The diminished triad is exactly like a
minor triad, except the fifth is lowered by a
semitone.
The diminished triad forms the basis for diminished chords -- notably the diminished seventh, which is often simply called "the diminished chord."
Other chords based on the diminished triad are usually notated explicitly, as minor chords with a flat fifth. Gm7b5, for example, consists of the diminished triad G Bb Db, with an added F (the seventh note of the G natural minor scale.)