A quartic surface defined by the following equation:

(x2 + y2 + z2 - µ2w2)2 - λpqrs = 0

where: λ ≡ (3µ2 - 1)/(3 - µ2)

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:

x4 + y4 + z4 - x2 - y2 - z2 - x2y2 - x2z2 - y2z2 + 1 = 0

or

x4 + y4 + z4 + a(x2 + y2 + z2) + b(x2y2 + x2z2 + y2z2) + cxyz - 1 = 0

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