Petersen Graph

This is a spatial model of Julius Petersen's graph, having 10 vertices and 15 edges.  This model is notable for a couple reasons.  First, it is framed using the geometry of a well-known spatial model of the projective space over GF(2).  Second, it has no false intersections.  That is, every pair of intersecting edges has only a common vertex as the intersection.  Due to a theorem of Neil Robertson, Paul Seymour, and Robin Thomas, therefore, such a model must contain a pair of cycles which realize a Hopf link.