Soda Pong with Tangents

While I was setting up a clean game of Soda Pong, I took a close look at the formation of the cups.  I then saw that the brims of the cups were externally tangent circles.  The cups touch at a point of tangency.  The radii of the cups are the same and they fit.  This makes it able for exactly six cups to fit around one center cup.  It was a great game that also allowed me to find my next Geometry Hunters post.(~KM5)