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Number of Configurations for Dodecahedron and Icosahedron Sequential Nets?

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  • pyth7
    Hello All, Is there a formula for giving the number of possible configurations for connecting sequentially all twelve faces of a dodecahedron so that each face
    Message 1 of 2 , Aug 8, 2007
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      Hello All,
      Is there a formula for giving the number of possible configurations for
      connecting sequentially all twelve faces of a dodecahedron
      so that each face is crossed no more than once? This probably can be
      expressed more simply by connecting the vertexes of the Icosahedron
      instead. I think the result will be an odd number.

      I believe the number for sequentially connecting the twenty vertexes of
      the dodecahedron so that each vertex is crossed no more than once is
      thirteen basic configurations with thirteen more as endomorphs. I
      obtained these figures with models, string, and time, but I won't stake
      my life on the correctness and am hoping for someone could provide a
      formula to confirm or deny those figures and avoid the tediousness of
      now figuring out its dual.


      Thanks!
      Russ Kinter
    • Alan Michelson
      What you need to do is go to: * Dodecahedral Graph -- from Wolfram MathWorld * Icosahedral Graph -- from
      Message 2 of 2 , Aug 8, 2007
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        What you need to do is go to:

        On a related note, you might also want to try:

        (Those were hemi-hedra, by the way.)

        --- In Polytopia@yahoogroups.com, "pyth7" <pyth7@...> wrote:

        > Hello All,

        > Is there a formula for giving the number of possible configurations for

        > connecting sequentially all twelve faces of a dodecahedron
        > so that each face is crossed no more than once? This probably can be
        > expressed more simply by connecting the vertexes of the Icosahedron
        > instead. I think the result will be an odd number.

        > I believe the number for sequentially connecting the twenty vertexes of
        > the dodecahedron so that each vertex is crossed no more than once is
        > thirteen basic configurations with thirteen more as endo-morphs. I
        > obtained these figures with models, string, and time, but I won't stake
        > my life on the correctness and am hoping for someone could provide a
        > formula to confirm or deny those figures and avoid the tediousness of
        > now figuring out its dual.

        > Thanks!
        > Russ Kinter

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