This Boolean function was initially found by adding another intersection to the inflated function barogi (shown on the right), creating an Euler diagram with an unusual geometry (which could be described as a torus). Each pair of circles overlap, so no two sets are disjoint or in a subset relationship. It turned out to be difficult to verify, that this function does not require gapspots.
The representation with spheres is not really useful. It is shown here as a step in the search for a good Euler diagram - which started with the circles, and ended with the curved planes.
(Only the front side of the spheres is shown, because the full version contains duplicates of the two vertices and the edge between them.)
This object has 13 cells, 22 faces, 12 edges and 2 vertices.
The edge between red and yellow is separate, and the others are two crosses on one axis.
Spot 3 is on its own an octant of the lower 3-split. Removing it causes this 3-split to disappear. The resulting function farofe still has the other one, and thus also requires an Euler diagram with 3 dimensions. Removing spot 2 as well, causes also the upper 3-split to lose its bottom front octant, so the resulting function niliko has a 2-dimensional Euler diagram. Removing spots 0 and 2 creates the new gapspot 11, which is on its own an octant of the new 3-split ABD. Theoretically the resulting function rudege has a 3D diagram, but no properties are lost in the 2D projection shown.
