Semiclassical Parabolic Systems Related to M24

Semiclassical parabolic systems belong to diagram geometries whose rank two residues are generalized n-gons or a triple cover of the generalized 4-gon for Sp(4, 2), and the latter really occurs. So semiclassical parabolic systems are a generalization of Tits chamber systems of classsical type. We classify all such systems of rank four assuming in addition that there is some residue belonging to a subdiagram of type . Among others iteresting examples showing up are systems for Co₁ and M(24).