Studies of Euler diagrams/gap variants/medusa

dummy

gap variants

medusa

unchanged shape

kusiga (without spot 0)

(gaps gray)

(gaps 3D)
0

changed shape

nosafu (without spot 2)

(gaps gray)

(gaps 3D)
2

Euler diagram

rudege (without spots 0, 2)

(gaps gray)

(gaps 3D)
0	2

with gapspot 11
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.

ternary

as gap variant of serabe
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.)

farofe (without spot 3)

Spot 3 is one of the octants of the 3-split ABC. Without it, it disappears.

(gaps gray)

(gaps 3D)
3

Euler diagram

vidita (without spots 1, 8, 9)

(gaps gray)

(gaps 3D)
1	9	8

Euler diagram

niliko (without spots 2, 3)

Without these two adjacent spots, both 3-splits (ABC and BCD) lose their bottom front octant, and disappear. Only the six 2-splits are left.

(gaps gray)

(gaps 3D)
2	3

Euler diagram

sapigi (without spots 0, 2, 4, 6)

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.

(gaps gray)

(gaps 3D)
0	2	4	6

graph and Euler diagram