In geometry, the Klein configuration, studied by , is a
geometric configuration
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the ...
related to
Kummer surface
In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variet ...
s that consists of 60 points and 60 planes, with each point lying on 15 planes and each plane passing through 15 points. The configurations uses 15 pairs of lines, 12 . 13 . 14 . 15 . 16 . 23 . 24 . 25 . 26 . 34 . 35 . 36 . 45 . 46 . 56 and their reverses. The 60 points are three concurrent lines forming an odd permutation, shown below. The sixty planes are 3 coplanar lines forming even permutations, obtained by reversing the last two digits in the points. For any point or plane there are 15 members in the other set containing those 3 lines.
udson, 1905
Coordinates of points and planes
A possible set of coordinates for points (and also for planes!) is the following:
References
*
*
* But in the original paper, the P43 coordinates are incorrect.
{{Incidence structures
Configurations (geometry)
Algebraic geometry