G := sub<Sym(12)|(2, 3)(4, 6)(5, 7)(8, 11),
(2, 4)(6, 8)(7, 9)(10, 12),
(1, 2)(3, 5)(7, 10)(8, 12)>;

involutions :=
[
[
G!(2, 3)(4, 6)(5, 7)(8, 11),
G!(2, 4)(6, 8)(7, 9)(10, 12),
G!(1, 2)(3, 5)(7, 10)(8, 12)
]

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;