In geometry, the Kummer configuration, named for Ernst Kummer, is a geometric configuration of 16 points and 16 planes such that each point lies on 6 of the planes and each plane contains 6 of the points. Further, every pair of points is incident with exactly two planes, and every two planes intersect in exactly two points. The configuration is therefore a biplane, specifically, a 2−(16,6,2) design. The 16 nodes and 16 tropes of a Kummer surface form a Kummer configuration.[1]
There are three different non-isomorphic ways to select 16 different 6-sets from 16 elements satisfying the above properties, that is, forming a biplane. The most symmetric of the three is the Kummer configuration, also called "the best biplane" on 16 points.[2]
^Hudson, R. W. H. T. (1990), Kummer's quartic surface, Cambridge Mathematical Library, Cambridge University Press, ISBN 978-0-521-39790-2, MR 1097176
^Assmus, E.F.; Sardi, J.E. Novillo (1981), "Generalized Steiner systems of type 3-(v, {4,6},1)", Finite Geometries and Designs, Proceedings of a Conference at Chelwood Gate (1980), Cambridge University Press, pp. 16–21
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doi:10.1016/0097-3165(83)90022-5, MR 0704251. Hudson, R. W. H. T. (1990), Kummer's quartic surface, Cambridge Mathematical Library, Cambridge University Press...
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following the method of H. Grassmann" (English translation of book) E. Kummer, "General theory of rectilinear ray systems" (English translation) M. Pasch...
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