## Kummer Quartic

Additional images: Anaglyph, Parallel Stereo

A Kummer surface is any one of a one parameter family of
algebraic surfaces defined by the polynomial equation of
degree four:

(x^2 + y^2 + z^2 - aa^2)^2 - lambda*p*q*r*s = 0.
Here aa is any real number.
lambda = (3*aa^2 - 1.0)/(3 - aa^2)
p = 1 - z - sqrt(2)*x
q = 1 - z + sqrt(2)*x
r = 1 + z + sqrt(2)*y
s = 1 + z - sqrt(2)*y

The family was described originally by Ernst Eduard Kummer
In 1864.

A Kummer surface has sixteen double points, the
maximum possible for a surface of degree four in
three-dimensional space. For the default case aa = 1.3,
all these double points are real and they appear in the
visualization as the vertices of five tetrahedra.

See also: ImplicitSurfaces.pdf

Supporting files: Description in PDF