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Dr. Lou Talman
Metro State

Dept. of Mathematical
and Computer Sciences

 http://clem.mscd.edu/~talmanl

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Dodecahedron

NCB Deposit  # 118
Euler stamp
V + F - E =2
Watch the dodecahedron morph into a plane figure.
dodecamorph

Click here to see the animation.

Background for the student. . . .

All platonic solids - the tetrahedron, cube, octahedron, dodecahedron and icosahedron - are Hamilton Circuits and may be traversed by crossing each vertex only once.
Please see  <  http://curvebank.calstatela.edu/hamiltoncircuit/hamiltoncircuit.htm  > for more information.
References
Modern graph theory texts will have extensive material on contributions by Leonhard Euler (1707-1783) and Sir William Rowan Hamilton (1805-1865).  This particular web page by Dr. Lou Talman followed Deposit # 115 by Dr. Peter Avery.
Brian Hopkins and Robin J. Wilson, "The Truth about Königsberg," The College Mathematics Journal, Vol. 35, No. 3, May 2004, pp. 198-207.
Harary, Frank, Graph Theory, Addison–Wesley, 1969.

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