The residually weakly primitive geometries of J2J_2

We announce the end of the classification of all firm and residually connected geometries satisfying the conditions $(IP)_2$ and $(2T)_1$ and on which the Hall-Janko group $J_2$ acts flag-transitively and residually weakly primitively.We state some facts regarding the results.The complete list of geometries is available as a supplement to this paper [9]

Algorithms for classifying regular polytopes with a fixed automorphism group

In this paper, various algorithms used in the classifications of regular polytopes for given groups are compared. First computational times and memory usages are analyzed for the original algorithm used in one of these classifications. Second, a possible algorithm for isomorphism testing among polytopes is suggested. Then, two improved algorithms are compared, and finally, results are given for a new classification of all regular polytopes for certain alternating groups and for the sporadic group $Co_3$