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Re: [Polytopia] Having Some Code Fun in Logic Garnet

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  • Alan Michelson
    ... From: Michael Donovan Subject: Re: [Polytopia] Having Some Code Fun in Tiling To: Polytopia@yahoogroups.com Date: Monday, September
    Message 1 of 52 , Aug 9, 2012
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      You can see how the colored struts would have been perpendicular to the corresponding colored planes that I had mentioned:

      --- On Mon, 9/13/04, Michael Donovan <michael1@...> wrote:
      From: Michael Donovan <michael1@...>
      Subject: Re: [Polytopia] Having Some Code Fun in Tiling
      To: Polytopia@yahoogroups.com
      Date: Monday, September 13, 2004, 12:25 PM

      Wonderful image,
      But the primary colors fit in another way, those four planes are combinations of the three primary.  Looks like one of Robert Webbs animations from Stella
      ----- Original Message -----
      Sent: Monday, September 13, 2004 2:57 PM
      Subject: Re: [Polytopia] Having Some Code Fun in Tiling

      rybo6 <rybo6@...> wrote:
      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 can see this in Octa-Planes in the Files Section
      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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