Generalized pentagonal geometries

A pentagonal geometry PENT( 𝑘,𝑟 ) is a partial linear space, where every line is incident with 𝑘 points, every point is incident with 𝑟 lines, and for each point 𝑥 , there is a line incident with precisely those points that are not collinear with 𝑥 . Here we generalize the concept by allowing the points not collinear with 𝑥 to form the point set of a Steiner system 𝑆(2,𝑘,𝑤) whose blocks are lines of the geometry.

This is the peer reviewed version of the following article:Forbes, A. D. and Rutherford, C. G., Generalized pentagonal geometries, J. Combin. Des. (2021), 1– 23., which has been published in final form at https://doi.org/10.1002/jcd.21811. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.