Geometric Hyperplanes: Desargues Encodes Doily

Metod Saniga (1)

1 Astronomical Institute of the Slovak Academy of Sciences

It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration and its line by a set of three hyperplanes such that one of them is the complement of the symmetric difference of the remaining two and they all share a pair of non-collinear points.

Mots clés: Geometric Hyperplane; Desargues Configuration; Generalized Quadrangle of Order Two

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Metod Saniga. Geometric Hyperplanes: Desargues Encodes Doily. 2010. ⟨hal-00550447⟩