G := Alt(12);

involutions :=

[
[
    G!(1, 12)(2, 4)(6, 9)(8, 11),
    G!(1, 2)(3, 10)(4, 11)(5, 8),
    G!(1, 4)(2, 3)(7, 10)(9, 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;