TIP:  There are only 3 TRULY DIFFERENT DIMINISHED SCALES:
considering the TONE , SEMITONE... pattern, and that there are only 12 notes to work
with, the cycle will start repeating itself every fourth note.
  This is an 8 NOTE SCALE so liberty must be taken with the naming (alpha/numeric
referencing) of notes.
  Notice the use of 2 different "7ths"; one double-flated(bb7) and one normal(7).

    Let's construct a "C DIMINISHED" scale:

 alpha  ~     C      D      Eb     F      Gb      Ab     Bbb(A)  B      C

numeric ~     1      2      b3     4      b5      b6     bb7     7      8(1)

spacing ~       tone   semi   tone   semi    tone    semi   tone   semi