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In response to the request for "a visualization of the hexahedral graph 5":
           HexahedraPolyhedron http://cs.smith.edu/~orourke/MathOverflow/HexahedralGraph.jpg

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Just to illustrate the point that there are multiple realizations of any polyhedral graph:
           Wheel5Graph http://cs.smith.edu/~orourke/MathOverflow/Wheel5ab.jpg

In response to the request for "a visualization of the hexahedral graph 5":
          

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Just to illustrate the point that there are multiple realizations of any polyhedral graph:
          

           HexahedraPolyhedron http://cs.smith.edu/~orourke/MathOverflow/HexahedralGraph.jpg

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Just to illustrate the point that there are multiple realizations of any polyhedral graph:
           Wheel5Graph http://cs.smith.edu/~orourke/MathOverflow/Wheel5ab.jpg

In response to the request for "a visualization of the hexahedral graph 5":
           HexahedraPolyhedron http://cs.smith.edu/~orourke/MathOverflow/HexahedralGraph.jpg

---

Just to illustrate the point that there are multiple realizations of any polyhedral graph:
           Wheel5Graph http://cs.smith.edu/~orourke/MathOverflow/Wheel5ab.jpg

           HexahedraPolyhedron http://cs.smith.edu/~orourke/MathOverflow/HexahedralGraph.jpg

           HexahedralGraph http://cs.smith.edu/~orourke/MathOverflow/Hexahedral5.png

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Just to illustrate the point that there are multiple realizations of any polyhedral graph:
           Wheel5Graph http://cs.smith.edu/~orourke/MathOverflow/Wheel5ab.jpg

           HexahedraPolyhedron http://cs.smith.edu/~orourke/MathOverflow/HexahedralGraph.jpg

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Just to illustrate the point that there are multiple realizations of any polyhedral graph:
           Wheel5Graph http://cs.smith.edu/~orourke/MathOverflow/Wheel5ab.jpg