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Minimum Colors for an Icosahedron

  1. Jul 7, 2010 #1
    How could you mathematically solve for the minimum amount of colors needed for each face of an icosahedron or any regular polyhedron to not touch? (E.g. a tetrahedron pyramid would need four unique colors.)
     
  2. jcsd
  3. Jul 7, 2010 #2
    "There is no obvious extension of the coloring problem to three-dimensional solid regions."
    -taken from http://en.wikipedia.org/wiki/Four_color_theorem.

    So it looks like it's guess and check mostly, and even then, you'd have a pretty tough time proving your solution is indeed minimal. It is an interesting problem though.
     
  4. Jul 7, 2010 #3

    CRGreathouse

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    If I'm reading this right, what you want is the chromatic number of the dodecahedral (!) graph, which is 3.
     
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