Moss Egg or Euclidean Egg
Drag the green dot to change the egg to fish.
See the construction:
https://youtu.be/JE-L0VarQzo
Based on Robert Dixon's Mathographics
https://books.google.com.hk/books?id=1fDgb17bgBkC&lpg=PP1&pg=PA3#v=onepage&q&f=false