> > Recently I made a puzzle simulator called RefleCube:
> >=20
> > http://nanma80.github.com/
> >=20
> > The idea is, instead of twisting a layer by 90 degrees like on the Rubi=
k's Cube, we can mirror a layer. For example, the top layer (U) can be mirr=
ored with respect to the plane bisecting the cube into left and right halve=
s. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR =
with UL.=20
> >=20
> > We can also think of reflecting a layer with respect to a diagonal plan=
e so that UFR<->UBL, UF<->UL, UR<->UB.
> >=20
> > I call the first transform "mirror +", and the second transform "mirror=
X".=20
> >=20
> > You can choose to play a puzzle with only one type of mirroring moves, =
or both of them (which implies the Rubik's Cube's twisting moves).
> >=20
> > I also included the common Rubik's cube and a half-turn cube (only allo=
ws 180 degree turns) because they are related.
> >=20
> > This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/c=
ube/mc2d.html) and the discussion about it. I also emulated this puzzle usi=
ng MC4D and MPUlt before implementing it. You know, we can use 4D rotation =
to emulate 3D reflection.
> >=20
> > I'm not going to tell you what can happen or cannot happen on RefleCube=
. Find out by yourself!
> >=20
> > Nan
> >
>
Thanks! By the way, how special do you think is special? The corners of mir=
ror x behave more like MC4D.=20
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Nice puzzle!
> Mirror+ and mirrorX solved, no special operations required :) Now tryin=
g mixed puzzle...
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Hi guys,
> >=20
> > Recently I made a puzzle simulator called RefleCube:
> >=20
> > http://nanma80.github.com/
> >=20
> > The idea is, instead of twisting a layer by 90 degrees like on the Rubi=
k's Cube, we can mirror a layer. For example, the top layer (U) can be mirr=
ored with respect to the plane bisecting the cube into left and right halve=
s. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR =
with UL.=20
> >=20
> > We can also think of reflecting a layer with respect to a diagonal plan=
e so that UFR<->UBL, UF<->UL, UR<->UB.
> >=20
> > I call the first transform "mirror +", and the second transform "mirror=
X".=20
> >=20
> > You can choose to play a puzzle with only one type of mirroring moves, =
or both of them (which implies the Rubik's Cube's twisting moves).
> >=20
> > I also included the common Rubik's cube and a half-turn cube (only allo=
ws 180 degree turns) because they are related.
> >=20
> > This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/c=
ube/mc2d.html) and the discussion about it. I also emulated this puzzle usi=
ng MC4D and MPUlt before implementing it. You know, we can use 4D rotation =
to emulate 3D reflection.
> >=20
> > I'm not going to tell you what can happen or cannot happen on RefleCube=
. Find out by yourself!
> >=20
> > Nan
> >
>
--f46d04083e0f63c49a04d10fb10a
Content-Type: text/plain; charset=ISO-8859-1
Very cool Nan! I really like the page you added, 'Wacky things to see',
with the spoilers of what can happen. I have a Rubik's Cube at home I keep
with a single twirled corner (I don't know why, it just makes me smile), so
it's nice to know I could actually solve it if it were a RefleCube :D
I thought I'd mention that David Vanderschel's Magic Cube
3D
supports these reflection moves as well. David introduced his program and
mentioned reflection twists in the following post:
http://games.groups.yahoo.com/group/4D_Cubing/message/290
It may be one of the topics that provided your inspiration, but this long
thread also has discussion about reflection twists, in various places:
http://games.groups.yahoo.com/group/4D_Cubing/message/546
Cheers,
Roice
On Mon, Dec 17, 2012 at 12:40 AM, schuma
> Hi guys,
>
> Recently I made a puzzle simulator called RefleCube:
>
> http://nanma80.github.com/
>
> The idea is, instead of twisting a layer by 90 degrees like on the Rubik's
> Cube, we can mirror a layer. For example, the top layer (U) can be mirrored
> with respect to the plane bisecting the cube into left and right halves.
> The result of the reflection is swapping UFR with UFL, UBR with UBL, UR
> with UL.
