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Re: Having Some Fun with Emotion Tetrahedron

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  • Alan M
    ... 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

    • Alan M
      ... …or in this case, the possible [transfer] points from the combinations of intersecting [subway] lines. ... This is from:
      Message 52 of 52 , Jan 12, 2013
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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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