Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you can r=
otate by clicking on corners and edges (corner&edge turns). Why is that pos=
sible?=20
I think I asked over 9000 questions so I just made this thread
--- In 4D_Cubing@yahoogroups.com, Anthony Deschamps
>
> As you move into higher dimensions, your algorithms will become a lot
> longer, but they're still based on the same concepts. If you write some
> macros and use those to build more complex macros, then most problems bec=
ome
> a matter of a few set up moves, applying the macro, and then those set up
> moves in reverse. Don't worry, the transition from 4D to 5D is much easi=
er
> than the transition from 3D to 4D.
I'm not sure in that. When I went from 3D to 4D, I converted "positional" a=
lgorithms for 3D (moving or rotating 2 or 3 pieces, leaving the rest in pla=
ce) to layer-by-layer algorithm in 4D - and for positioning of 2C of the la=
st layer I had to use operation that moves 6 pieces at once (two 3-cycles).=
It was difficult but possible. But as a result, I have no "positional" ope=
rations for 4D and there's nothing to use for solving of 4^5 :)
Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca= Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca= Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca= Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca= Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca=
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Hmm good question. i want to know the answer too because im not 100% sure
why you can rotate by clicking on corners and edges. Can any one elaborate
on this?
On Mon, Jul 26, 2010 at 5:23 PM, deustfrr
>
>
> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you can
> rotate by clicking on corners and edges (corner&edge turns). Why is that
> possible?
> I think I asked over 9000 questions so I just made this thread
>
>=20
>
--00163628391ad2caf4048c5eec4a
Content-Type: text/html; charset=windows-1252
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sure why you can rotate by clicking on corners and edges. Can any one elab=
orate on this?
=A0
gt; wrote:; PADDING-LEFT: 1ex" class=3D"gmail_quote">
n rotate by clicking on corners and edges (corner&edge turns). Why is t=
hat possible?
I think I asked over 9000 questions so I just made this t=
hread
--00163628391ad2caf4048c5eec4a--
From: Chris Locke <project.eutopia@gmail.com>
Date: Tue, 27 Jul 2010 23:40:27 +0900
Subject: Re: [MC4D] New: Questions thread...
--0015177408fc6ca2cb048c5f7b2e
Content-Type: text/plain; charset=UTF-8
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It's more of a shortcut than anything really. For each face in 4D, there
are 24 possible twists (that includes the identity twist - i.e. the
do-nothing twist). There are three axis through each face, and if you labe=
l
a quarter-twist of the axes X, Y, Z respectively, then it turns out all the
possible twists can be built from a combination of these elementary twists.
The corner and edge twists are basically a combination of these fundamental
twists and are not necessary. They were added because we can use our 3D
intuition to see that it should be possible to twist along an axis that is
not the x, y, or z axis. Such rotation axes go through edge and corner
pieces, so it is added as an possible twist.
In 5D there are most definitely many ways of twisting a given face that are
simply defined by just 2c pieces, but there are basically 3 reasons why onl=
y
these are available. One, it is much harder for us to visualize a 4D face
to 'see' what possible ways you can twist it that are not the 2c fundamenta=
l
twists. Two, how one would allow the user to execute these twists in the
given interface is a difficult problem. Three, since all twists can be
built up by those fundamental 2c twists anyway, it is already a completely
operational 5D puzzle, and the additional twists would just make it possibl=
e
to push twist counts to lower values.
So yes, while it would be possible to implement such a feature, I imagine i=
t
would have little pay-off and a lot of headache to implement. Besides,
extra overhead could possibly just end up cluttering the interface.
Hope what I've said is accurate. Let me know if I've made a mistake in my
observations.
Chris
2010/7/27 Jonathan Mecias
>
>
> Hmm good question. i want to know the answer too because im not 100% sure
> why you can rotate by clicking on corners and edges. Can any one elaborat=
e
> on this?
>
>
> On Mon, Jul 26, 2010 at 5:23 PM, deustfrr
>
>>
>>
>> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you ca=
n
>> rotate by clicking on corners and edges (corner&edge turns). Why is that
>> possible?
