Extended Partial Geometries: Nets and Dual Nets

Abstract

Extended partial geometries (EpGs) are natural generalisations of extended generalised quadrangles. We develop some general results for any EpG, and then consider the special cases of nets and dual nets in detail. Extended dual nets have diameter at most 2, and are almost characterised, with examples, but extended nets are both more complex and perhaps more interesting: there are many examples, but also many open cases, and ‘reasonable’ conjectures. © 1990, Academic Press Limited. All rights reserved.