Five pictures of the ubiquitous Petersen graph are shown below. The Petersen graph has cycles of four different lengths: 5, 6, 8, and 9. Each of the first four pictures uses one of these cycle lengths for the outer boundary.
To see an animation that shows the isomorphism between the first two pictures, click here.
An SVG picture of a rotating Petersen graph can be seen here. You will need an SVG-enabled browser. Firefox and Safari do not currently (October 2008) support animation tags.