>> I think I asked over 9000 questions so I just made this thread
>>
>>
>=20=20
>
--0015177408fc6ca2cb048c5f7b2e
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
It's more of a shortcut than anything really.=C2=A0 For each face in 4D=
, there are 24 possible twists (that includes the identity twist - i.e. the=
do-nothing twist).=C2=A0 There are three axis through each face, and if yo=
u label a quarter-twist of the axes X, Y, Z respectively, then it turns out=
all the possible twists can be built from a combination of these elementar=
y twists.=C2=A0 The corner and edge twists are basically a combination of t=
hese fundamental twists and are not necessary.=C2=A0 They were added becaus=
e we can use our 3D intuition to see that it should be possible to twist al=
ong an axis that is not the x, y, or z axis.=C2=A0 Such rotation axes go th=
rough edge and corner pieces, so it is added as an possible twist.
In 5D there are most definitely many ways of twisting a given face that=
are simply defined by just 2c pieces, but there are basically 3 reasons wh=
y only these are available.=C2=A0 One, it is much harder for us to visualiz=
e a 4D face to 'see' what possible ways you can twist it that are n=
ot the 2c fundamental twists.=C2=A0 Two, how one would allow the user to ex=
ecute these twists in the given interface is a difficult problem.=C2=A0 Thr=
ee, since all twists can be built up by those fundamental 2c twists anyway,=
it is already a completely operational 5D puzzle, and the additional twist=
s would just make it possible to push twist counts to lower values.
So yes, while it would be possible to implement such a feature, I imagi=
ne it would have little pay-off and a lot of headache to implement.=C2=A0 B=
esides, extra overhead could possibly just end up cluttering the interface.=
Hope what I've said is accurate.=C2=A0 Let me know if I've made=
a mistake in my observations.
Chrisr-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
=C2=A0
=20=20=20=20=20=20
=20=20=20=20=20=20
ause im not 100% sure why you can rotate by clicking on corners and edges. =
Can any one elaborate on this?
=C2=A0
tfrr@yahoo.ca> wrote:mail_quote">
n rotate by clicking on corners and edges (corner&edge turns). Why is t=
hat possible?
I think I asked over 9000 questions so I just made this t=
hread
=20=20=20=20=20
=20=20=20=20
=20=20
--0015177408fc6ca2cb048c5f7b2e--
From: Roice Nelson <roice3@gmail.com>
Date: Tue, 27 Jul 2010 10:52:07 -0500
Subject: Re: [MC4D] New: Questions thread...
--90e6ba615074c1ae57048c607b77
Content-Type: text/plain; charset=ISO-8859-1
Chris covered everything well, but I figured I'd still mention that I've
always liked the MC4D FAQ answer to the question of what it means to
twist
I think it helps in understanding differences like this between the 3D and
4D puzzles.
> Q8: So what does it mean to "twist" on a 4D magic cube?
> A: People generally think of twists in 3D as turning something about an
> axis. It's just a quirk of three dimensions that that makes any sense,
> and is no help in the general case. It's better to think about a twist on
> the 4D cube as follows: Take the face you want to twist and remove it from
> the larger object. Turn it around any way you like without flipping it over,
> and then put it back so that it fits exactly like it did before. On a 3D
> magic cube, there are therefore only four possible ways to put the face back
> on. With a "face" of a 4D cube, it's like taking a cube out of a box,
> turning it any which way (but not turning it inside-out), and putting it
> back in its box. There are 24 different ways to do this.
Roice
On Tue, Jul 27, 2010 at 9:40 AM, Chris Locke
>
>
> It's more of a shortcut than anything really. For each face in 4D, there
> are 24 possible twists (that includes the identity twist - i.e. the
> do-nothing twist). There are three axis through each face, and if you label
> a quarter-twist of the axes X, Y, Z respectively, then it turns out all the
> possible twists can be built from a combination of these elementary twists.