>
> We can also think of reflecting a layer with respect to a diagonal plane
> so that UFR<->UBL, UF<->UL, UR<->UB.
>
> I call the first transform "mirror +", and the second transform "mirror X".
>
> You can choose to play a puzzle with only one type of mirroring moves, or
> both of them (which implies the Rubik's Cube's twisting moves).
>
> I also included the common Rubik's cube and a half-turn cube (only allows
> 180 degree turns) because they are related.
>
> This puzzle is inspired by Magic Cube 2D (
> http://www.superliminal.com/cube/mc2d.html) and the discussion about it.
> I also emulated this puzzle using MC4D and MPUlt before implementing it.
> You know, we can use 4D rotation to emulate 3D reflection.
>
> I'm not going to tell you what can happen or cannot happen on RefleCube.
> Find out by yourself!
>
> Nan
>
>
>
--f46d04083e0f63c49a04d10fb10a
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
Very cool Nan! =A0I really like the page you added, 'Wacky things to se=
e', with the spoilers of what can happen. =A0I have a Rubik's Cube =
at home I keep with a single twirled corner (I don't know why, it just =
makes me smile), so it's nice to know I could actually solve it if it w=
ere a RefleCube :D
I thought I'd mention that David Vanderschel's //david-v.home.texas.net/MC3D/" target=3D"_blank">Magic Cube 3D=A0progr=
am supports these reflection moves as well. =A0David introduced his program=
and mentioned reflection twists in the following post:
at provided your inspiration, but this long thread also has discussion abou=
t reflection twists, in various places:
chuma <=3D"_blank">mananself@gmail.com> wrote:=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex">
Hi guys,
Recently I made a puzzle simulator called RefleCube:
http://nanma80.git=
hub.com/
The idea is, instead of twisting a layer by 90 degrees like on the Rubik=
9;s Cube, we can mirror a layer. For example, the top layer (U) can be mirr=
ored with respect to the plane bisecting the cube into left and right halve=
s. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR =
with UL.
We can also think of reflecting a layer with respect to a diagonal plane so=
that UFR<->UBL, UF<->UL, UR<->UB.
I call the first transform "mirror +", and the second transform &=
quot;mirror X".
You can choose to play a puzzle with only one type of mirroring moves, or b=
oth of them (which implies the Rubik's Cube's twisting moves).
I also included the common Rubik's cube and a half-turn cube (only allo=
ws 180 degree turns) because they are related.
This puzzle is inspired by Magic Cube 2D (l.com/cube/mc2d.html" target=3D"_blank">http://www.superliminal.com/cube/mc=
2d.html) and the discussion about it. I also emulated this puzzle using=
MC4D and MPUlt before implementing it. You know, we can use 4D rotation to=
emulate 3D reflection.
I'm not going to tell you what can happen or cannot happen on RefleCube=
. Find out by yourself!
Nan
Corners of mirror x behave like stickers of FTO :) Most complicated operati=
on was [[2,2],1] may be with 1 or 2 setup reflections - to reflect two corn=
ers of mirror x or mixed puzzle. I know that I could reduce it to 8 moves (=
like 3-cycle of corners in 3^3), but what I've used is more easy to re-inve=
nt when I see what do I want to do.
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Thanks! By the way, how special do you think is special? The corners of m=
irror x behave more like MC4D.=20
>=20
> --- In 4D_Cubing@yahoogroups.com, "Andrey"
> >
> > Nice puzzle!
> > Mirror+ and mirrorX solved, no special operations required :) Now try=
ing mixed puzzle...
> >=20
> > Andrey
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "schuma"
> > >
> > > Hi guys,
> > >=20
> > > Recently I made a puzzle simulator called RefleCube:
> > >=20
> > > http://nanma80.github.com/
> > >=20
> > > The idea is, instead of twisting a layer by 90 degrees like on the Ru=
bik's Cube, we can mirror a layer. For example, the top layer (U) can be mi=
rrored with respect to the plane bisecting the cube into left and right hal=
ves. The result of the reflection is swapping UFR with UFL, UBR with UBL, U=
R with UL.=20
> > >=20
> > > We can also think of reflecting a layer with respect to a diagonal pl=
ane so that UFR<->UBL, UF<->UL, UR<->UB.
