Here is a GeoGebra version of a Moss Egg, from a book by Dixon, Robert, called Mathographics. Dover Edition, Mineola N.Y., 1987.
There's an online source by Freyja Hreinsdóttir called Euclidean Eggs, University of Iceland, Lifelong Learning Programme, at the site
http://www.dm.unipi.it/~georgiev/club/progects/DYNAMAT/PUBLIC/D9_EBook/PDF_English/IS_EN_01_B_Euclidean_Eggs.pdf