# Generalized hexagon of order (2,2)
U33:=PSU(3,3);
Hs:=Subgroups(U33:OrderEqual:=#U33 div 63);
#Hs eq 2;
Gs:=[CosetImage(U33,H`subgroup):H in Hs];
G1s:=[Stabilizer(G,1):G in Gs];
reps:=[{Random(o):o in Orbits(G1)|#o eq 6}:G1 in G1s];
orthGs:=[OrbitalGraph(Gs[i],1,reps[i]):i in [1,2]];
acs:=[AllCliques(orthG,3):orthG in orthGs];
V63s:=[VertexSet(orthG):orthG in orthGs];
Ds:=[IncidenceStructure<63|{{Index(x):x in c}:c in ac}>:ac in acs];
GHs:=[IncidenceGraph(D):D in Ds];
&and{Girth(GH) eq 12 and Diameter(GH) eq 6:GH in GHs};
not IsIsomorphic(Ds[1],Ds[2]);
IsIsomorphic(Ds[1],Dual(Ds[2]));