Diagram 20: 4-Couple Square Set.
At the start of the fourth repeat following the progression, 2341, or of the second repeat following the less usual progression, 4123.
Note that the numbered Places of the Dancers in the Full set (the Places in which they started the dance) are shown as 1 2 3 4, i.e., in Times New Roman font in the upper left part of the Dancer's symbol; their numbered Places in the Active set (the Places in which they started the Repeat) are shown as 1 2 3 4, i.e., in Helvetica font in the lower right part.
For Dancers disposed as in Diagram 20, the name, Square set, is intuitive since it is easy to visualize the square, ABCD, formed by extending the lines joining the Positions of the Man and the Lady of each Couple. There is no difficulty in making The set neat in shape, even though there are no markers for the points, A B C D. However, the extension of this concept does not work well in the less-favourably named, Triangular set. It would have been more fortunate if the Square set had been called an Octagonal Set, i.e, the shape of the shaded polygon formed by joining the Positions of the adjacent Dancers.
There are also a few Square sets for Partner groups other than Couples.
The Craven Twelvesome has the format of the 4-couple square set but with threesomes, a Man between two Ladies, at the Top and Bottom and on each Side of the Square set.
The Reel of Five has five individual Dancers arranged in the format of the 5-couple square set and so should be called a 5-Dancer Square set; confusingly, the RSCDS has chosen to use the term, Diamond Formation (though this would be completely logical if the Square set were renamed as the Octagonal Set and the Triangular set as the Hexagonal Set).
Domino Five also has five individual Dancers arranged in the format of the 5-couple square set. Here, the deviser chose to define The set rotated 45° clockwise and with Dancers 1-4 at the corners of The set; this has the disadvantage that the style of the Square set is lost and it is not unambiguously clear which is the 1st Dancer.