One could easily get the impression, that the gapspot 11 is needed,
and that the graph is a prism based on the hexagon of foravo.
(This seems indeed unavoidable, if one wants to represent set B by the inside of the green circle.)

gapless

Set B can be represented by the outside of the green circle. This leads to a gapspot at the edge of the image, which can be removed, by moving it beyond the edge.
Without set B this is the foravo hexagon with 6 cells.
Without any one of the other sets it is the bunese triangle with 7 cells.

Here the three-border crossing point is enlarged into an arbitrary gapspot. (This should be avoided. It is like a gapspot in the central triangle of foravo.)

Without these four adjacent spots, the 2-split AD loses its quadrant on the right. It disappears, and the two borders A and D are now parallel.
The only fullspot in the overlap of A and D is 9. But the 2-split BC requires four quadrants in each of the three AD regions.
The missing three quadrants besides 9 are the gapspots 11, 13 and 15. The shape is like that of barogi.