> > >=20
> > > I call the first transform "mirror +", and the second transform "mirr=
or X".=20
> > >=20
> > > You can choose to play a puzzle with only one type of mirroring moves=
, or both of them (which implies the Rubik's Cube's twisting moves).
> > >=20
> > > I also included the common Rubik's cube and a half-turn cube (only al=
lows 180 degree turns) because they are related.
> > >=20
> > > This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com=
/cube/mc2d.html) and the discussion about it. I also emulated this puzzle u=
sing MC4D and MPUlt before implementing it. You know, we can use 4D rotatio=
n to emulate 3D reflection.
> > >=20
> > > I'm not going to tell you what can happen or cannot happen on RefleCu=
be. Find out by yourself!
> > >=20
> > > Nan
> > >
> >
>
Correction: it was [[1,1],1] - 10 moves
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Corners of mirror x behave like stickers of FTO :) Most complicated opera=
tion was [[2,2],1] may be with 1 or 2 setup reflections - to reflect two co=
rners of mirror x or mixed puzzle. I know that I could reduce it to 8 moves=
(like 3-cycle of corners in 3^3), but what I've used is more easy to re-in=
vent when I see what do I want to do.
>=20
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Thanks! By the way, how special do you think is special? The corners of=
mirror x behave more like MC4D.=20
> >=20
> > --- In 4D_Cubing@yahoogroups.com, "Andrey"
> > >
> > > Nice puzzle!
> > > Mirror+ and mirrorX solved, no special operations required :) Now t=
rying mixed puzzle...
> > >=20
> > > Andrey
> > >=20
> > > --- In 4D_Cubing@yahoogroups.com, "schuma"
> > > >
> > > > Hi guys,
> > > >=20
> > > > Recently I made a puzzle simulator called RefleCube:
> > > >=20
> > > > http://nanma80.github.com/
> > > >=20
> > > > The idea is, instead of twisting a layer by 90 degrees like on the =
Rubik's Cube, we can mirror a layer. For example, the top layer (U) can be =
mirrored with respect to the plane bisecting the cube into left and right h=
alves. The result of the reflection is swapping UFR with UFL, UBR with UBL,=
UR with UL.=20
> > > >=20
> > > > We can also think of reflecting a layer with respect to a diagonal =
plane so that UFR<->UBL, UF<->UL, UR<->UB.
> > > >=20
> > > > I call the first transform "mirror +", and the second transform "mi=
rror X".=20
> > > >=20
> > > > You can choose to play a puzzle with only one type of mirroring mov=
es, or both of them (which implies the Rubik's Cube's twisting moves).
> > > >=20
> > > > I also included the common Rubik's cube and a half-turn cube (only =
allows 180 degree turns) because they are related.
> > > >=20
> > > > This puzzle is inspired by Magic Cube 2D (http://www.superliminal.c=
om/cube/mc2d.html) and the discussion about it. I also emulated this puzzle=
using MC4D and MPUlt before implementing it. You know, we can use 4D rotat=
ion to emulate 3D reflection.
> > > >=20
> > > > I'm not going to tell you what can happen or cannot happen on Refle=
Cube. Find out by yourself!
> > > >=20
> > > > Nan
> > > >
> > >
> >
>
Hi Roice,
I'm glad that you like this puzzle. And thanks for the links to previous po=
sts. I don't remember David Vanderschel's program and the fact that it supp=
orted reflection. And I only remember the conversation in this group about =
reflection after I joined in 2010.
But I don't feel bad about it. Before I implemented it, I played it using 3=
^4. I found it a very neat puzzle to solve: not tedious, but also not trivi=
al. And I didn't expect mirror + and mirror X were so different when solvin=
g them. Then I decided that it deserved more attention so I went on and mad=
e the puzzle.
So, does any one know of more reflection based puzzles that were implemente=
d, like in 4D?
