Intrinsically Knotted Graphs
In 1983, Conway and Gordon proved that for every 3D embedding of (the complete graph on seven points), at least one of the 7-cycles would be knotted. The graph is thus called an intrinsically knotted graph.[more]
Similarly, the graph is intrinsically linked, because it will always contain two linked 3-cycles.[less]
The 23 given point embeddings have the property that no set of four points is on a plane.