This is the most intuitive form of Reflection; each Dancer of a pair is in the mirror-image Position of the other. If a half-silvered mirror were placed on the Centreline, each Dancer's Reflection would coincide with his/her "Partner". Mathematicians will recognize this as Reflection in one dimension.
At its simplest, this is the situation when the Couples are Standing, Facing Partner in a Longwise set, as shown in the diagram. More importantly, it arises in Figures such as Mirror reels of three, as in bars 17-24 of Helen's Reel, where each Man's Position is the Mirror reflection of his Partner's. This form of Reflection is particularly conducive to Covering.
Note that MiniCrib uses the term Reflection as a synonym for Mirror reflection; we prefer to abbreviate it to Mirror in order to differentiate it from the other forms of Reflection.
Diagonal Reflection / Inverted
This is a very common but much less intuitive form of Reflection; the two Dancers are Positioned as though Reflected through a point in the Centre of The set. Every (imaginary) line between the pairs of Dancers (and indeed between every distinct part of each Dancer when they are of the same build) should have its midpoint at that Centre point. Mathematicians will recognize this as Reflection in two dimensions.
More simply, it is the same as rotation through 180°; the modifying term, Inverted, is often used with Figures such as The knot or Allemande when these are performed upside-down. In most of those 4-couple set dances where 3rd and 4th couples Start on Opposite sides, 4th couple Start by performing an Inverted version of the Figure being performed by 1st couple While 3rd couple perform an Inverted version of that by 2nd couple.
At its simplest, the Dancers Standing in the First corner positions in a Longwise set are Diagonally reflected as are those in the Second corner positions and also those in 2nd place. More importantly, and very commonly, it arises in Figures such as Reels of three across, as in bars 25-32 of Mairi's Wedding, which Starts with the Dancing man and Dancing lady each Giving left shoulder to their own First corner and in Teapots as in bars 9-16 of Langholm Fair. The Dancing couple are Diagonally reflected as are the First corners and also the Second corners; this form of Reflection is not readily conducive to Covering.
This would only be accepted as a form of Reflection (in zero dimensions) by mathematicians but it is included here as an important form of Symmetry. The two Dancers are Positioned the same distance apart, measured in the same Direction; they also Face in the same Direction.
Parallel symmetry almost always involves Figures with the axes On the sides of The set as in almost all occurrences of Reels of 4 On the sides of a Longwise set. New Year Jig shows two other examples: in bars 1-8, for 1st couple in their Parallel Figures of 8 On the sides; in bars 9-16, for all three Couples in their Parallel Reels of 3 On the sides. Covering with this form of Reflection is not nearly so conducive as in Mirror reflection.