as far as i understand it, diminished chords can be named as any of the four notes played, therefore;
A Dim = A+D#+C+F#.
or
C Dim. or D#Dim or F# Dim.
you can also play the same chord on the 5th fret [for A Dim] or on the 7th fret or 10th fret, which will be the same notes in a different order ; A+D#+C+F#. or C+F#+D#+A, OR D#+A+F#+C, they also count as any of the notes become the chord name.
here's something you might like to try, you can stick it in a song for effect, i have many times;
play A Dim on the 2nd fret, then same shape on the 5th fret then the 7th fret then 10th fret, it gives a kind of run-up feel, play with it a while see what you can come up with...
your not just limited to A by the way, you can use the same shape for any diminished chord, just find the root note which can be on any of the 4 high strings, and away you go. a little practice till you find the most effective for the section your playing.
hope this helps
phill