Pilzchen surface

(z^3 - a^3)^2 + (-a^2 + x^2 + y^2)^3 = 0

6

V = 1/27 π a^3 (9 (2F1(2/3, 2/3, 5/3, -1) + 2 2^(1/3)) - 4 sqrt(3) π)

algebraic surfaces | closed surfaces | sextic surfaces | surfaces of revolution