The following is the Sulanke Earth-Moon Map.
A planet and moon have each been divided into eleven contiguous regions. In both maps, the regions 1-3, 3-5, 5-2, 2-4, and 4-1 do not touch, while all other regions touch. For the map coloring, all regions of the same number must have the same color and regions that touch on either map must have different colors. Regions 6 to 11 touch, or $K_6$, requiring six colors. The cycle 1-3-5-2-4 requires three more colors. The Earth-Moon map thus needs nine colors. I took a look at this Earth-Moon problem and found 790 solutions of type $K_6 + C_5$. I'd hoped to find different solution types, but only found similar cases.
Does any have a good method for turning these 790 solutions into nice maps? The program offers planar vertex graphs, but it would be better to give the dual graphs of these, optimized in some way. The Sulanke picture looks better than my vertex-based solutions.