Message #3828

From: Melinda Green <>
Subject: Re: [MC4D] Melinda’s physical 2^4 puzzle, mirrors
Date: Sun, 19 Nov 2017 17:00:53 -0800

It’s not so much an issue as a useful quirk of 3D space into which MC4D has been projected because it lets us specify twists according to clockwise and counterclockwise rotations about an axis. That only works in 3D. In general you need to specify a 2D plane about which to rotate such that no point ends up at a different distance from that plane than it started. I don’t know if the concept of handedness can be meaningfully extended to higher dimensions, but I barely feel like I have a grip on the concept in 3D. I’ll also note that the original Rubik’s cube has the same issues. If you require 6 particular colors in 3 particular pairs, then after you’ve stickered 2 pairs of faces, you’ll be faced with a choice of 2 ways to add the final pair. So for example, if you look for the corner with red, white, and blue stickers, they will be arranged clockwise in one arrangement and counterclockwise in it’s mirrored twin.


On 11/19/2017 2:05 AM, ‘Eduard Baumann’ [4D_Cubing] wrote:
> 2^4 MCD4 is handed  (is that a programming issue?)
> *_/Not an easy/_* thema.
> Foundation Mathematics for Computer Science: A Visual Approach <>
> Seite übersetzen <>
> John Vince <>- 2015 - ‎Computers
> 6.5 a A/left-handed/system. b A right-handed system Fig. …_It also worth noting that/handedness /has no meaning in spaces with/4 dimensions/or more_.
> But see also:
> Best regards
> Ed
> —– Original Message —–
> *From:* Marc Ringuette [4D_Cubing] <[4D_Cubing]>
> *To:* <>
> *Sent:* Saturday, November 18, 2017 5:03 PM
> *Subject:* Re: [MC4D] Melinda’s physical 2^4 puzzle, mirrors [1 Attachment]
> Hi, Ed,
> (1) There are 16 = 2*2*2*2 color combinations.   Each piece has either
> W/Y, R/O, B/G, P/V.   There is one piece of each combination.
> (2) The pieces each have one of the two possible handednesses.  So,
> people assembling their own puzzle must take care to get the handedness
> of each piece correct.
> (3) This is also true for the 2^4 hypercube: there are 16 four-color
> pieces, in 2*2*2*2 color combinations, and there is only one of the two
> handednesses of each.  The MC4D program arbitrarily chose a
> handedness.   Even if the 4th dimension allows any 3D face to be turned
> "inside out" to reach the other handedness, the twists and rotations
> allowed for the n^4 hypercube puzzle do not allow access to that other
> handedness.
> (4) Your version of mc4d is fine.  When I built my first physical
> puzzle, I created a text file, facecolors.txt, with some custom colors
> to match the virtual with the physical version.   If you save the
> attached file in the same folder with mc4d.jar, then restart MC4D and
> open the 2^4 hypercube, the colors will hopefully match. This is not
> well documented, but I saw it mentioned somewhere deep down in some old
> release notes for MC4D, and messed with it until I made it look OK for me.
> Cheers
> Marc