A

quartic surface defined by the following equation:

(x^{2} + y^{2} + z^{2} - µ^{2}w^{2})^{2} - λpqrs = 0

where:
λ ≡ (3µ^{2} - 1)/(3 - µ^{2})

p, q, r, and s are the tetrahedral coordinates

p = w - z - x√2

q = w - z + x√2

r = w + z + y√2

s = w + z - y√2

The Kummer Surface has the largest number of ordinary double points (16) known to exist for a quartic surface.

One can also use the following equations to plot a Kummer Surface:

x^{4} + y^{4} + z^{4} - x^{2} - y^{2} - z^{2} - x^{2}y^{2} - x^{2}z^{2} - y^{2}z^{2} + 1 = 0

or

x^{4} + y^{4} + z^{4} + a(x^{2} + y^{2} + z^{2}) + b(x^{2}y^{2} + x^{2}z^{2} + y^{2}z^{2}) + cxyz - 1 = 0