Crossing Number

Crossing Number (Ed Pegg Jr)

In recent work with Geoff Exoo, the crossing numbers of cubic symmetric graphs have been record-setters.
So far, no smaller cubic graphs have had higher crossing numbers.
Each of the graphs above 6 vertices also has at least one irregular two with the same vertex count and CR.
See the center image of DesarguesGraph for an image on how to draw it with 6 crossings (found by Ed Pegg Jr).

4	tetrahedral graph	Y	CR 0
6	utility graph	Y	CR 1
10	Petersen graph	N	CR 2
14	Heawood graph	Y	CR 3
16	Möbius-Kantor graph	Y	CR 4
18	Pappus graph	Y	CR 5
20	Desargues graph	Y	CR 6

Might be interesting to have a contest that extended the crossing numbers of the cubic symmetrics.
As part 2 of scoring, let the closest vertices be distance 1 apart -- what is the size of the entire graph ?

For a given graph, what is the smallest number of edge crossings?
For CR 0 to CR 6, the smallest graphs are cubic symmetric graphs.