Polytope of Type {108,4}

s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)(230,358)(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)(238,350)(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)(246,342)(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)(262,422)(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363);;
s1 := (  1,253)(  2,256)(  3,255)(  4,254)(  5,261)(  6,264)(  7,263)(  8,262)(  9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)( 16,286)( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)( 24,278)( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)( 32,270)( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)( 56,246)( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)( 64,238)( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)( 72,230)( 73,321)( 74,324)( 75,323)( 76,322)( 77,317)( 78,320)( 79,319)( 80,318)( 81,313)( 82,316)( 83,315)( 84,314)( 85,309)( 86,312)( 87,311)( 88,310)( 89,305)( 90,308)( 91,307)( 92,306)( 93,301)( 94,304)( 95,303)( 96,302)( 97,297)( 98,300)( 99,299)(100,298)(101,293)(102,296)(103,295)(104,294)(105,289)(106,292)(107,291)(108,290)(109,361)(110,364)(111,363)(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)(128,390)(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)(136,382)(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)(144,374)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)(160,358)(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)(168,350)(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)(176,342)(177,337)(178,340)(179,339)(180,338)(181,429)(182,432)(183,431)(184,430)(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)(192,422)(193,417)(194,420)(195,419)(196,418)(197,413)(198,416)(199,415)(200,414)(201,409)(202,412)(203,411)(204,410)(205,405)(206,408)(207,407)(208,406)(209,401)(210,404)(211,403)(212,402)(213,397)(214,400)(215,399)(216,398);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,326)(218,325)(219,328)(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)(236,343)(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)(244,351)(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)(252,359)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)(268,375)(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)(276,383)(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)(284,391)(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)(308,415)(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)(316,423)(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)(324,431);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

s0 := Sym(432)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(111,112)(113,117)(114,118)(115,120)(116,119)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)(128,139)(129,133)(130,134)(131,136)(132,135)(145,213)(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(177,181)(178,182)(179,184)(180,183)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,357)(230,358)(231,360)(232,359)(233,353)(234,354)(235,356)(236,355)(237,349)(238,350)(239,352)(240,351)(241,345)(242,346)(243,348)(244,347)(245,341)(246,342)(247,344)(248,343)(249,337)(250,338)(251,340)(252,339)(253,429)(254,430)(255,432)(256,431)(257,425)(258,426)(259,428)(260,427)(261,421)(262,422)(263,424)(264,423)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363);
s1 := Sym(432)!(  1,253)(  2,256)(  3,255)(  4,254)(  5,261)(  6,264)(  7,263)(  8,262)(  9,257)( 10,260)( 11,259)( 12,258)( 13,285)( 14,288)( 15,287)( 16,286)( 17,281)( 18,284)( 19,283)( 20,282)( 21,277)( 22,280)( 23,279)( 24,278)( 25,273)( 26,276)( 27,275)( 28,274)( 29,269)( 30,272)( 31,271)( 32,270)( 33,265)( 34,268)( 35,267)( 36,266)( 37,217)( 38,220)( 39,219)( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)( 49,249)( 50,252)( 51,251)( 52,250)( 53,245)( 54,248)( 55,247)( 56,246)( 57,241)( 58,244)( 59,243)( 60,242)( 61,237)( 62,240)( 63,239)( 64,238)( 65,233)( 66,236)( 67,235)( 68,234)( 69,229)( 70,232)( 71,231)( 72,230)( 73,321)( 74,324)( 75,323)( 76,322)( 77,317)( 78,320)( 79,319)( 80,318)( 81,313)( 82,316)( 83,315)( 84,314)( 85,309)( 86,312)( 87,311)( 88,310)( 89,305)( 90,308)( 91,307)( 92,306)( 93,301)( 94,304)( 95,303)( 96,302)( 97,297)( 98,300)( 99,299)(100,298)(101,293)(102,296)(103,295)(104,294)(105,289)(106,292)(107,291)(108,290)(109,361)(110,364)(111,363)(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)(121,393)(122,396)(123,395)(124,394)(125,389)(126,392)(127,391)(128,390)(129,385)(130,388)(131,387)(132,386)(133,381)(134,384)(135,383)(136,382)(137,377)(138,380)(139,379)(140,378)(141,373)(142,376)(143,375)(144,374)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)(153,329)(154,332)(155,331)(156,330)(157,357)(158,360)(159,359)(160,358)(161,353)(162,356)(163,355)(164,354)(165,349)(166,352)(167,351)(168,350)(169,345)(170,348)(171,347)(172,346)(173,341)(174,344)(175,343)(176,342)(177,337)(178,340)(179,339)(180,338)(181,429)(182,432)(183,431)(184,430)(185,425)(186,428)(187,427)(188,426)(189,421)(190,424)(191,423)(192,422)(193,417)(194,420)(195,419)(196,418)(197,413)(198,416)(199,415)(200,414)(201,409)(202,412)(203,411)(204,410)(205,405)(206,408)(207,407)(208,406)(209,401)(210,404)(211,403)(212,402)(213,397)(214,400)(215,399)(216,398);
s2 := Sym(432)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,326)(218,325)(219,328)(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)(229,338)(230,337)(231,340)(232,339)(233,342)(234,341)(235,344)(236,343)(237,346)(238,345)(239,348)(240,347)(241,350)(242,349)(243,352)(244,351)(245,354)(246,353)(247,356)(248,355)(249,358)(250,357)(251,360)(252,359)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)(261,370)(262,369)(263,372)(264,371)(265,374)(266,373)(267,376)(268,375)(269,378)(270,377)(271,380)(272,379)(273,382)(274,381)(275,384)(276,383)(277,386)(278,385)(279,388)(280,387)(281,390)(282,389)(283,392)(284,391)(285,394)(286,393)(287,396)(288,395)(289,398)(290,397)(291,400)(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)(301,410)(302,409)(303,412)(304,411)(305,414)(306,413)(307,416)(308,415)(309,418)(310,417)(311,420)(312,419)(313,422)(314,421)(315,424)(316,423)(317,426)(318,425)(319,428)(320,427)(321,430)(322,429)(323,432)(324,431);
poly := sub<Sym(432)|s0,s1,s2>;

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