Nan
--- In 4D_Cubing@yahoogroups.com, Roice Nelson
>
> Very cool Nan! I really like the page you added, 'Wacky things to see',
> with the spoilers of what can happen. I have a Rubik's Cube at home I ke=
ep
> with a single twirled corner (I don't know why, it just makes me smile), =
so
> it's nice to know I could actually solve it if it were a RefleCube :D
>=20
> I thought I'd mention that David Vanderschel's Magic Cube
> 3D
> supports these reflection moves as well. David introduced his program an=
d
> mentioned reflection twists in the following post:
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/message/290
>=20
> It may be one of the topics that provided your inspiration, but this long
> thread also has discussion about reflection twists, in various places:
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/message/546
>=20
> Cheers,
> Roice
>=20
--------------090503010507090408080501
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Indeed, your new puzzle is awesome, Nan! I find your UI to be very easy
to understand and manipulate. I was able to solve the Mirror + version
intuitively which surprised me. I did restart a few times when I felt
stuck near the end so maybe that let me skip the whacky things that can
happen. I like this puzzle a lot, perhaps because so many things that
are tricky to do in the original puzzle can be done here with a single
move.
For those wanting to see reflection moves in David's MC3D, the key is to
type ctrl-q before a mouse click.
Here is a puzzle: What is the simplest way to perform a 90 degree face
twist on the Mirror + or Mirror X puzzles?
-Melinda
On 12/17/2012 9:27 AM, Roice Nelson wrote:
>
>
> Very cool Nan! I really like the page you added, 'Wacky things to
> see', with the spoilers of what can happen. I have a Rubik's Cube at
> home I keep with a single twirled corner (I don't know why, it just
> makes me smile), so it's nice to know I could actually solve it if it
> were a RefleCube :D
>
> I thought I'd mention that David Vanderschel's Magic Cube 3D
>
> reflection moves as well. David introduced his program and mentioned
> reflection twists in the following post:
>
> http://games.groups.yahoo.com/group/4D_Cubing/message/290
>
> It may be one of the topics that provided your inspiration, but this
> long thread also has discussion about reflection twists, in various
> places:
>
> http://games.groups.yahoo.com/group/4D_Cubing/message/546
>
> Cheers,
> Roice
>
>
>
> On Mon, Dec 17, 2012 at 12:40 AM, schuma
>
> Hi guys,
>
> Recently I made a puzzle simulator called RefleCube:
>
> http://nanma80.github.com/
>
> The idea is, instead of twisting a layer by 90 degrees like on the
> Rubik's Cube, we can mirror a layer. For example, the top layer
> (U) can be mirrored with respect to the plane bisecting the cube
> into left and right halves. The result of the reflection is
> swapping UFR with UFL, UBR with UBL, UR with UL.
>
> We can also think of reflecting a layer with respect to a diagonal
> plane so that UFR<->UBL, UF<->UL, UR<->UB.
>
> I call the first transform "mirror +", and the second transform
> "mirror X".
>
> You can choose to play a puzzle with only one type of mirroring
> moves, or both of them (which implies the Rubik's Cube's twisting
> moves).
>
> I also included the common Rubik's cube and a half-turn cube (only
> allows 180 degree turns) because they are related.
>
> This puzzle is inspired by Magic Cube 2D
> (http://www.superliminal.com/cube/mc2d.html) and the discussion
> about it. I also emulated this puzzle using MC4D and MPUlt before
> implementing it. You know, we can use 4D rotation to emulate 3D
> reflection.
>
> I'm not going to tell you what can happen or cannot happen on
> RefleCube. Find out by yourself!
>
> Nan
>
>
>
>
>
--------------090503010507090408080501
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
http-equiv="Content-Type">
Indeed, your new puzzle is awesome, Nan! I find your UI to be very
easy to understand and manipulate. I was able to solve the Mirror +
version intuitively which surprised me. I did restart a few times
when I felt stuck near the end so maybe that let me skip the whacky
things that can happen. I like this puzzle a lot, perhaps because so
many things that are tricky to do in the original puzzle can be done
here with a single move.
For those wanting to see reflection moves in David's MC3D, the key
is to type ctrl-q before a mouse click.
Here is a puzzle: What is the simplest way to perform a 90 degree
face twist on the Mirror + or Mirror X puzzles?
-Melinda
wrote:
type="cite">
Very cool Nan! I really like the page you added, 'Wacky things to
see', with the spoilers of what can happen. I have a Rubik's Cube
at home I keep with a single twirled corner (I don't know why, it
just makes me smile), so it's nice to know I could actually solve
it if it were a RefleCube :D
I thought I'd mention that David Vanderschel's
href="http://david-v.home.texas.net/MC3D/" target="_blank">Magic
Cube 3D program supports these reflection moves as well.
David introduced his program and mentioned reflection twists in
the following post:
target="_blank">http://games.groups.yahoo.com/group/4D_Cubing/message/290
but this long thread also has discussion about reflection
twists, in various places:
schuma < href="mailto:mananself@gmail.com" target="_blank">mananself@gmail.com>
wrote:
Hi guys,
Recently I made a puzzle simulator called RefleCube:
href="http://nanma80.github.com/" target="_blank">http://nanma80.github.com/
The idea is, instead of twisting a layer by 90 degrees
like on the Rubik's Cube, we can mirror a layer. For
example, the top layer (U) can be mirrored with respect to
the plane bisecting the cube into left and right halves.
The result of the reflection is swapping UFR with UFL, UBR
with UBL, UR with UL.
We can also think of reflecting a layer with respect to a
diagonal plane so that UFR<->UBL, UF<->UL,
UR<->UB.
I call the first transform "mirror +", and the second
transform "mirror X".
You can choose to play a puzzle with only one type of
mirroring moves, or both of them (which implies the
Rubik's Cube's twisting moves).
I also included the common Rubik's cube and a half-turn
cube (only allows 180 degree turns) because they are
related.
This puzzle is inspired by Magic Cube 2D (
href="http://www.superliminal.com/cube/mc2d.html"
target="_blank">http://www.superliminal.com/cube/mc2d.html)
and the discussion about it. I also emulated this puzzle
using MC4D and MPUlt before implementing it. You know, we
can use 4D rotation to emulate 3D reflection.
I'm not going to tell you what can happen or cannot happen
on RefleCube. Find out by yourself!
Nan
--------------090503010507090408080501--
Good puzzle about 90 deg twist. I can do both VERY quickly :)
And mixed puzzle needs two reflections.
Andrey
--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
=20
Indeed, your new puzzle is awesome, Nan! I find your UI to be very easy=20
to understand and manipulate. I was able to solve the Mirror + version=20
intuitively which surprised me. I did restart a few times when I felt=20
stuck near the end so maybe that let me skip the whacky things that can=20
happen. I like this puzzle a lot, perhaps because so many things that=20
are tricky to do in the original puzzle can be done here with a single=20
move.
=20
For those wanting to see reflection moves in David's MC3D, the key is to=20
type ctrl-q before a mouse click.
=20
Here is a puzzle: What is the simplest way to perform a 90 degree face=20
twist on the Mirror + or Mirror X puzzles?
=20
-Melinda
=20
On 12/17/2012 9:27 AM, Roice Nelson wrote:
=20
=20
Very cool Nan! I really like the page you added, 'Wacky things to=20
see', with the spoilers of what can happen. I have a Rubik's Cube at=20
home I keep with a single twirled corner (I don't know why, it just=20
makes me smile), so it's nice to know I could actually solve it if it=20
were a RefleCube :D
=20
I thought I'd mention that David Vanderschel's Magic Cube 3D=20
program supports these=20
reflection moves as well. David introduced his program and mentioned=20
reflection twists in the following post:
=20
http://games.groups.yahoo.com/group/4D_Cubing/message/290
=20
It may be one of the topics that provided your inspiration, but this=20
long thread also has discussion about reflection twists, in various=20
places:
=20
http://games.groups.yahoo.com/group/4D_Cubing/message/546
=20
Cheers,
Roice
=20
=20
=20
On Mon, Dec 17, 2012 at 12:40 AM, schuma wrote:
=20
Hi guys,
=20
Recently I made a puzzle simulator called RefleCube:
=20
http://nanma80.github.com/
=20
The idea is, instead of twisting a layer by 90 degrees like on the
Rubik's Cube, we can mirror a layer. For example, the top layer
(U) can be mirrored with respect to the plane bisecting the cube
into left and right halves. The result of the reflection is
swapping UFR with UFL, UBR with UBL, UR with UL.
