This surface is first studied by Kummer in 1864 and it shows all the coordinates that satisfies

(x^2 + y^2 + z^2 - mu^2 w^2)^2 - l p q r s =0

where l = (3 mu^2 - 1) / (3 - mu^2). The values for p,q,r and s are given by

p = w - z - sqrt(2) x
q = w - z + sqrt(2) x
r = w + z + sqrt(2) y
s = w + z - sqrt(2) y

This model shows the real projection at w=10 and mu = sqrt(2).