# 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 2^{n} 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 3^{n} 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 3^{4} = 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 |