> The corner and edge twists are basically a combination of these fundamental
> twists and are not necessary. They were added because we can use our 3D
> intuition to see that it should be possible to twist along an axis that is
> not the x, y, or z axis. Such rotation axes go through edge and corner
> pieces, so it is added as an possible twist.
>
> In 5D there are most definitely many ways of twisting a given face that are
> simply defined by just 2c pieces, but there are basically 3 reasons why only
> these are available. One, it is much harder for us to visualize a 4D face
> to 'see' what possible ways you can twist it that are not the 2c fundamental
> twists. Two, how one would allow the user to execute these twists in the
> given interface is a difficult problem. Three, since all twists can be
> built up by those fundamental 2c twists anyway, it is already a completely
> operational 5D puzzle, and the additional twists would just make it possible
> to push twist counts to lower values.
>
> So yes, while it would be possible to implement such a feature, I imagine
> it would have little pay-off and a lot of headache to implement. Besides,
> extra overhead could possibly just end up cluttering the interface.
>
> Hope what I've said is accurate. Let me know if I've made a mistake in my
> observations.
>
> Chris
>
> 2010/7/27 Jonathan Mecias
>
>
>>
>> Hmm good question. i want to know the answer too because im not 100% sure
>> why you can rotate by clicking on corners and edges. Can any one elaborate
>> on this?
>>
>>
>> On Mon, Jul 26, 2010 at 5:23 PM, deustfrr
>>
>>>
>>>
>>> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you can
>>> rotate by clicking on corners and edges (corner&edge turns). Why is that
>>> possible?
>>> I think I asked over 9000 questions so I just made this thread
>>>
>>>
>>
>
>
>
>
--90e6ba615074c1ae57048c607b77
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t=A0I've always liked the MC4D FAQ ube/faq.html#Q8">answer to the question of what it means to twist.=A0 I=
think it helps in understanding differences like this=A0between=A0the 3D a=
nd 4D=A0puzzles.; PADDING-LEFT: 1ex" class=3D"gmail_quote">Q8: So what does it mean to &quo=
t;twist" on a 4D magic cube?
A: People generally think of twists in=
3D as turning something about an axis. It's just a quirk of three dime=
nsions that that makes any sense,
and is no help in the general case. It's better to think about a twist =
on the 4D cube as follows: Take the face you want to twist and remove it fr=
om the larger object. Turn it around any way you like without flipping it o=
ver, and then put it back so that it fits exactly like it did before. On a =
3D magic cube, there are therefore only four possible ways to put the face =
back on. With a "face" of a 4D=A0 cube, it's like taking a cu=
be out of a box, turning it any which way (but not turning it inside-out), =
and putting it back in its box. There are 24 different ways to do this.ockquote>
opia@gmail.com> wrote:; PADDING-LEFT: 1ex" class=3D"gmail_quote">
It's more of a shortcut than anything really.=A0 For each =
face in 4D, there are 24 possible twists (that includes the identity twist =
- i.e. the do-nothing twist).=A0 There are three axis through each face, an=
d if you label a quarter-twist of the axes X, Y, Z respectively, then it tu=
rns out all the possible twists can be built from a combination of these el=
ementary twists.=A0 The corner and edge twists are basically a combination =
of these fundamental twists and are not necessary.=A0 They were added becau=
se we can use our 3D intuition to see that it should be possible to twist a=
long an axis that is not the x, y, or z axis.=A0 Such rotation axes go thro=
ugh edge and corner pieces, so it is added as an possible twist.
In 5D there are most definitely many ways of twisting a given face that=
are simply defined by just 2c pieces, but there are basically 3 reasons wh=
y only these are available.=A0 One, it is much harder for us to visualize a=
4D face to 'see' what possible ways you can twist it that are not =
the 2c fundamental twists.=A0 Two, how one would allow the user to execute =
these twists in the given interface is a difficult problem.=A0 Three, since=
all twists can be built up by those fundamental 2c twists anyway, it is al=
ready a completely operational 5D puzzle, and the additional twists would j=
ust make it possible to push twist counts to lower values.
So yes, while it would be possible to implement such a feature, I imagi=
ne it would have little pay-off and a lot of headache to implement.=A0 Besi=
des, extra overhead could possibly just end up cluttering the interface.
