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A graph on ten vertices; all nodes have degree three (they are connected to three other nodes).

Again, we run across the problem of graph/node/tree representation on e2. I can't find a way to draw them in ascii text, and this is definitely a defintion that could benefit from a diagram. Any suggestions are welcome.

--back to combinatorics--
A couple of facts about the Petersen graph (depicted somewhat poorly below):
It is nonhamiltonian. That is, there is no cycle within it that contains every vertex (also known as a Hamilton cycle). It is not a planar graph. That is, there is no way to move the vertices and edges around (keeping them attatched!) so that none of the edges intersect.


The vertices are designated by the shapes 
made of #'s, and the edges are the lines between them.


                           #
                        __###__ 
                     __/   #   \__
                  __/      |      \__
               __/         |         \__
            __/            #            \__
         __/              ###              \__
      __/                / # \                \__
 # __/                   |   |                   \__ #
###,__                  /     \                  __,###
 #    \__#              |     |              #__/    #
 \      ###------------/-------\------------###     /
  |      #\_           |       |           _/#      |
  \         \_        /         \        _/        /
   |          \_      |         |      _/          |
   \            \__  /           \  __/           /
    |              \_|           |_/              |
    \               /\_         _/\              /
     |              |  \_     _/  |              |
     \             /     \___/     \            /
      |            |     _/ \_     |            |
      \           /    _/     \_    \          /
       |          |  _/         \_  |          |
       \         # _/             \_ #        / 
        |       ###                 ###       | 
        \     _/ #                   # \_    /
         |   /                           \   |
          \#/                             \#/
          ###-----------------------------###
           #                               #

I'm open to any suggestions--about how to improve this representation of the Petersen graph, about whether it's illustrative enough to even be worth it, about life in general...whatever.

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