Studies of Euler diagrams/ternary labels
details of two files shown below
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 balanced ternary numbers (with 0 in the middle).
These segments are among the k-faces of the n-orthoplex. See e.g. this list of 34 = 81 (tesseract and) 16-cell faces.
The ternary vectors of cells have only + and − 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:
| + | in the set |
| 0 | on the border |
| − | outside |
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| foravo | logota | medusa | farofe |