=20
We can also think of reflecting a layer with respect to a diagonal
plane so that UFR UBL, UF UL, UR UB.
=20
I call the first transform "mirror +", and the second transform
"mirror X".
=20
You can choose to play a puzzle with only one type of mirroring
moves, or both of them (which implies the Rubik's Cube's twisting
moves).
=20
I also included the common Rubik's cube and a half-turn cube (only
allows 180 degree turns) because they are related.
=20
This puzzle is inspired by Magic Cube 2D
(http://www.superliminal.com/cube/mc2d.html) and the discussion
about it. I also emulated this puzzle using MC4D and MPUlt before
implementing it. You know, we can use 4D rotation to emulate 3D
reflection.
=20
I'm not going to tell you what can happen or cannot happen on
RefleCube. Find out by yourself!
=20
Nan
=20
=20
=20
=20
=20
I don't get it. How can you turn a face by 90 degrees on Mirror + only, or =
Mirror X only? I think it's impossible because of the orbit constraints. An=
d the centers never move, so you can't play any trick on the global orienta=
tion.
Nan
--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
=20
Good puzzle about 90 deg twist. I can do both VERY quickly :)
And mixed puzzle needs two reflections.
=20
Andrey
=20
--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
=20=20
Indeed, your new puzzle is awesome, Nan! I find your UI to be very easy=20
to understand and manipulate. I was able to solve the Mirror + version=20
intuitively which surprised me. I did restart a few times when I felt=20
stuck near the end so maybe that let me skip the whacky things that can=20
happen. I like this puzzle a lot, perhaps because so many things that=20
are tricky to do in the original puzzle can be done here with a single=20
move.
=20=20
For those wanting to see reflection moves in David's MC3D, the key is to=
=20
type ctrl-q before a mouse click.
=20=20
Here is a puzzle: What is the simplest way to perform a 90 degree face=20
twist on the Mirror + or Mirror X puzzles?
=20=20
-Melinda
=20=20
Yes, it's the answer. Both puzzles require zero moves because they are impo=
ssible, so you don't even try to solve them.
--- In 4D_Cubing@yahoogroups.com, "schuma" wrote:
=20
I don't get it. How can you turn a face by 90 degrees on Mirror + only, or=
Mirror X only? I think it's impossible because of the orbit constraints. A=
nd the centers never move, so you can't play any trick on the global orient=
ation.
=20
Nan
=20
--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
=20=20
Good puzzle about 90 deg twist. I can do both VERY quickly :)
And mixed puzzle needs two reflections.
=20=20
Andrey
=20=20
--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
=20=20=20
Indeed, your new puzzle is awesome, Nan! I find your UI to be very easy=
=20
to understand and manipulate. I was able to solve the Mirror + version=20
intuitively which surprised me. I did restart a few times when I felt=20
stuck near the end so maybe that let me skip the whacky things that can=
=20
happen. I like this puzzle a lot, perhaps because so many things that=20
are tricky to do in the original puzzle can be done here with a single=20
move.
=20=20=20
For those wanting to see reflection moves in David's MC3D, the key is to=
=20
type ctrl-q before a mouse click.
=20=20=20
Here is a puzzle: What is the simplest way to perform a 90 degree face=20
twist on the Mirror + or Mirror X puzzles?
=20=20=20
-Melinda
Ah ha, I think I see that there are 3 orbits corresponding to the 3
major planes. Each edge piece always stays within it's plane.
