The slightly different geometry of the Triangular set means that the Lady three Dancers away on the right of a Man (his Second corner) is actually directly opposite him in that form of Circular set; it also means that the Dancers Progress, anticlockwise, one third of the way around The set (rather than one quarter as in the Square set) and so return to their Original Places after only three repetitions, taking 12 bars. This 12-bar Figure is sometimes called a Triangular reel of six; it occurs in bars 17-28 of Round Hay of Six.
One consequence of the Man's Second corner being opposite him in the Triangular set is that the Men must make a more conscious effort to Give left shoulder as they Pass in the Centre of The set; it will often help to keep the correct shape of the Triangular set if the Men Dance Left hands across halfway on bars 1-2 and the Ladies do the same on bars 3-4. This is recommended in the Reel, The Trefoil Badge, where the Figure occurs in bars 17-20 and then from the Dancers' new Places in bars 21-24; Diagram 109 shows the first two bars of the Figure as it occurs there in bars 17-18.
One Third Schiehallion Reel: Bars 1-2.
Bars 1-2 of One third schiehallion reel in a triangular set; 1st couple's paths shown emboldened, the ladies' broken; arrow heads show the positions of the equally spaced dancers at the end of bar 2.
A more mathematical consequence is that this Figure is the same as Interlocking reels Across in a Triangular set but most Dancers will find the association with Schiehallion reels more helpful.
The Ladies' One third schiehallion reel is equally possible as a reverse form in a Triangular set in which the Ladies follow their Second corners, the Men follow their Partners, the Dancers Progress clockwise around The set, the Ladies Dance Left hands across halfway on bars 1-2 and the Men do the same on bars 3-4.