Thread: "4D puzzle math"

From: tytheguy246@gmail.com
Date: Wed, 20 Jul 2016 13:36:22 -0500
Subject: 4D puzzle math



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For in-space views of a hypercube (and other shapes) that you can fly
through, check out the following...

- Nan Ma's *Inside H3* applet: http://nan.ma/InsideH3/index.html
- Jeff Weeks' *Curved Spaces* software:
http://geometrygames.org/CurvedSpaces/index.html.en

Both are awesome!

Roice


On Wed, Jul 20, 2016 at 11:54 AM, llamaonacid@gmail.com [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:

>
>
> Imagine you are inside a 4-cube and each cell is a different color. If yo=
u
> are in the center you would see the six sides like you were inside a cube
> but I wonder what you would see while you do a rotation such as X-U. It
> would be nice if someone already made an animation of this.
>
>
>
>
>=20
>

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For in-space views of a hypercube (and other shapes) that =
you can fly through, check out the following...
Both are awesome!

Roice
r>

On =
Wed, Jul 20, 2016 at 11:54 AM, lla=
maonacid@gmail.com [4D_Cubing] <4D_Cubing@yahoogroups.com" target=3D"_blank">4D_Cubing@yahoogroups.com&=
gt; wrote:
0 .8ex;border-left:1px #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20

















Imagine you are inside a 4-cube and each cell is a different color. If you =
are in the center you would see the six sides like you were inside a cube b=
ut I wonder what you would see while you do a rotation such as X-U. It woul=
d be nice if someone already made an animation of this.


span>
























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From: Ashton Santee <ashtonsantee@gmail.com>
Date: Wed, 20 Jul 2016 19:25:58 +0000
Subject: Re: [MC4D] 4D puzzle math



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I believe you are looking for more information about that specific
notation. I don't know enough about it to tell you how to read it but there
is a Wikipedia page on this notation.
https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol
"Regular n-polytopes" is the section that has the definition of a hypercube
so that might be a good place to start then see how this notation can be
used for other multi dimension shapes.
I am not sure what inputs MC4D will accept and not accept in this notation.
You will have to experiment with it and report back and let us know what
the limits of this notation are in MC4D.

On Wed, Jul 20, 2016 at 11:28 AM tytheguy246@gmail.com [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:

>
>
> Does anyone know about the numbers of four-dimensional puzzles? For
> example, why is {4,3,3} a hypercube? Also, how do I "invent my own" as th=
e
> button says? Would a 4D equivalent to the 3x3x5 be possible using this
> code? If anyone knows about an article about this or would just like to
> tell me, please let me know!
>
> Thanks,
>
> Ty
>=20
>
--=20
Ashton Santee
916-7766-775

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I believe you are looking for more information about that =
specific notation. I don't know enough about it to tell you how to read=
it but there is a Wikipedia page on this notation.=C2=A0e-height:1.5">">https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol
"R=
egular n-polytopes" is the section that has the definition of a hyperc=
ube so that might be a good place to start then see how this notation can b=
e used for other multi dimension shapes.
I am not sure what input=
s MC4D will accept and not accept in this notation. You will have to experi=
ment with it and report back and let us know what the limits of this notati=
on are in MC4D.

=
On Wed, Jul 20, 2016 at 11:28 AM t=
ytheguy246@gmail.com [4D_Cubing] <roups.com">4D_Cubing@yahoogroups.com> wrote:
ass=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;p=
adding-left:1ex">












=20

=C2=A0







=20=20=20=20=20=20
=20=20=20=20=20=20

Does anyone know about the numbers of four-dimensional puzzle=
s? For example, why is {4,3,3} a hypercube? Also, how do I "invent my =
own" as the button says? Would a 4D equivalent to the 3x3x5 be possibl=
e using this code? If anyone knows about an article about this or would jus=
t like to tell me, please let me know!

Thanks,v>

Ty




=20=20=20=20=20

=20=20=20=20







=20=20






--
il_signature">
Ashton Santee
916-7766-775
iv>


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From: Roice Nelson <roice3@gmail.com>
Date: Wed, 20 Jul 2016 14:52:24 -0500
Subject: Re: [MC4D] 4D puzzle math



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Yep, Ashton is right. Those are Schl=C3=A4fli symbols
. Here are a few
articles discussing them (in the context of honeycombs, but the info is
there):

- Hexagonal Hyperbolic Honeycombs
neycombs/>,
by John Baez
- The dual {5,3,4} and {4,3,5}


In the case of the hypercube...

- {4} designates a square.
- {4,3} means squares with 3 squares surrounding each vertex (i.e. a
cube).
- {4,3,3} means {4,3} cubes with 3 cubes surrounding each edge, the
hypercube.

