Parallelograms are a difficult concept to master -- few dancers do.

There are some basic facts about parallelograms that must be understood if you are to become competent in the use of the concept.

Parallelograms are offset formations, normally considered as columns or lines. The following diagram illustrates this:

Notice that the waves and columns are offset by two spots on the floor. Other offsets are possible. It is extremely rare to see any other offset at C2 or C3A with the exception of lines that are completely offset.

A parallelogram is considered to be a 6x2 (or 2x6) formation. That is, each formation has 12 spots. It is important to remember the number 12 because sometimes a call that starts in a 6x2 formation can end up as a 4x3 formation. More on this later. You do not dance to the extra spots. They just define the odd shape of the distorted formation. This figure demonstrates this 12 spot formation.

The "X" shows the spots that define the formation but are not used

If you do a Parallelogram In Roll Circulate from ocean waves, you do the In Roll Circulate to the 8 dancer spots. You do not use the extra spots in the 6x2 formation.

There is a dividing line between each line or column of the parallelogram. This line is called the "shear line". The important thing to remember about shear lines is the direction of the shear line doesn't change during the parallelogram call. If the shear line starts from side wall to side wall, it will end from side wall to side wall no matter what happens during the call.

If the call ends with dancers on the shear line, the parallelogram concept is finished. Do not restore the parallelogram.

There is also a diagonal line which helps to define the offset.

The direction of the diagonal doesn't change from the start of the parallelogram call to the finish of the parallelogram call.

To illustrate this, consider a parallelogram ferris wheel from parallelogram 2-faced lines:

If this call were to be done from normal (non-parallelogram) 2-faced lines, the resulting formation would be columns. This sample demonstrates that the shear line and the diagonal don't change and shows how a parallelogram (2x6) formation can change into a triple column (3x4) formation.

In a parallelogram situation, the resulting formation is still columns but because the original formation was offset, the resulting formation must be offset.

Remember the rule -- the shear line and the diagonal don't change direction.

But why aren't the resulting boxes completely offset? The original formation was defined as a parallelogram -- a 2x6 formation containing 12 spots.

The resulting formation must also have 12 spots. Since the end formation is columns of 4 people, it must be 3 spots wide to keep the original 12 spots.

This is also called a triple column formation, 3 columns of 4 spots with only 8 spots occupied.

Notice that the shear line remained the same and the diagonal remained the same.

The items to remember are:

• There are 12 spots in the formation with only 8 spots occupied (no phantoms)
• There is a shear line whose direction doesn't change during the call.
• The is a diagonal line whose direction doesn't change during the call.

A case of mistaken identity is shown here. There is a difference in calls that are preceded with the phrase "in your parallelogram" and calls that are done while your formation is a parallelogram setup. In order for the parallelogram rules to apply, the call must be preceded with the phrase "in your parallelogram". Otherwise, the call is just another call to be done from whatever position you are standing in.

The rules for parallelograms that apply to parallelograms also apply to offset line/wave formations. They are also 12 spot formationsthat begin as 3x4 and end in parallelograms.

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Examples of Parallelogram, Offset Line Formations and Counter Rotates

The following examples show many cases of parallelogram concept applications. Simple cases, such as, Pass Thru, Partner Trade and Partner Tags are not shown.