On the thin regular geometries of rank four for the Janko group \(J_1\) (Q2493446)

The Janko group \(J_{1}\) is the smallest of a series of four groups of the twenty-six sporadic finite simple groups. Its order is 175560. In 1999, the authors started to build up an atlas of regular thin geometries and groups, which act regularly on these geometries [see Math. Comput. 68, No. 228, 1631--1647 (1999; Zbl 0941.51010)]. This work is now extended to include all geometries on which \(J_{1}\) acts regularly. The classification of these geometries has been obtained by using a series of MAGMA programs.