The data provided is a list of lists called "involutions" containing list of triples of involutions and a list called "geometries" which contains the coset geometries associated to the involutions in "involutions".
Below is an annotated example for G := PGL(2,27). The commentaries are after // which do not appear in the original .txt file.

G := PGL(2,27); // Automorphism group (type preserving) of the geometry.

involutions := // List containing 2 lists of involutions.

[
[ // First triple of involutions in PGL(2,27).
    G!(2, 19)(3, 26)(4, 21)(5, 7)(6, 12)(8, 15)(9, 27)(10, 23)(11, 17)(13, 28)(14,
        24)(16, 18)(20, 25),
    G!(1, 20)(2, 22)(3, 10)(4, 21)(6, 26)(7, 24)(8, 27)(9, 13)(11, 16)(12, 17)(14,
        28)(15, 19)(18, 25),
    G!(1, 7)(2, 28)(3, 10)(4, 22)(5, 18)(6, 12)(8, 23)(9, 19)(11, 13)(14, 25)(15, 
        20)(16, 27)(21, 26)
]
,
[ // Second triple of involutions in PGL(2,27).
    G!(2, 24)(3, 9)(5, 28)(6, 25)(7, 18)(8, 27)(10, 14)(11, 12)(13, 16)(15, 
        26)(17, 20)(19, 23)(21, 22),
    G!(1, 8)(2, 4)(3, 23)(6, 9)(7, 14)(11, 13)(12, 20)(15, 24)(16, 26)(17, 27)(18,
        22)(19, 28)(21, 25),
    G!(1, 16)(2, 19)(3, 25)(4, 18)(5, 11)(6, 17)(7, 20)(8, 10)(9, 21)(13, 22)(14, 
        23)(15, 27)(26, 28)
]

];

geometries := [* *];

// Construction of the coset geometries associated to the involutions.

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;