The "negative harmony" bit (i.e. pitch class inversion) works here by 180 degree rotation exactly the same way it works on string instruments. (We can imagine a musical instrument based on this Tonnetz mesh).
For instance if you take a C major scale pattern laid out somewhere on the first four strings of the guitar (we avoid the inconsistency of the G to B string being a major third) and you rotate it 180, you get a Phrygian pattern:
Ionian:
-*---*-*-
-*-*---*-
---*---*-
Phrygian:
-*---*---
-*---*-*-
-*-*---*-
The intervals are different in this mesh but the rotation inverts them the same way.
For instance if you take a C major scale pattern laid out somewhere on the first four strings of the guitar (we avoid the inconsistency of the G to B string being a major third) and you rotate it 180, you get a Phrygian pattern:
Ionian:
Phrygian: The intervals are different in this mesh but the rotation inverts them the same way.