# Message #1096

From: Jonathan Mecias <jonathan.mecias001@mymdc.net>

Subject: Re: [MC4D] New: Questions thread…

Date: Tue, 27 Jul 2010 21:14:58 -0400

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 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 <roice3@gmail.com> wrote:

>

>>

>>

>> 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 <http://superliminal.com/cube/faq.html#Q8>. 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 <project.eutopia@gmail.com>wrote:

>>

>>>

>>>

>>> 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 <jonathan.mecias001@mymdc.net>

>>>

>>>

>>>>

>>>> 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 <deustfrr@yahoo.ca> wrote:

>>>>

>>>>>

>>>>>

>>>>> 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

>>>>>

>>>>>

>>>>

>>>

>>>

>>>

>>

>>

>

>