Texas Star--a traditional square dance
Form a square set, gents on the left, ladies on the right, all 4 couples will do the same basic moves at the same time.
A1 Ladies to the center and back to the bar (All ladies take three steps to the center, clap, and back to place) (Symmetry: Center of symmmetry; opposite ladies are always equidistant from the center along a line)
Gents to the center with a right hand star (4 Gents to the center, look clockwise and extend right hands to the center, holding the wrist in front to make a "basket weave;" walk forward once around) (Symmetry: 4-fold rotation)
A2 Other way back with a left hand star; Wave to your own and pass her by, catch that next girl on the fly; star promenade. (Gents turn in place, form a left hand star, walk forward; pass your own partner with a wave and while holding the star, scoop up your right hand lady around the waist and keep walking ahead side by side in the Texas Star) (Symmetry: 4 fold rotation, but the extra 1/4 rotation to pick up the next lady represents a 4-fold screw axis)
B1 Gents step out and ladies swing in, 1 1/2 times and you're gone again; Star Promenade! (Break the star on the inside and each couple turns together with arms around waists, gents turn backwards, ladies forward, one and a half times so the ladies finish on the inside of the set, and they make a right hand star; turn clockwise and walk forward) (Symmetry: when couples are turning on the outside, they are doing a 2-fold rotation at the 4 corners of a square; then back to a star that is a 4-fold rotation)
B2 Ladies step out and gents swing in, 1 1/2 times and your gone again; Star Promenade! (Same as above, only ladies step backwards, gents forward into their own right hand star) (Symmetry: 2 fold rotation followed by 4 fold)
C1 Gents step out and all 4 couples swing and whirl (Last time, gents break their star, step back, and swing their partner--it's customary to do the partner swing in the "ballroom" position--gents left hand to ladies right, gents left hand around the waist--gent dances forward in clockwise rotation), or you can just do a right elbow swing. (Symmetry: 2 fold rotation in the swing. OK, the ballroom swing isn't exactly a 2-fold rotation, but if you do an elbow swing it is; but, hey, a regular swing is how the dance goes, and it's a lot more fun!)
C2 Right and Left Grand: Find your corner and allemende left (turn by left hand around your corner); Hand over hand in a right and left grand (give right hand to your partner, pull past, give left to the next, and keep going until you meet your partner on the far side of the set. Promenade to the gents home place (cross hands in front,walk two-by-two counter-clockwise, gents on the inside, ladies on the outside, half around the set to the gents home place. Note--gent will start the dance the next time through with a new partner); (Symmetry: Allemende left is a 2-fold axis; Right and left grand is a 4-fold rotation, and note that the gents rotate counter-clockwise, ladies rotate clockwise; the promenade is a 4-fold rotation with couples walking counter-clockwise).
REPEAT another 3X and all dancers should be back to their original positions with their original partners.