Title Constructions of rank five geometries for the Mathieu group M_22
Author Dimitri Leemans
Reference J. Geom. 79(2004), nr. 1-2, 146-155.
Abstract We construct nine rank five incidence geometries that are firm and residually connected and on which the Mathieu group M_22 acts flag-transitively. The constructions use mainly objects arising from the Steiner system S(3,6,22). One of these geometries was constructed by Meixner and Pasini. Three of them are obtained from the geometry of Meixner and Pasini using doubling or similar constructions. The remaining five are new and four of them have a star diagram. These latter four geometries are constructed using special partitions of the 22 points of the Steiner system S(3,6,22).

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