This is a bit of a thematic reach, but in honor of America's Independence Day, here's a simple cotillion mixer figure featuring American flags. It is taken from H. Layton Walker's Twentieth Century Cotillion Figures, (Buffalo, NY: Two Step Publishing Company, 1912), which compiled figures from a variety of different sources. The diagram at left is from Walker, in which it is arranged for fifty-seven couples, but the figure can easily be performed by a smaller (or larger) number.
The essence of the figure is to divide the dancing couples into groups of increasing size, with each group in turn (smallest to largest) first two-stepping and then, at a signal, forming a circle as the next group begins to dance. Each new circle forms around the previous one(s) and circles in the opposite direction. Once each group is circling, a signal starts the dancers doing a grand right and left in their own circle -- this is the mixer element -- and then, at the last signal, taking the person they are now facing as their partner for a final two-step.
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