Studies of Euler diagrams/ternary labels

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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

foravo	logota	medusa	farofe