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2^4 MCD4 is handed (is that a programming issue?)
Not an easy thema.
Foundation Mathematics for Computer Science: A Visual Approachhttps://books=
.google.ch/books?isbn=3D3319214373 - Diese Seite =C3=BCbersetzen
John Vince - 2015 - =E2=80=8EComputers
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:
https://math.stackexchange.com/questions/1884953/what-are-the-higher-dimens=
ional-analogues-of-left-and-right-handedness
Best regards
Ed
----- Original Message -----=20
From: Marc Ringuette ringuette@solarmirror.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, November 18, 2017 5:03 PM
Subject: Re: [MC4D] Melinda's physical 2^4 puzzle, mirrors [1 Attachment]
=20=20=20=20
[Attachment(s) from Marc Ringuette included below]
=20=20=20
Hi, Ed,
(1) There are 16 =3D 2*2*2*2 color combinations. Each piece has either=
=20
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,=20
people assembling their own puzzle must take care to get the handedness=20
of each piece correct.
(3) This is also true for the 2^4 hypercube: there are 16 four-color=20
pieces, in 2*2*2*2 color combinations, and there is only one of the two=20
handednesses of each. The MC4D program arbitrarily chose a=20
handedness. Even if the 4th dimension allows any 3D face to be turned=20
"inside out" to reach the other handedness, the twists and rotations=20
allowed for the n^4 hypercube puzzle do not allow access to that other=20
handedness.
(4) Your version of mc4d is fine. When I built my first physical=20
puzzle, I created a text file, facecolors.txt, with some custom colors=20
to match the virtual with the physical version. If you save the=20
attached file in the same folder with mc4d.jar, then restart MC4D and=20
open the 2^4 hypercube, the colors will hopefully match. This is not=20
well documented, but I saw it mentioned somewhere deep down in some old=20
release notes for MC4D, and messed with it until I made it look OK for me=
.
Cheers
Marc
=20=20
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=EF=BB=BF
Hi, Ed,
(1) There are 16 =3D 2*2*2*2 color combinations. &=
nbsp;=20
Each piece has either
W/Y, R/O, B/G, P/V. There is one pi=
ece=20
of each combination.
(2) The pieces each have one of the two possible=
=20
handednesses. So,
people assembling their own puzzle must take =
care=20
to get the handedness
of each piece correct.
(3) This is also true=
for=20
the 2^4 hypercube: there are 16 four-color
pieces, in 2*2*2*2 color=20
combinations, and there is only one of the two
handednesses of each.&=
nbsp;=20
The MC4D program arbitrarily chose a
handedness. Even if =
the=20
4th dimension allows any 3D face to be turned
"inside out" to reach t=
he=20
other handedness, the twists and rotations
allowed for the n^4 hyperc=
ube=20
puzzle do not allow access to that other
handedness.
(4) Your vers=
ion=20
of mc4d is fine. When I built my first physical
puzzle, I creat=
ed a=20
text file, facecolors.txt, with some custom colors
to match the virtu=
al=20
with the physical version. If you save the
attached file =
in=20
the same folder with mc4d.jar, then restart MC4D and
open the 2^4=20
hypercube, the colors will hopefully match. This is not
well document=
ed,=20
but I saw it mentioned somewhere deep down in some old
release notes =
for=20
MC4D, and messed with it until I made it look OK for=20
me.
Cheers
Marc