Symmetric 3-pire map

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Awhile ago, Martin Gardner introduced Scott Kim's symmetric 2-pire map. There are 12 empires, each with two regions. All twelve empires share a border. This is a 2-pire solution for the Empire Coloring Problem.



Scott Kim's 2-pire map



In 3D, the 2-pire map becomes a dodecahedron with each face split.



Kim Dodecahedron



For 3-pires, an 18 empire solution by Taylor is known. It's not symmetric.



Taylor 3-pire



Is there a symmetric 18 empire 3-pire map?




graph-theory recreational-mathematics coloring polyhedra




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    up vote
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    Awhile ago, Martin Gardner introduced Scott Kim's symmetric 2-pire map. There are 12 empires, each with two regions. All twelve empires share a border. This is a 2-pire solution for the Empire Coloring Problem.



    Scott Kim's 2-pire map



    In 3D, the 2-pire map becomes a dodecahedron with each face split.



    Kim Dodecahedron



    For 3-pires, an 18 empire solution by Taylor is known. It's not symmetric.



    Taylor 3-pire



    Is there a symmetric 18 empire 3-pire map?




    graph-theory recreational-mathematics coloring polyhedra




    share|cite|improve this question





















      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Awhile ago, Martin Gardner introduced Scott Kim's symmetric 2-pire map. There are 12 empires, each with two regions. All twelve empires share a border. This is a 2-pire solution for the Empire Coloring Problem.



      Scott Kim's 2-pire map



      In 3D, the 2-pire map becomes a dodecahedron with each face split.



      Kim Dodecahedron



      For 3-pires, an 18 empire solution by Taylor is known. It's not symmetric.



      Taylor 3-pire



      Is there a symmetric 18 empire 3-pire map?




      graph-theory recreational-mathematics coloring polyhedra




      share|cite|improve this question











      Awhile ago, Martin Gardner introduced Scott Kim's symmetric 2-pire map. There are 12 empires, each with two regions. All twelve empires share a border. This is a 2-pire solution for the Empire Coloring Problem.



      Scott Kim's 2-pire map



      In 3D, the 2-pire map becomes a dodecahedron with each face split.



      Kim Dodecahedron



      For 3-pires, an 18 empire solution by Taylor is known. It's not symmetric.



      Taylor 3-pire



      Is there a symmetric 18 empire 3-pire map?





      graph-theory recreational-mathematics coloring polyhedra





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      share|cite|improve this question




      share|cite|improve this question









      asked Aug 2 at 15:56









      Ed Pegg

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