A Parallelogram is an offset 2 x 4 which is typically in the following shape:
| |   |  |   |  | From here... |  | or here... |  |  |  |   |  | Think of working here. | 
 | 
The Parallelograms diagrammed above have what is referred to as a 50% offset,
  since the two 1 x 4's are shifted relative to each other by half of their
  total length.  This is the most common type of Parallelogram.  Be aware,
  however, that the Parallelogram could be 25%, 75%, or 100% offset.
| |   |  | 25% offset | 
 | |   |  | 75% offset | 
 | |   |  | 100% offset | 
 | 
When doing a call from a Parallelogram, do the call as if the two 1 x 4s
  were shifted into a normal setup.
At C2, the caller generally restricts Parallelogram calls to easy calls which
  are not shape-changers.  If the given call is a shape changer (that is, you are
  unable to end on the same set of footprints because the original 2 x 4
  has rotated by 90°), then retain the Shear Line and the Shift Direction.
  See Appendix A 
for a discussion on Shape-Changing.
| Parallelogram Recycle 
 |   |  |   |  | before Parallelogram Recycle
 |  | after 
 | 
 | 
Note that in the above diagrams there are a total of 12 spots in the before
  picture and 12 spots in the after picture.
When dancing a Parallelogram call, it is sometimes (but not always) 
  necessary to adjust to a 'normal' setup (by removing the offset), do the 
  given call, & then re-adjust so as to retain the original Shear Line and 
  Shift Direction.  Some callers and dancers believe you should always do this.  
  We strongly disagree, since it is often awkward, clumsy, and time-consuming
  to dance.  Whether or not to remove the offset before doing a given call is
  a call-dependent (and dancer-dependent) decision.  For a call such as
  Parallelogram In Roll Circulate, you need not take out the offset.
  The footprints do not change, the traffic pattern is clear for all dancers,
  and In Roll Circulate is not a long, complicated call.
  However, for a call such as Parallelogram Magic Transfer The Column,
  there is no way to execute this call without taking out the
  offset.  This is analogous to In Your Block Walk & Dodge versus In Your
  Block Square Chain The Top.  In the first case, do the call working directly
  to the footprints of the distorted formation; in the second case, start
  with a distorted formation, blend into a normal setup, complete the call,
  and the re-establish the footprints of the distorted formation.
 See also