The Petersen graph is a unit distance graph, and this embedding is shown below, where each edge of the graph is one unit in length.
Is there a ruler and compass construction for this embedding? If so, what is it?
It seems like the kind of thing that you can construct with a ruler and compass, but my brief attempt and google search failed.
I tried by constructing the outer pentagon, and then drawing unit radius arcs inside it, centered at each vertex. The inner star should have it's vertices on those arcs.
I did come fairly close by eyeballing the "radius" of the star and drawing the smaller circle, but I suspect this was cheating :p