Hope what I've said is accurate.=A0 Let me know if I've made a =
mistake in my observations.
Chris
jonathan.=
mecias001@mymdc.net>=20pt 0pt 0.8ex; PADDING-LEFT: 1ex" class=3D"gmail_quote">
sure why you can rotate by clicking on corners and edges. Can any one elab=
orate on this?
=A0
tfrr@yahoo.ca> wrote:l_quote">
n rotate by clicking on corners and edges (corner&edge turns). Why is t=
hat possible?
I think I asked over 9000 questions so I just made this t=
hread
/div>
--90e6ba615074c1ae57048c607b77--
From: Jonathan Mecias <jonathan.mecias001@mymdc.net>
Date: Tue, 27 Jul 2010 21:13:06 -0400
Subject: Re: [MC4D] New: Questions thread...
--00163630f191fbf8cf048c6851d7
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wow! I understand it perfectly now. Thanks Cris and Roice! now.. lemme ask
a crazy question. whats a 4D twist like is it just a combination of
"elementary 3D twists "? I think i know what a rotation in 4D is ie like on
the MC5D like the Y-U button . So, a 5D rotation would be U-V ? i was
always curious about this, but i never was too sure on the subject.
Jonathan
On Tue, Jul 27, 2010 at 11:52 AM, Roice Nelson
>
>
> Chris covered everything well, but I figured I'd still mention that I've
> always liked the MC4D FAQ answer to the question of what it means to twis=
t
> I think it helps in understanding differences like this between the 3D an=
d
> 4D puzzles.
>
>
>> Q8: So what does it mean to "twist" on a 4D magic cube?
>> A: People generally think of twists in 3D as turning something about an
>> axis. It's just a quirk of three dimensions that that makes any sense,
>> and is no help in the general case. It's better to think about a twist o=
n
>> the 4D cube as follows: Take the face you want to twist and remove it fr=
om
>> the larger object. Turn it around any way you like without flipping it o=
ver,
>> and then put it back so that it fits exactly like it did before. On a 3D
>> magic cube, there are therefore only four possible ways to put the face =
back
>> on. With a "face" of a 4D cube, it's like taking a cube out of a box,
>> turning it any which way (but not turning it inside-out), and putting it
>> back in its box. There are 24 different ways to do this.
>
>
> Roice
>
>
> On Tue, Jul 27, 2010 at 9:40 AM, Chris Locke
rote:
>
>>
>>
>> It's more of a shortcut than anything really. For each face in 4D, ther=
e
>> are 24 possible twists (that includes the identity twist - i.e. the
>> do-nothing twist). There are three axis through each face, and if you l=
abel
>> a quarter-twist of the axes X, Y, Z respectively, then it turns out all =
the
>> possible twists can be built from a combination of these elementary twis=
ts.
>> The corner and edge twists are basically a combination of these fundamen=
tal
>> twists and are not necessary. They were added because we can use our 3D
>> intuition to see that it should be possible to twist along an axis that =
is
>> not the x, y, or z axis. Such rotation axes go through edge and corner
>> pieces, so it is added as an possible twist.
>>
>> In 5D there are most definitely many ways of twisting a given face that
>> are simply defined by just 2c pieces, but there are basically 3 reasons =
why
>> only these are available. One, it is much harder for us to visualize a =
4D
>> face to 'see' what possible ways you can twist it that are not the 2c
>> fundamental twists. Two, how one would allow the user to execute these
>> twists in the given interface is a difficult problem. Three, since all
>> twists can be built up by those fundamental 2c twists anyway, it is alre=
ady
>> a completely operational 5D puzzle, and the additional twists would just
>> make it possible to push twist counts to lower values.
>>
>> So yes, while it would be possible to implement such a feature, I imagin=
e
>> it would have little pay-off and a lot of headache to implement. Beside=
s,
>> extra overhead could possibly just end up cluttering the interface.
>>
>> Hope what I've said is accurate. Let me know if I've made a mistake in =
my
>> observations.