-Melinda
On 12/17/2012 8:09 PM, schuma wrote:
> I don't get it. How can you turn a face by 90 degrees on Mirror + only, or Mirror X only? I think it's impossible because of the orbit constraints. And the centers never move, so you can't play any trick on the global orientation.
>
> Nan
>
> --- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>
> Good puzzle about 90 deg twist. I can do both VERY quickly :)
> And mixed puzzle needs two reflections.
>
> Andrey
>
> --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Indeed, your new puzzle is awesome, Nan! I find your UI to be very easy
> to understand and manipulate. I was able to solve the Mirror + version
> intuitively which surprised me. I did restart a few times when I felt
> stuck near the end so maybe that let me skip the whacky things that can
> happen. I like this puzzle a lot, perhaps because so many things that
> are tricky to do in the original puzzle can be done here with a single
> move.
>
> For those wanting to see reflection moves in David's MC3D, the key is to
> type ctrl-q before a mouse click.
>
> Here is a puzzle: What is the simplest way to perform a 90 degree face
> twist on the Mirror + or Mirror X puzzles?
>
> -Melinda
>
>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>
And in mirror X each corner stays in its tetrahedron.
Andrey
--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
=20
Ah ha, I think I see that there are 3 orbits corresponding to the 3=20
major planes. Each edge piece always stays within it's plane.
-Melinda
=20
On 12/17/2012 8:09 PM, schuma wrote:
I don't get it. How can you turn a face by 90 degrees on Mirror + only, o=
r Mirror X only? I think it's impossible because of the orbit constraints. =
And the centers never move, so you can't play any trick on the global orien=
tation.
=20
Nan
=20
--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
=20=20=20=20
Good puzzle about 90 deg twist. I can do both VERY quickly :)
And mixed puzzle needs two reflections.
=20=20=20=20
Andrey
=20=20=20=20
--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
=20=20=20=20=20
Indeed, your new puzzle is awesome, Nan! I find your UI to be very eas=
y
to understand and manipulate. I was able to solve the Mirror + version
intuitively which surprised me. I did restart a few times when I felt
stuck near the end so maybe that let me skip the whacky things that ca=
n
happen. I like this puzzle a lot, perhaps because so many things that
are tricky to do in the original puzzle can be done here with a single
move.
=20=20=20=20=20
For those wanting to see reflection moves in David's MC3D, the key is =
to
type ctrl-q before a mouse click.
=20=20=20=20=20
Here is a puzzle: What is the simplest way to perform a 90 degree face
twist on the Mirror + or Mirror X puzzles?
=20=20=20=20=20
-Melinda
=20=20=20=20=20
=20
=20
=20
=20
------------------------------------
=20
Yahoo! Groups Links
=20
=20
=20
=20
--f46d042c6aebd6d5b904d1242e11
Content-Type: text/plain; charset=ISO-8859-1
On Mon, Dec 17, 2012 at 4:59 PM, schuma wrote:
>
> So, does any one know of more reflection based puzzles that were
> implemented, like in 4D?
>
> Nan
>
>
I don't think anyone has made a 4D reflection puzzle yet, but this would be
a great addition, especially for the 3^4. Single unsolved twirled corners
seem like they would be possible for sure. Maybe even a single unsolved
corner in a 4-cycle would be possible?
Roice
--f46d042c6aebd6d5b904d1242e11
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
eft:1px #ccc solid;padding-left:1ex">
So, does any one know of more reflection based puzzles that were implemente=
d, like in 4D?
Nan
--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
=20
Maybe even a single unsolved
corner in a 4-cycle would be possible?
=20
Roice
I don't think so. Every reflection will change orientation of 8 corner cube=
s, so at any moment you will have even number of wrong oriented corners. Bu=
t 3-loop twist of single 4C may be possible. Permutation of 4C is always ev=
en. Single 3C or single 2C can't have wrong orientation too. But probably w=
e'll can have odd permutation of only 3C or only 2C.
Andrey=20
Hi RefleCube solvers. Thank you all for your support.
