Catillion?

A Christian Mingle? Google is your friend.

From wikipedia: The cotillion is a type of patterned social dance that originated in France in the 18th century. It was originally made up of four couples in a square formation, the forerunner of the quadrille; in the United States the square dance, where the "figures" are called aloud by the caller, is a form of rural "contredanse" that also descended from the urban cotillion...the gathered participants were able to introduce themselves and to flirt with other dancers through the exchange of partners within the formation network of the dance.

Old Southern tradition. Think of it as a factory showroom presentation of the Stepford Wives. ...

Sheldon talks about it in an episode of The Big Bang Theory

Is this it?