Studies of Euler diagrams/ternary labels

A cell is either in or outside of a set. Therefore cell labels are among 2n binary numbers (starting with 0). A segment in general (including edges and vertices) can also be on the border of a set. Therefore segment labels are among 3n numbers (with 0 in the middle).

These segments are among the of the n-. See e.g. this list of 34 = 81 (tesseract and) 16-cell faces.

The ternary vectors of cells have only + and &minus; entries, corresponding to binary 1 and 0.

The sign in place i of the ternary vector shows where the segment is relative to set i: