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

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

];

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;