>>
>> Chris
>>
>> 2010/7/27 Jonathan Mecias
>>
>>
>>>
>>> Hmm good question. i want to know the answer too because im not 100% su=
re
>>> why you can rotate by clicking on corners and edges. Can any one elabor=
ate
>>> on this?
>>>
>>>
>>> On Mon, Jul 26, 2010 at 5:23 PM, deustfrr
>>>
>>>>
>>>>
>>>> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you
>>>> can rotate by clicking on corners and edges (corner&edge turns). Why i=
s that
>>>> possible?
>>>> I think I asked over 9000 questions so I just made this thread
>>>>
>>>>
>>>
>>
>>
>>
>=20=20
>
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lemme ask a crazy question. whats a 4D twist like is it just a combination =
of "elementary=A03D twists "? I think i know what a rotation in 4=
D is ie like on the MC5D like the Y-U button . So, a 5D rotation would be=
=A0=A0 U-V=A0? i was always curious about this, but i never was too sure on=
the subject.
span dir=3D"ltr"><roice3@gmail.coma>> wrote:; PADDING-LEFT: 1ex" class=3D"gmail_quote">
t=A0I've always liked the MC4D FAQ ube/faq.html#Q8" target=3D"_blank">answer to the question of what it means =
to twist.=A0 I think it helps in understanding differences like this=A0=
between=A0the 3D and 4D=A0puzzles.Q8:=
So what does it mean to "twist" on a 4D magic cube?
A: People=
generally think of twists in 3D as turning something about an axis. It'=
;s just a quirk of three dimensions that that makes any sense,
and is no help in the general case. It's better to think about a twist =
on the 4D cube as follows: Take the face you want to twist and remove it fr=
om the larger object. Turn it around any way you like without flipping it o=
ver, and then put it back so that it fits exactly like it did before. On a =
3D magic cube, there are therefore only four possible ways to put the face =
back on. With a "face" of a 4D=A0 cube, it's like taking a cu=
be out of a box, turning it any which way (but not turning it inside-out), =
and putting it back in its box. There are 24 different ways to do this.ockquote>
It's more of a shortcut than anything really.=A0 For each =
face in 4D, there are 24 possible twists (that includes the identity twist =
- i.e. the do-nothing twist).=A0 There are three axis through each face, an=
d if you label a quarter-twist of the axes X, Y, Z respectively, then it tu=
rns out all the possible twists can be built from a combination of these el=
ementary twists.=A0 The corner and edge twists are basically a combination =
of these fundamental twists and are not necessary.=A0 They were added becau=
se we can use our 3D intuition to see that it should be possible to twist a=
long an axis that is not the x, y, or z axis.=A0 Such rotation axes go thro=
ugh edge and corner pieces, so it is added as an possible twist.
In 5D there are most definitely many ways of twisting a given face that=
are simply defined by just 2c pieces, but there are basically 3 reasons wh=
y only these are available.=A0 One, it is much harder for us to visualize a=
4D face to 'see' what possible ways you can twist it that are not =
the 2c fundamental twists.=A0 Two, how one would allow the user to execute =
these twists in the given interface is a difficult problem.=A0 Three, since=
all twists can be built up by those fundamental 2c twists anyway, it is al=
ready a completely operational 5D puzzle, and the additional twists would j=
ust make it possible to push twist counts to lower values.
So yes, while it would be possible to implement such a feature, I imagi=
ne it would have little pay-off and a lot of headache to implement.=A0 Besi=
des, extra overhead could possibly just end up cluttering the interface.
Hope what I've said is accurate.=A0 Let me know if I've made a =
mistake in my observations.
Chris
jonathan.=
mecias001@mymdc.net>=20l_quote">
sure why you can rotate by clicking on corners and edges. Can any one elab=
orate on this?
=A0
tfrr@yahoo.ca> wrote:l_quote">
n rotate by clicking on corners and edges (corner&edge turns). Why is t=
hat possible?
