The Kummer surfaces are a family of quartic surfaces given by the algebraic equation

where

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




and w is a parameter which, in the above plots, is set to w = 1. The above plots correspond to

(double sphere), 2/3, 1

(Roman surface),,

(four planes), 2, and 5. The case corresponds to four real points.
The following table gives the number of ordinary double points for various ranges of corresponding to the preceding illustrations.
4 12

4 12

16 0

16 0
The Kummer surfaces can be represented parametrically by hyperelliptic theta functions/u].Most of the Kummer surfaces admit 16 [u]ordinary double points, the maximum possible for a quartic surface. A special case of a Kummer surface is the tetrahedroid.
Nordstrand gives the implicit equations as

or