Journal of Geometry

, Volume 108, Issue 3, pp 1083–1084 | Cite as

Hyper-reguli in PG(5,\(\varvec{q}\))

  • S. G. Barwick
  • Wen-Ai Jackson


A simple counting argument is used to show that for all q, an André hyper-regulus \({\mathbb {X}}\) in \(\mathrm{PG}(5,q)\) has exactly two switching sets. Moreover, there are exactly \(2(q^2+q+1)\) planes in \(\mathrm{PG}(5,q)\) that meet every plane of \({\mathbb {X}}\) in a point, namely the planes in the switching sets.


Circle geometry covers hyper-reguli 

Mathematics Subject Classification



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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical ScienceUniversity of AdelaideAdelaideAustralia

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