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
>>>
>>>
>>
>
>
>
>