Boy's Surface

Model of the projective plane without singularities. Found by Werner Boy on assignment from David Hilbert to disprove its existence.
Polynomial by Francois Apery.

Parametric equation:

     
      x =(2/3)*(cos(u)*cos(2*v)+sqrt(2)*sin(u)*cos(v))*cos(u) /
			(sqrt(2) - sin(2*u)*sin(3*v))
      y =(2/3)*(cos(u)*sin(2*v)-sqrt(2)*sin(u)*sin(v))*cos(u) /
			(sqrt(2)-sin(2*u)*sin(3*v))
      z =sqrt(2)*cos(u)^2 / (sqrt(2) - sin(2*u)*sin(2*v))

Polynomial:

      64*(1-z)^3*z^3-48*(1-z)^2*z^2*(3*x^2+3*y^2+2*z^2)+
      12*(1-z)*z*(27*(x^2+y^2)^2-24*z^2*(x^2+y^2)+
      36*sqrt(2)*y*z*(y^2-3*x^2)+4*z^4)+
      (9*x^2+9*y^2-2*z^2)*(-81*(x^2+y^2)^2-72*z^2*(x^2+y^2)+
      108*sqrt(2)*x*z*(x^2-3*y^2)+4*z^4)=0

Here is the PoV3-source I used

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