I think I asked over 9000 questions so I just made this t=
hread
=
--00163630f191fbf8cf048c6851d7--
From: Jonathan Mecias <jonathan.mecias001@mymdc.net>
Date: Tue, 27 Jul 2010 21:14:58 -0400
Subject: Re: [MC4D] New: Questions thread...
--001636283b829f62b0048c685863
Content-Type: text/plain; charset=windows-1252
Content-Transfer-Encoding: quoted-printable
Wow i just reread the email. Sorry for messy grammer :/
On Tue, Jul 27, 2010 at 9:13 PM, Jonathan Mecias <
jonathan.mecias001@mymdc.net> wrote:
> wow! I understand it perfectly now. Thanks Cris and Roice! now.. lemme a=
sk
> a crazy question. whats a 4D twist like is it just a combination of
> "elementary 3D twists "? I think i know what a rotation in 4D is ie like =
on
> the MC5D like the Y-U button . So, a 5D rotation would be U-V ? i was
> always curious about this, but i never was too sure on the subject.
>
> Jonathan
>
> On Tue, Jul 27, 2010 at 11:52 AM, Roice Nelson
:
>
>>
>>
>> Chris covered everything well, but I figured I'd still mention that I've
>> always liked the MC4D FAQ answer to the question of what it means to
>> twist
>> understanding differences like this between the 3D and 4D puzzles.
>>
>>
>>> Q8: So what does it mean to "twist" on a 4D magic cube?
>>> A: People generally think of twists in 3D as turning something about an
>>> axis. It's just a quirk of three dimensions that that makes any sense,
>>> and is no help in the general case. It's better to think about a twist =
on
>>> the 4D cube as follows: Take the face you want to twist and remove it f=
rom
>>> the larger object. Turn it around any way you like without flipping it =
over,
>>> and then put it back so that it fits exactly like it did before. On a 3=
D
>>> magic cube, there are therefore only four possible ways to put the face=
back
>>> on. With a "face" of a 4D cube, it's like taking a cube out of a box,
>>> turning it any which way (but not turning it inside-out), and putting i=
t
>>> back in its box. There are 24 different ways to do this.
>>
>>
>> Roice
>>
>>
>> On Tue, Jul 27, 2010 at 9:40 AM, Chris Locke
wrote:
>>
>>>
>>>
>>> It's more of a shortcut than anything really. For each face in 4D, the=
re
>>> are 24 possible twists (that includes the identity twist - i.e. the
>>> do-nothing twist). There are three axis through each face, and if you =
label
>>> a quarter-twist of the axes X, Y, Z respectively, then it turns out all=
the
>>> possible twists can be built from a combination of these elementary twi=
sts.
>>> The corner and edge twists are basically a combination of these fundame=
ntal
>>> twists and are not necessary. They were added because we can use our 3=
D
>>> intuition to see that it should be possible to twist along an axis that=
is
>>> not the x, y, or z axis. Such rotation axes go through edge and corner
>>> pieces, so it is added as an possible twist.
>>>
>>> In 5D there are most definitely many ways of twisting a given face that
>>> are simply defined by just 2c pieces, but there are basically 3 reasons=
why
>>> only these are available. One, it is much harder for us to visualize a=
4D
>>> face to 'see' what possible ways you can twist it that are not the 2c
>>> fundamental twists. Two, how one would allow the user to execute these
>>> twists in the given interface is a difficult problem. Three, since all
>>> twists can be built up by those fundamental 2c twists anyway, it is alr=
eady
>>> a completely operational 5D puzzle, and the additional twists would jus=
t
>>> make it possible to push twist counts to lower values.
>>>
>>> So yes, while it would be possible to implement such a feature, I imagi=
ne
>>> it would have little pay-off and a lot of headache to implement. Besid=
es,
>>> extra overhead could possibly just end up cluttering the interface.
>>>
>>> Hope what I've said is accurate. Let me know if I've made a mistake in
>>> my observations.
>>>
>>> Chris
>>>
>>> 2010/7/27 Jonathan Mecias
>>>
>>>
>>>>
>>>> Hmm good question. i want to know the answer too because im not 100%
>>>> sure why you can rotate by clicking on corners and edges. Can any one
>>>> elaborate on this?
