Barth Decic

This picture is showing (the real points of a part of) the Barth-decic, an algebraic surface in complex three-dimensional projective space with a ton of double points - count 'em yourself. Polynomial:

     t= (1+Sqrt[5])/2
     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 

Here is the PoV3-source I used