It's basically doing a diamond pushup, but doing it on the medicine ball makes your stabilizer muscles kick in that much more. Just like using a swiss ball instead of a bench for lifts.
My medicine ball is the hard rubber one, a little smaller than a basketball, but the rubber is thicker to add weight.
It also helps me because my left wrist does not like the pushup position and on the med ball I can change the angle so it doesn't hurt.
We should all take ourselves seriously...and then crumple that image up and toss it out the window.