I've always been more of an application type guitar player over theory, but I learned some stuff on the subject in my high school music theory class.

From memory and some old textbook review a diminished chord is made up of 4 notes all a minor third apart. The symmetry in the notes intervals apart is what make these chords so unique.
Because they are all the same interval apart, one chord can equally represent four different notes, without one taking priority. One chord could be called four different names, depending on the context.

Unofortunately, I dont have much experience in in-depth music theory, and rarely find myself playing a diminished 7th chord, however, I hope my answer was adequate for your purposes.

My head hurts, I'm gonna go run through some good old pentatonic scales and power chords.
Source(s):
music theory textbook

memory

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