Symmetry describes a specific kind of balance. It indicates that when some condition exists on one side of the square, it exists on the other side as well. There are different kinds of symmetry. Three important kinds are:
Read the explanation of the terms formation, arrangement, and sequence in the article about FASR.If the dancers don't make any mistakes, and dance what is typically called at most open dances, all of these symmetries exist at the same time. In fact, these symmetries exist at all times. It is possible, and in fact interesting at times, to have 'Asymmetric Choreography' that deliberately upsets one or more of these symmetries causing certain kinds of imbalance in the square.
Symmetry is very powerful in that it substantially reduces the number of combinations possible with 8 dancers.
Formation SymmetryIf the square has Formation Symmetry, that means if one dancer is on a given spot, facing a given direction, another dancer is automatically on the mirror opposite spot in the formation, and is facing the opposite direction. Usually this other dancer is the first dancer's diagonal, or mirror opposite - the same sex dancer that is directly across the square when squared up at home. Any two mirror opposite dancers (or simply 'opposites') are always equal distances from the flagpole center of the formation. If you drew a line between these two dancers at any time during any symmetric dance sequence, the line would always cross the flagpole center of the formation. The flagpole center of the formation would always be at the midpoint of this line.
Arrangement SymmetryIf the square has Arrangement Symmetry, all mirror opposite dancers, as described above, would be the same sex. From a Squared Set, if the #1 couple only does a Roll Away With A Half Sashay then we have Arrangement Asymmetry because the heads' mirror opposites are different sex. If a caller avoids all sex dependent calls, and calls to this square, any sequence asymmetry will persist. Upon using a sex dependent call (assuming it were legal for everyone) the resulting formation would likely be asymmetric given that dancers may be facing the wrong way from their opposite.
Sequence SymmetryIf the square has Sequence Symmetry, then certain dancers will always be mirror opposites:
last Update: 10.12.1999