A Diagonal Column  Line  Wave is a Distorted Column  Line  Wave
in which the facing directions of the dancers are off by 45°
relative to the Column  Line  Wave (i.e., if everybody individually turned 45°
to the Right or Left, then they would be in the named formation).
For example, from a Butterfly formation, there are
two Diagonal Columns or two Diagonal Lines  Waves.
Diagonal Column Dixie Style To A Wave: 
Normally, calls done within a Diagonal ColumnLineWave start and end on
the four footprints of the Diagonal ColumnLineWave. Occasionally, from
a Butterfly, the caller may give a call which rotates the Diagonal by 90°
(such as Diagonal Wave Lockit or Diagonal Wave Spin The Top). In
this case, the dancers end in the footprints of the other 1x4.
Diagonal Wave Spin The Top: 
 
 From Interlocked Blocks you have Diagonal Lines of 3...   Think of working here. 

 These are (Parallel) Diagonal Lines. You can work in
a single Line or in Parallel Lines depending upon the call. 
