On a rank four geometry for the Hall–Janko sporadic group

Starting from the well-known rank three graph of degree 63 on 100 points associated to the Hall–Janko group J2, we construct a rank four residually connected and firm geometry Γ on which J2 acts flag-transitively and residually weakly primitively (RWPRI). It is the first rank four geometry satisfying RWPRI that is currently known for J2 and it shows that the RWPRI rank of J2 is at least four. The diagram of Γ is the following: