G := PSz(8);

involutions :=

[
[
    G!(1, 61)(2, 65)(3, 32)(4, 22)(5, 17)(6, 23)(7, 47)(8, 60)(9, 10)(11, 63)(12, 
        29)(13, 57)(14, 25)(15, 39)(16, 18)(19, 64)(20, 28)(21, 27)(24, 55)(26, 
        33)(30, 34)(31, 42)(35, 56)(36, 46)(37, 54)(38, 44)(40, 48)(41, 62)(43, 
        53)(49, 51)(50, 58)(52, 59),
    G!(1, 13)(2, 27)(3, 12)(4, 47)(5, 44)(6, 39)(7, 40)(8, 50)(9, 20)(10, 53)(11, 
        16)(14, 26)(15, 63)(17, 62)(18, 49)(19, 61)(21, 48)(22, 65)(23, 51)(25, 
        43)(28, 33)(29, 36)(30, 45)(31, 56)(32, 35)(34, 55)(37, 38)(41, 52)(42, 
        46)(54, 59)(57, 60)(58, 64),
    G!(1, 28)(2, 46)(3, 57)(4, 39)(5, 13)(7, 44)(8, 29)(9, 58)(10, 54)(11, 23)(12,
        27)(14, 64)(15, 55)(16, 50)(17, 30)(18, 33)(19, 48)(20, 65)(21, 35)(22, 
        38)(24, 47)(25, 62)(26, 37)(31, 60)(32, 53)(34, 43)(36, 52)(40, 49)(41, 
        51)(42, 56)(45, 63)(59, 61)
]
,
[
    G!(1, 33)(2, 5)(3, 7)(4, 26)(6, 62)(8, 54)(9, 18)(10, 64)(11, 29)(12, 40)(13, 
        28)(14, 47)(15, 42)(16, 36)(17, 39)(19, 57)(20, 49)(21, 41)(22, 55)(23, 
        25)(27, 44)(30, 38)(31, 35)(32, 56)(34, 65)(37, 45)(43, 51)(46, 63)(48, 
        52)(50, 59)(53, 58)(60, 61),
    G!(1, 53)(2, 42)(3, 34)(4, 50)(5, 36)(7, 63)(8, 40)(9, 25)(10, 65)(11, 26)(12,
        41)(13, 52)(14, 19)(15, 31)(16, 39)(17, 22)(18, 47)(20, 54)(21, 59)(23, 
        37)(24, 33)(27, 51)(28, 32)(29, 49)(30, 38)(35, 61)(43, 57)(44, 45)(46, 
        56)(48, 64)(55, 60)(58, 62),
    G!(1, 36)(2, 64)(3, 62)(4, 27)(5, 12)(6, 14)(7, 16)(8, 31)(9, 38)(10, 44)(11, 
        53)(13, 48)(15, 56)(17, 29)(18, 47)(19, 65)(20, 50)(21, 22)(23, 25)(24, 
        49)(26, 34)(28, 58)(30, 33)(32, 41)(35, 39)(37, 59)(40, 57)(42, 60)(43, 
        63)(46, 61)(51, 55)(52, 54)
]
,
[
    G!(1, 25)(2, 56)(3, 46)(4, 47)(5, 63)(6, 40)(7, 43)(8, 38)(9, 41)(10, 44)(11, 
        59)(12, 45)(13, 42)(14, 64)(15, 51)(17, 21)(18, 26)(19, 27)(20, 28)(22, 
        54)(23, 58)(24, 65)(29, 33)(30, 39)(31, 36)(32, 50)(34, 37)(35, 62)(48, 
        57)(49, 53)(52, 61)(55, 60),
    G!(1, 34)(2, 53)(3, 14)(4, 33)(5, 9)(6, 50)(7, 36)(8, 42)(10, 30)(11, 23)(12, 
        24)(13, 61)(15, 17)(16, 28)(18, 32)(19, 38)(20, 49)(21, 52)(22, 51)(25, 
        26)(27, 60)(29, 59)(31, 48)(35, 39)(37, 54)(40, 55)(41, 45)(44, 46)(47, 
        63)(56, 57)(58, 64)(62, 65),
    G!(1, 3)(2, 25)(4, 19)(5, 24)(6, 12)(7, 15)(8, 65)(9, 40)(10, 54)(11, 14)(13, 
        36)(16, 17)(18, 59)(20, 47)(21, 42)(23, 55)(26, 38)(27, 37)(28, 33)(29, 
        35)(30, 34)(31, 32)(39, 41)(43, 64)(44, 50)(45, 53)(46, 63)(48, 61)(49, 
        60)(51, 57)(52, 56)(58, 62)
]
,
[
    G!(1, 11)(2, 46)(3, 51)(4, 9)(5, 32)(6, 31)(7, 63)(8, 55)(10, 47)(12, 62)(13, 
        49)(14, 26)(15, 28)(16, 35)(17, 38)(18, 21)(19, 52)(20, 58)(22, 61)(23, 
        33)(24, 34)(25, 53)(27, 64)(29, 50)(30, 54)(37, 40)(39, 41)(42, 43)(44, 
        57)(45, 65)(48, 60)(56, 59),
    G!(1, 42)(2, 40)(3, 53)(4, 6)(5, 63)(7, 18)(8, 60)(9, 11)(10, 58)(12, 44)(13, 
        59)(14, 30)(15, 64)(16, 61)(17, 27)(19, 34)(20, 23)(21, 49)(22, 31)(24, 
        50)(25, 36)(26, 37)(28, 47)(29, 54)(32, 39)(33, 41)(35, 52)(38, 65)(43, 
        46)(45, 56)(48, 62)(51, 55),
    G!(1, 48)(2, 63)(3, 28)(4, 59)(5, 14)(6, 53)(7, 29)(8, 41)(9, 34)(10, 20)(11, 
        45)(12, 49)(13, 46)(15, 54)(16, 56)(17, 39)(18, 50)(19, 31)(22, 60)(23, 
        64)(24, 42)(25, 51)(26, 33)(27, 65)(30, 58)(32, 35)(36, 62)(37, 47)(38, 
        57)(40, 55)(43, 61)(44, 52)
]

];

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;