You'll want to start out with the heptagon
and work your way up. This one's the same as all the others, just with a 13-sided regular polygon. Observe the tangencies to diagonals of circles centered at intersections of diagonals, when the circles are resized (by dragging).
This is a smaller version that works well on most monitors (zoom in with two-finger touch). Bigger version here
Tags: Tridecagon, diagonals, circles, tangents, intersections, puzzler, intricate, confusing, wow