RWPRI Geometries for the Alternating Group A 8

We give an exhaustive list of the residually connected, flag-transitive geometries of the alternating group A 8 satisfying the (IP)2 and RWPRI properties. The list was obtained with the aid of a computer and the software package MAGMA[1]. The programs used are based on the algorithms described in [15] and [16]. Many geometries were predicted by a theory of inductively minimal geometries. For the remaining geometries, we give an explicit construction proving their existence. These constructions rely on various geometrical objects resulting from the well-known isomorphisms A 8 ≌ PSL(4, 2) ≌ PO; +(6, 2).