# Message #1090

From: Roice Nelson <roice3@gmail.com>

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

Date: Tue, 27 Jul 2010 10:52:07 -0500

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

>>>

>>>

>>

>

>

>

>