"Diminished scales are the major scale with the third and fifth notes flatted."
The way I learnt them, is that they are a sequence of whole tone, half tone. Then there are really only three of them -
C : C - D - Eb - F - F# - G# - A - B - C
C# : C# - D# - E - F# - G - A - Bb - C - C#
D : D - E - F - G - G# - A# - B - C# - D
Eb is just a rotation of C, E of C# and so on.
Of course it's a question of what's in a name, but I prefer this definition because the scale shape reflects the symmetrical. circular nature of the diminished arpeggio (which is just a sequence of minor thirds, or gaps of 3 semitones.
For added fun, you can also have a diminished scale that goes half step - whole step ... you can play the first type ascending, the second descending. I leave that as an exercise for the musical reader.