Note on Discovering Doily in PG(2,5)

Stefano Innamorati ()
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Stefano Innamorati: Department of Industrial and Information Engineering and Economics, University of L’Aquila, Piazzale Ernesto Pontieri, 1 (Monteluco di Roio), I-67100 L’Aquila, Italy

Mathematics, 2023, vol. 11, issue 9, 1-5

Abstract: W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), whose representation was dubbed “the doily” by Stan Payne in 1973. In this note, we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order 2.

Keywords: Desargues configuration; generalized quadrangle of order two; projective plane of order five (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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