Boy's surface of degree 6

Boy's surface is an immersion of the real projective plane in 3-space found by W. Boy in 1901. This was the topic of his dissertation under D. Hilbert (who has asked him to prove the inexistence of such immersions).

In 1984, F. Apéry proved that it is also an algebraic surface of degree 6, given by the equations \begin{gather*} \begin{split} 0 &= 2S_0^3 + z(8-9z)S_0^2\\ +& 2z(z(2-3z)(4-3z)+B-A)S_0 + 8z^2(1-z)B\\ S_0 &= 3(x^2+y^2+z^2)-4z, \\ A &= 3\sqrt3 x (x^2-3y^2),\quad B = 3\sqrt3 y (3x^2-y^2). \end{split} \end{gather*}