The star figure dates back at least to the Regency era (1810s), when Thomas Wilson either composed it himself or found it common enough to include in his 1815 quadrille manual, though I have never seen it used in a quadrille other than Wilson's own Royal Scotch Quadrilles (1824). After a long absence, it reappeared in a late 1870s manual of cotillion figures (in the sense of party games or "Germans" rather than the 18th century French dance), intended to be used as part of a full evening of dance games. I have previously discussed the challenges in reconstructing this figure; the following is a practical description of how to dance it and how to use it as a German. See the end of this post for a video of dancers performing the Star.
The original source described the figure briefly:
Four ladies, right hand across, swing opposite gentleman to center. Cross right hands, and half circling, swing their partners to center. This is continued until the gentlemen again reach their partners and dance.
Anon., The German. How to give it. How to lead it. How to dance it. (Chicago, 1878)
In the 19th century, "swing" meant to turn your partner by the hand rather than the modern contra "buzz swing".
This is not the sort of figure that can be easily called "cold", but if dancers are taught the figure in advance, it makes a lovely addition to a ball or evening of cotillions.
Initiating the figure
The leader calls for two couples to rise and waltz or polka (either type of music will work for this figure; the original source makes a point of not specifying). At a signal (a whistle works well) from the leader, the two couples separate and each take a new partner. This leaves four couples on the floor. At a second signal, the couple form a quadrille set and dance the star figure. The leader must be careful to signal for the set with plenty of time to allow the dancers to arrange themselves before the beginning of a musical phrase. I have also found that it helps to give a third signal to indicate when they should actually begin the star.
As the dancers form the square set, each should take special note of his or her opposite; throughout the figure, the dancer will alternate turning partners and opposites only and will always take or touch hands with the person of the same sex in the opposite couple. The head couples and side couples never directly interact.
The star itself
The ladies move to the center and join right hands there, giving left to their partners, forming a cross. Then all drop left hands and each dancer move forward one quarter round the set, the ladies traveling clockwise in right-hand moulinet formation and the gentlemen moving counter-clockwise around the outside. Give left hands so the cross reforms with all the dancers in new places. Each person will have their opposite by the left hand. Turn by the left hand so that the gentlemen are on the inside, where they take right hands briefly. Resist the tendency to turn this into a "high five"! Continue turning to put the ladies on the inside again. Everyone again move one quarter round (ladies moulinet, gentlemen outside) and again take left hands to form the cross. Each dancer will be with their original partner, but everyone will be halfway around the set. Turn the gentlemen in. Repeat the turn of the ladies in, the quarter-progression, and the turn of the gentlemen in twice more. The third turn will be with opposites and the final turn will once again be with partners back in their original quadrant of the set. Each sequence (ladies in, progress, gentlemen in) fits nicely into four bars, giving sixteen for the entire figure. The figure ends in cross formation with the gentlemen in the center. At the end, gentlemen should turn outward to their partners, take ballroom position, and waltz or polka around the room once more.
In waltz time, the dancers should move with three steps to each measure of music. In polka time, it is unclear whether the dancers should switch to a walking step or continue to polka as individuals. I favor the latter, as the extra traveling motion of the polka step (vs. a regular walk) makes it much easier to perform the figure.
Precise timing is critical. In polka time, four bars of polka = eight counts (1&2, 3&4, 5&6, 7&8). The gentlemen should complete each quarter of the figure by touching hands in the center on count eight. No earlier, no later. In waltz time, there is more time to do the figure (four bars = 1-2-3, 2-2-3, 3-2-3, 4-2-3), so the dancers can move in larger loops and the gentlemen should touch hands at the beginning of the fourth bar (the 4 in "4-2-3"). In both polka and waltz time, note that the first quarter of the figure is different from the final three because the couple start in their original positions rather than with the gentlemen in the center. The dancers must move further on the final three quarters than they do on the first one.
Extending the figure
In a large ballroom in a modern reenactment event, the problem with figures like the star is that they leave eight people dancing and everyone else watching. At an actual historical evening of cotillion figures, different couples would take turns leading the figure, allowing everyone to participate sequentially. Possible modern compromises (since the period solution would eat up a lot of time) would be to either start the figure with four couples instead of two (resulting in two four-couple sets after the split) or to continue dancing and repeat the figure again, with the couples first splitting so that the second time there are eight couples and two sets. It is possible to continue this until the entire room is dancing, but the chaos of trying to form sets with too many couples on the floor - one couple will always be at the opposite end of the room from the set that needs them - makes it a challenge.
Below is a video of myself and seven friends in Regency costume performing the Royal Scotch Quadrilles figure which includes the Star. The video begins in mid-figure, but watch it through to see the Star figure repeated three more times.
My thanks to Franzo for pointing out that in waltz time, touching hands on the downbeat of the last bar makes more sense and feels more musical than doing it on the final beat. You were right!