Diagonals of a Rectangle

While I should have been sleeping, Paula Beardell Krieg posts the first star. Then Simon Gregg the 2nd. Then Malke Rosenfeld. Then Mike Lawler shared his connection. I wanted to play, too, so I tried to think of a variation on Mike’s. Came out pretty! To see their pictures: http://mathhombre.tumblr.com/post/133929220214/mtbos-stars-while-i-should-have-been-sleeping But now I’m wondering how the stats on the diagonals compare to the regular polygon? How many intersections of each order?
More GeoGebra at bit.ly/mh-ggb