9. C Half-Diminshed Chord Diagram

(Locrian / Locrian ♯2)

Last but certainly not least let’s take a look at the C Half Diminished Chord Diagram.
The difference between Locrian and Locrian ♯2 is only that the latter contains a usable tension 9, therefore providing 1 more layer of symbol/sound.
For most musical situations the basic symbol (a2) is enough but by all means use the others if necessary.

Color codes for chord trees
C Half-Diminished Chord Tree