Since you guys find these puzzles interesting and have solved them quickly,=
I just added several sizes: 2x2, 4x4 and 5x5. For each size all the mirror=
ing styles are supported. Use shift+click and alt+click to turn the deeper =
layers.=20
Imagine what kind of weird parities you'll see on the 4x4. Have fun!
Nan
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> Nice puzzle!
> Mirror+ and mirrorX solved, no special operations required :) Now tryin=
g mixed puzzle...
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, "schuma"
> >
> > Hi guys,
> >=20
> > Recently I made a puzzle simulator called RefleCube:
> >=20
> > http://nanma80.github.com/
> >=20
> > The idea is, instead of twisting a layer by 90 degrees like on the Rubi=
k's Cube, we can mirror a layer. For example, the top layer (U) can be mirr=
ored with respect to the plane bisecting the cube into left and right halve=
s. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR =
with UL.=20
> >=20
> > We can also think of reflecting a layer with respect to a diagonal plan=
e so that UFR<->UBL, UF<->UL, UR<->UB.
> >=20
> > I call the first transform "mirror +", and the second transform "mirror=
X".=20
> >=20
> > You can choose to play a puzzle with only one type of mirroring moves, =
or both of them (which implies the Rubik's Cube's twisting moves).
> >=20
> > I also included the common Rubik's cube and a half-turn cube (only allo=
ws 180 degree turns) because they are related.
> >=20
> > This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/c=
ube/mc2d.html) and the discussion about it. I also emulated this puzzle usi=
ng MC4D and MPUlt before implementing it. You know, we can use 4D rotation =
to emulate 3D reflection.
> >=20
> > I'm not going to tell you what can happen or cannot happen on RefleCube=
. Find out by yourself!
> >=20
> > Nan
> >
>
Awesome, Nan!
Would someone please calculate the number of unique positions in the 2^3
Mirror+, MirrorX or Half turn puzzles? If their state graphs are small
enough we might learn something about the common features of puzzle
state graphs. By "unique" I mean that it should not be possible to
rotate the whole puzzle from one state into another, nor should it be
possible to recolor one state to produce another one.
Thanks for the new puzzles Nan!
-Melinda
On 12/30/2012 4:01 PM, schuma wrote:
> Hi RefleCube solvers. Thank you all for your support.
>
> Since you guys find these puzzles interesting and have solved them quickly, I just added several sizes: 2x2, 4x4 and 5x5. For each size all the mirroring styles are supported. Use shift+click and alt+click to turn the deeper layers.
>
> Imagine what kind of weird parities you'll see on the 4x4. Have fun!
>
> Nan
>
> --- In 4D_Cubing@yahoogroups.com, "Andrey"
>> Nice puzzle!
>> Mirror+ and mirrorX solved, no special operations required :) Now trying mixed puzzle...
>>
>> Andrey
>>
>> --- In 4D_Cubing@yahoogroups.com, "schuma"
>>> Hi guys,
>>>
>>> Recently I made a puzzle simulator called RefleCube:
>>>
>>> http://nanma80.github.com/
>>>
>>> The idea is, instead of twisting a layer by 90 degrees like on the Rubik's Cube, we can mirror a layer. For example, the top layer (U) can be mirrored with respect to the plane bisecting the cube into left and right halves. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR with UL.
>>>
>>> We can also think of reflecting a layer with respect to a diagonal plane so that UFR<->UBL, UF<->UL, UR<->UB.
>>>
>>> I call the first transform "mirror +", and the second transform "mirror X".
>>>
>>> You can choose to play a puzzle with only one type of mirroring moves, or both of them (which implies the Rubik's Cube's twisting moves).
>>>
>>> I also included the common Rubik's cube and a half-turn cube (only allows 180 degree turns) because they are related.
>>>
>>> This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/cube/mc2d.html) and the discussion about it. I also emulated this puzzle using MC4D and MPUlt before implementing it. You know, we can use 4D rotation to emulate 3D reflection.
>>>
>>> I'm not going to tell you what can happen or cannot happen on RefleCube. Find out by yourself!
>>>
>>> Nan
>>>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>