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• ## Re: Having Some Fun with Emotion Tetrahedron

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• ... you mean ... (0,0,±1) ? ... …and you can notice that in http://cubicao.com/theory/tetrahedron.html ...
Message 1 of 52 , Sep 16, 2011
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--- In Polytopia@yahoogroups.com, "Alan Michelson" <amichelson2002@...> wrote:

> You are absolutely correct that it came from the Stella program. These
> four planes have Miller indeces of (±1,±1,±1). Now, what do you mean
> by the three primary? Do you mean (±1,0,0) & (0,±1,0) & (0,0,±1) ?

> Each color represents a set of planes that are perpendicular to a
> cube's body diagonal. The cube's body diagonals have Miller indeces of
> [±1,±1,±1].

> Primary colors can be red-yellow-blue or red-green-blue. Notice why
> the arbitrary colors red-yellow-green-blue were chosen: Just mosey
> down to your local neighborhood toy store and you will see that the
> toys are colored with plenty of reds & yellows & greens & blues. In
> fact, while you are in that toy shop, you will notice that the regular
> Polydron (ages 4+ years) are in these very same colors!

and you can notice that in http://cubicao.com/theory/tetrahedron.html

> --- In Polytopia@yahoogroups.com, "Michael Donovan" michael1@m... wrote:

> > Wonderful image,
> > But the primary colors fit in another way, those four planes are
> > combinations of the three primary. Looks like one of Robert Webb's
> > animations from Stella

> > ----- Original Message -----
> > From: Alan Michelson
> > To: Polytopia@yahoogroups.com
> > Sent: Monday, September 13, 2004 2:57 PM
> > Subject: Re: [Polytopia] Having Some Code Fun in Tiling

> > rybo6 rybo6@u... wrote:
> > http://www.codefun.com/Geometry_tile1.htm

> > Rybo

> > By the way, if you go to that web page, notice the tetrahedron at
> > http://www.codefun.com/Images/Geometry/DodecTile/image004.jpg

> > Each vertice of the tetrahedron has a color that matches its
> > opposite face. This is because if you were to truncate each
> > vertice, you will get a plane that is parallel to and therefore
> > matches its opposite face.

> > You could also see the red, yellow, green, blue color-coded planes
> > in http://www.superliminal.com/geometry/infinite/stereo/
> > The upper picture has truncated tetrahedra.
> > The lower picture has truncated octahedra.
> > These were built using Polydron. The colored hexagons are oriented
> > according to the corresponding tetrahedron planes.

> > You can see how this applies to the coloring problem in
> > http://www.codefun.com/Images/Geometry/DodecTile/image006.jpg

• ... …or in this case, the possible [transfer] points from the combinations of intersecting [subway] lines. ... This is from:
Message 52 of 52 , Jan 12
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> Those same colors were used on the St. Petersburg subway system in
> Russia, before the new Frunzensko-Primorsk aya Line. Notice the
> different combinations of subway lines at the transfer stations
> (Like the edges of the simplex joining the vertexes.)
or in this case, the possible [transfer] points from the combinations of intersecting [subway] lines.

--- In Polytopia@yahoogroups.com, "Alan M" wrote:
>
>
> --- In Polytopia@yahoogroups.com, Alan Michelson wrote:
> >
> > The new Frunzensko-Primorsk aya Line should intersect the other
> > lines, giving more transfer combinations. (Like the edges of the
> > simplex joining the vertexes.)
> or in this case, the possible [transfer] points from the combinations of intersecting [subway] lines.
>
This is from:
http://mathworld.wolfram.com/Combination.html
http://en.wikipedia.org/wiki/Combination
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