In this paper, we use the 11-point biplane and its automorphisms in to label and study the Livingstone graph () and , with an aim of using the simplest methods possible. We detail the action of on , along with the adjacencies and coadjacencies (vertices at maximum distance) in . In the last section, we use this apparatus to describe the generation of subgroups of the form and an elegant substructure of fixed by a maximal subgroup of isomorphic to .
"Using the 11-point biplane and to understand ." Rocky Mountain J. Math. 52 (1) 105 - 126, February 2022. https://doi.org/10.1216/rmj.2022.52.105