Polytope of Type {8,102}

s0 := (103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204)(205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);;
s1 := (  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)( 40,234)( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)( 48,226)( 49,225)( 50,224)( 51,223)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,290)( 70,306)( 71,305)( 72,304)( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)( 80,296)( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,358)(104,374)(105,373)(106,372)(107,371)(108,370)(109,369)(110,368)(111,367)(112,366)(113,365)(114,364)(115,363)(116,362)(117,361)(118,360)(119,359)(120,392)(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)(128,401)(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)(136,393)(137,375)(138,391)(139,390)(140,389)(141,388)(142,387)(143,386)(144,385)(145,384)(146,383)(147,382)(148,381)(149,380)(150,379)(151,378)(152,377)(153,376)(154,307)(155,323)(156,322)(157,321)(158,320)(159,319)(160,318)(161,317)(162,316)(163,315)(164,314)(165,313)(166,312)(167,311)(168,310)(169,309)(170,308)(171,341)(172,357)(173,356)(174,355)(175,354)(176,353)(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)(184,345)(185,344)(186,343)(187,342)(188,324)(189,340)(190,339)(191,338)(192,337)(193,336)(194,335)(195,334)(196,333)(197,332)(198,331)(199,330)(200,329)(201,328)(202,327)(203,326)(204,325);;
s2 := (  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(205,223)(206,222)(207,238)(208,237)(209,236)(210,235)(211,234)(212,233)(213,232)(214,231)(215,230)(216,229)(217,228)(218,227)(219,226)(220,225)(221,224)(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(256,274)(257,273)(258,289)(259,288)(260,287)(261,286)(262,285)(263,284)(264,283)(265,282)(266,281)(267,280)(268,279)(269,278)(270,277)(271,276)(272,275)(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(307,325)(308,324)(309,340)(310,339)(311,338)(312,337)(313,336)(314,335)(315,334)(316,333)(317,332)(318,331)(319,330)(320,329)(321,328)(322,327)(323,326)(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)(358,376)(359,375)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)(374,377)(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)(400,402);;
poly := Group([s0,s1,s2]);;

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

s0 := Sym(408)!(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)(151,202)(152,203)(153,204)(205,307)(206,308)(207,309)(208,310)(209,311)(210,312)(211,313)(212,314)(213,315)(214,316)(215,317)(216,318)(217,319)(218,320)(219,321)(220,322)(221,323)(222,324)(223,325)(224,326)(225,327)(226,328)(227,329)(228,330)(229,331)(230,332)(231,333)(232,334)(233,335)(234,336)(235,337)(236,338)(237,339)(238,340)(239,341)(240,342)(241,343)(242,344)(243,345)(244,346)(245,347)(246,348)(247,349)(248,350)(249,351)(250,352)(251,353)(252,354)(253,355)(254,356)(255,357)(256,358)(257,359)(258,360)(259,361)(260,362)(261,363)(262,364)(263,365)(264,366)(265,367)(266,368)(267,369)(268,370)(269,371)(270,372)(271,373)(272,374)(273,375)(274,376)(275,377)(276,378)(277,379)(278,380)(279,381)(280,382)(281,383)(282,384)(283,385)(284,386)(285,387)(286,388)(287,389)(288,390)(289,391)(290,392)(291,393)(292,394)(293,395)(294,396)(295,397)(296,398)(297,399)(298,400)(299,401)(300,402)(301,403)(302,404)(303,405)(304,406)(305,407)(306,408);
s1 := Sym(408)!(  1,205)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,209)( 15,208)( 16,207)( 17,206)( 18,239)( 19,255)( 20,254)( 21,253)( 22,252)( 23,251)( 24,250)( 25,249)( 26,248)( 27,247)( 28,246)( 29,245)( 30,244)( 31,243)( 32,242)( 33,241)( 34,240)( 35,222)( 36,238)( 37,237)( 38,236)( 39,235)( 40,234)( 41,233)( 42,232)( 43,231)( 44,230)( 45,229)( 46,228)( 47,227)( 48,226)( 49,225)( 50,224)( 51,223)( 52,256)( 53,272)( 54,271)( 55,270)( 56,269)( 57,268)( 58,267)( 59,266)( 60,265)( 61,264)( 62,263)( 63,262)( 64,261)( 65,260)( 66,259)( 67,258)( 68,257)( 69,290)( 70,306)( 71,305)( 72,304)( 73,303)( 74,302)( 75,301)( 76,300)( 77,299)( 78,298)( 79,297)( 80,296)( 81,295)( 82,294)( 83,293)( 84,292)( 85,291)( 86,273)( 87,289)( 88,288)( 89,287)( 90,286)( 91,285)( 92,284)( 93,283)( 94,282)( 95,281)( 96,280)( 97,279)( 98,278)( 99,277)(100,276)(101,275)(102,274)(103,358)(104,374)(105,373)(106,372)(107,371)(108,370)(109,369)(110,368)(111,367)(112,366)(113,365)(114,364)(115,363)(116,362)(117,361)(118,360)(119,359)(120,392)(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)(128,401)(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)(136,393)(137,375)(138,391)(139,390)(140,389)(141,388)(142,387)(143,386)(144,385)(145,384)(146,383)(147,382)(148,381)(149,380)(150,379)(151,378)(152,377)(153,376)(154,307)(155,323)(156,322)(157,321)(158,320)(159,319)(160,318)(161,317)(162,316)(163,315)(164,314)(165,313)(166,312)(167,311)(168,310)(169,309)(170,308)(171,341)(172,357)(173,356)(174,355)(175,354)(176,353)(177,352)(178,351)(179,350)(180,349)(181,348)(182,347)(183,346)(184,345)(185,344)(186,343)(187,342)(188,324)(189,340)(190,339)(191,338)(192,337)(193,336)(194,335)(195,334)(196,333)(197,332)(198,331)(199,330)(200,329)(201,328)(202,327)(203,326)(204,325);
s2 := Sym(408)!(  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(205,223)(206,222)(207,238)(208,237)(209,236)(210,235)(211,234)(212,233)(213,232)(214,231)(215,230)(216,229)(217,228)(218,227)(219,226)(220,225)(221,224)(239,240)(241,255)(242,254)(243,253)(244,252)(245,251)(246,250)(247,249)(256,274)(257,273)(258,289)(259,288)(260,287)(261,286)(262,285)(263,284)(264,283)(265,282)(266,281)(267,280)(268,279)(269,278)(270,277)(271,276)(272,275)(290,291)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(307,325)(308,324)(309,340)(310,339)(311,338)(312,337)(313,336)(314,335)(315,334)(316,333)(317,332)(318,331)(319,330)(320,329)(321,328)(322,327)(323,326)(341,342)(343,357)(344,356)(345,355)(346,354)(347,353)(348,352)(349,351)(358,376)(359,375)(360,391)(361,390)(362,389)(363,388)(364,387)(365,386)(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(372,379)(373,378)(374,377)(392,393)(394,408)(395,407)(396,406)(397,405)(398,404)(399,403)(400,402);
poly := sub<Sym(408)|s0,s1,s2>;

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;