Sometimes the symbols are not unique, e.g. the {4}x{4} (a duoprism
of square prisms) is also a
hypercube, as is {4,3}x{} (a cubical prism).

I don't think there is a Schl=C3=A4fli symbol for a rectangular cuboid, so
unfortunately you won't be able to make what you are wanting in the "invent
my own" functionality of MC4D. Andrey's magic puzzle ultimate supports
these though, and includes some by default like the 2x2x2x3 and the
2x3x4x5. (Note that to make a 4D equivalent of a 3x3x5, you'll need to
choose a 4th number!) You could take a look at his configuration for those
in the MPUlt_puzzles.txt file, and adapt to make your own new cuboid
puzzles of whatever size.

Roice


On Wed, Jul 20, 2016 at 2:25 PM, Ashton Santee ashtonsantee@gmail.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> I believe you are looking for more information about that specific
> notation. I don't know enough about it to tell you how to read it but the=
re
> is a Wikipedia page on this notation.
> https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol
> "Regular n-polytopes" is the section that has the definition of a
> hypercube so that might be a good place to start then see how this notati=
on
> can be used for other multi dimension shapes.
> I am not sure what inputs MC4D will accept and not accept in this
> notation. You will have to experiment with it and report back and let us
> know what the limits of this notation are in MC4D.
>
> On Wed, Jul 20, 2016 at 11:28 AM tytheguy246@gmail.com [4D_Cubing] <
> 4D_Cubing@yahoogroups.com> wrote:
>
>>
>>
>> Does anyone know about the numbers of four-dimensional puzzles? For
>> example, why is {4,3,3} a hypercube? Also, how do I "invent my own" as t=
he
>> button says? Would a 4D equivalent to the 3x3x5 be possible using this
>> code? If anyone knows about an article about this or would just like to
>> tell me, please let me know!
>>
>> Thanks,
>>
>> Ty
>>
>> --
> Ashton Santee
> 916-7766-775
>
>
>=20
>

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Yep, Ashton is right.=C2=A0 Those are=C2=A0s://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol" target=3D"_blank">Schl=C3=
=A4fli symbols.=C2=A0 Here are a few articles discussing them (in the c=
ontext of honeycombs, but the info is there):
In t=
he case of the hypercube...
  • {4} designates a square.
    • =
  • {4,3} means squares with 3 squares surrounding each vertex (i.e. a cube=
    ).
  • {4,3,3} means {4,3} cubes with 3 cubes surrounding each edge, th=
    e hypercube.
Sometimes the symbols are not unique, e.g. the {4}x{4=
} (a duoprism of squ=
are prisms) is also a hypercube, as is {4,3}x{} (a cubical prism).
>

I don't think there is a Schl=C3=A4fli symbol for =
a rectangular cuboid, so unfortunately you won't be able to make what y=
ou are wanting in the "invent my own" functionality of MC4D.=C2=
=A0 Andrey's magic puzzle ultimate supports these though, and includes =
some by default like the 2x2x2x3 and the 2x3x4x5. =C2=A0(Note that to make =
a 4D equivalent of a 3x3x5, you'll need to choose a 4th number!) =C2=A0=
You could take a look at his configuration for those in the=C2=A0MPUlt_puzz=
les.txt file, and adapt to make your own new cuboid puzzles of whatever siz=
e.

Roice

xtra">
On Wed, Jul 20, 2016 at 2:25 PM, Ashto=
n Santee ashtonsantee@gmail.coma> [4D_Cubing] <s.com" target=3D"_blank">4D_Cubing@yahoogroups.com> wrote:>
px #ccc solid;padding-left:1ex">






=20=20=20=20=20=20=20=20

















I believe you are looking for more information about that =
specific notation. I don't know enough about it to tell you how to read=
it but there is a Wikipedia page on this notation.=C2=A0e-height:1.5">" target=3D"_blank">https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol<=
/span>
"Regular n-polytopes" is the section that has the defi=
nition of a hypercube so that might be a good place to start then see how t=
his notation can be used for other multi dimension shapes.
I am n=
ot sure what inputs MC4D will accept and not accept in this notation. You w=
ill have to experiment with it and report back and let us know what the lim=
its of this notation are in MC4D.

s=3D"gmail_quote">
=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padd=
ing-left:1ex">












=20

=C2=A0







=20=20=20=20=20=20
=20=20=20=20=20=20

Does anyone know about the numbers of four-dimensional pu=
zzles? For example, why is {4,3,3} a hypercube? Also, how do I "invent=
my own" as the button says? Would a 4D equivalent to the 3x3x5 be pos=
sible using this code? If anyone knows about an article about this or would=
just like to tell me, please let me know!

Thanks,=

Ty




=20=20=20=20=20

=20=20=20=20







=20=20






"#888888">
--
ure">
Ashton Santee
916-7766-775
=
























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