Based on Pat's example of four-tile play, Joanne reported that the 120 degree angle was determined by subtracting the two 90 degree angles of each of the side squares, and the 60 degree angle of the hollow equilateral triangle from a 360 degree circle.
The central square placed inside of the obtuse 120 degree angle took up 90 degrees, so there was 30 degrees left, and the two "slits" on each side were determined to be 15 degree angles.
That is, the two "slits" represent two new angles that measure 15 degrees each, which along with the newly formed 120 degree angles, resulted from practice exercises carried out through Parquet Tile play.
Adding all the angles together again makes 360 degrees. Thus, 90+90+60+90+15+15=360. Maybe that is why Pat was seeing circles! Peggy saw a tree.