This figure is also called a Pull Through Star.
For Four (Square, 8 bars)
(2) Star by the Right hand exactly 1/2 the way around the set. Stepping: 3s.
(2) All 4: Slipsides through the center all at once going back-to-back with the person whose hand you held. Leave room for the others. You are now near where you started, but you are facing the same compass direction as when you started the slipsides. Turn your head to face the center, but don't turn your body.
(4) Repeat, other hand to place.
(Syllabus of Irish Dances, Terry O'Neal)
When doing the pull through, give solid tension to the opposite lady or man and launch yourself through the center of the set. Take tiny steps, otherwise you'll overshoot the set and have to lean or run to catch up during the star. If you are a lady, you are always starring to a lady's position or pulling through to a lady's position. Same goes for men and men's position.
For Three (Triangle, 8 Bars)
(2) Star by the Right hand exactly 1/3 the way around the set to the next point in the triangle.
(2) All 3: Slipsides along the edge of the triangle going back to back with the other two dancers. You are now at the third point of the triangle. You start on one point of the equilateral triangle, and star to the next point in the triangle, then slip to the third.
(4) Repeat, other hand to place.