>>>>
>>>>
>>>> On Mon, Jul 26, 2010 at 5:23 PM, deustfrr
>>>>
>>>>>
>>>>>
>>>>> Ok so, on MC5D and the 3D cube, you have face turns, but on MC4D, you
>>>>> can rotate by clicking on corners and edges (corner&edge turns). Why =
is that
>>>>> possible?
>>>>> I think I asked over 9000 questions so I just made this thread
>>>>>
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Wow i just reread the email. Sorry for messy grammer=A0 :/
<jona=
than.mecias001@mymdc.net> wrote:; PADDING-LEFT: 1ex" class=3D"gmail_quote">
lemme ask a crazy question. whats a 4D twist like is it just a combination =
of "elementary=A03D twists "? I think i know what a rotation in 4=
D is ie like on the MC5D like the Y-U button . So, a 5D rotation would be=
=A0=A0 U-V=A0? i was always curious about this, but i never was too sure on=
the subject.
span dir=3D"ltr"><=
roice3@gmail.com> wrote:; PADDING-LEFT: 1ex" class=3D"gmail_quote">
t=A0I've always liked the MC4D FAQ ube/faq.html#Q8" target=3D"_blank">answer to the question of what it means =
to twist.=A0 I think it helps in understanding differences like this=A0=
between=A0the 3D and 4D=A0puzzles.Q8:=
So what does it mean to "twist" on a 4D magic cube?
A: People=
generally think of twists in 3D as turning something about an axis. It'=
;s just a quirk of three dimensions that that makes any sense,
and is no help in the general case. It's better to think about a twist =
on the 4D cube as follows: Take the face you want to twist and remove it fr=
om the larger object. Turn it around any way you like without flipping it o=
ver, and then put it back so that it fits exactly like it did before. On a =
3D magic cube, there are therefore only four possible ways to put the face =
back on. With a "face" of a 4D=A0 cube, it's like taking a cu=
be out of a box, turning it any which way (but not turning it inside-out), =
and putting it back in its box. There are 24 different ways to do this.ockquote>
It's more of a shortcut than anything really.=A0 For each =
face in 4D, there are 24 possible twists (that includes the identity twist =
- i.e. the do-nothing twist).=A0 There are three axis through each face, an=
d if you label a quarter-twist of the axes X, Y, Z respectively, then it tu=
rns out all the possible twists can be built from a combination of these el=
ementary twists.=A0 The corner and edge twists are basically a combination =
of these fundamental twists and are not necessary.=A0 They were added becau=
se we can use our 3D intuition to see that it should be possible to twist a=
long an axis that is not the x, y, or z axis.=A0 Such rotation axes go thro=
ugh edge and corner pieces, so it is added as an possible twist.
In 5D there are most definitely many ways of twisting a given face that=
are simply defined by just 2c pieces, but there are basically 3 reasons wh=
y only these are available.=A0 One, it is much harder for us to visualize a=
4D face to 'see' what possible ways you can twist it that are not =
the 2c fundamental twists.=A0 Two, how one would allow the user to execute =
these twists in the given interface is a difficult problem.=A0 Three, since=
all twists can be built up by those fundamental 2c twists anyway, it is al=
ready a completely operational 5D puzzle, and the additional twists would j=
ust make it possible to push twist counts to lower values.
So yes, while it would be possible to implement such a feature, I imagi=
ne it would have little pay-off and a lot of headache to implement.=A0 Besi=
des, extra overhead could possibly just end up cluttering the interface.
Hope what I've said is accurate.=A0 Let me know if I've made a =
mistake in my observations.
Chris
jonathan.=
mecias001@mymdc.net>=20l_quote">
sure why you can rotate by clicking on corners and edges. Can any one elab=
orate on this?
=A0
tfrr@yahoo.ca> wrote:l_quote">
n rotate by clicking on corners and edges (corner&edge turns). Why is t=
hat possible?
I think I asked over 9000 questions so I just made this t=
hread
=
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