This animation shows the Barth surface, a level surface of the decic polynomial
8 (x^2-t^4 y^2) (y^2-t^4 z^2) (z^2-t^4 x^2)*(x^4+y^4+z^4-2 x^2 y^2-2 x^2 z^2-2 y^2 z^2)+
  (3+5t) (x^2+y^2+z^2-w^2)^2 (x^2+y^2+z^2-(2-t) w^2)^2 w^2 = 0
where t is a parameter which is changed. The surface is usually considered when t is the golden ratio. It has then icosahedral symmetry. The constant w is chosen to be 1. The background music is a few seconds from Ennio Morricones "Toto E Alfredo".