Polytope of Type {4,12,6,3}

s0 := (  1,111)(  2,112)(  3,109)(  4,110)(  5,115)(  6,116)(  7,113)(  8,114)(  9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,337)(230,338)(231,340)(232,339)(233,345)(234,346)(235,348)(236,347)(237,341)(238,342)(239,344)(240,343)(241,349)(242,350)(243,352)(244,351)(245,357)(246,358)(247,360)(248,359)(249,353)(250,354)(251,356)(252,355)(253,397)(254,398)(255,400)(256,399)(257,405)(258,406)(259,408)(260,407)(261,401)(262,402)(263,404)(264,403)(265,409)(266,410)(267,412)(268,411)(269,417)(270,418)(271,420)(272,419)(273,413)(274,414)(275,416)(276,415)(277,421)(278,422)(279,424)(280,423)(281,429)(282,430)(283,432)(284,431)(285,425)(286,426)(287,428)(288,427)(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)(296,371)(297,365)(298,366)(299,368)(300,367)(301,373)(302,374)(303,376)(304,375)(305,381)(306,382)(307,384)(308,383)(309,377)(310,378)(311,380)(312,379)(313,385)(314,386)(315,388)(316,387)(317,393)(318,394)(319,396)(320,395)(321,389)(322,390)(323,392)(324,391);;
s2 := (  1,253)(  2,256)(  3,255)(  4,254)(  5,261)(  6,264)(  7,263)(  8,262)(  9,257)( 10,260)( 11,259)( 12,258)( 13,269)( 14,272)( 15,271)( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)( 24,274)( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)( 32,282)( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)( 56,230)( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)( 64,250)( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)( 72,242)( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)( 80,298)( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)( 88,306)( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)( 96,310)( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)(104,318)(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)(128,374)(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)(136,394)(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)(144,386)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)(160,342)(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)(168,346)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)(184,398)(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)(192,402)(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)(200,410)(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)(208,430)(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)(216,422);;
s3 := (  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);;
s4 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);;
poly := Group([s0,s1,s2,s3,s4]);;

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

s0 := Sym(432)!(  1,111)(  2,112)(  3,109)(  4,110)(  5,115)(  6,116)(  7,113)(  8,114)(  9,119)( 10,120)( 11,117)( 12,118)( 13,123)( 14,124)( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)( 23,129)( 24,130)( 25,135)( 26,136)( 27,133)( 28,134)( 29,139)( 30,140)( 31,137)( 32,138)( 33,143)( 34,144)( 35,141)( 36,142)( 37,147)( 38,148)( 39,145)( 40,146)( 41,151)( 42,152)( 43,149)( 44,150)( 45,155)( 46,156)( 47,153)( 48,154)( 49,159)( 50,160)( 51,157)( 52,158)( 53,163)( 54,164)( 55,161)( 56,162)( 57,167)( 58,168)( 59,165)( 60,166)( 61,171)( 62,172)( 63,169)( 64,170)( 65,175)( 66,176)( 67,173)( 68,174)( 69,179)( 70,180)( 71,177)( 72,178)( 73,183)( 74,184)( 75,181)( 76,182)( 77,187)( 78,188)( 79,185)( 80,186)( 81,191)( 82,192)( 83,189)( 84,190)( 85,195)( 86,196)( 87,193)( 88,194)( 89,199)( 90,200)( 91,197)( 92,198)( 93,203)( 94,204)( 95,201)( 96,202)( 97,207)( 98,208)( 99,205)(100,206)(101,211)(102,212)(103,209)(104,210)(105,215)(106,216)(107,213)(108,214)(217,327)(218,328)(219,325)(220,326)(221,331)(222,332)(223,329)(224,330)(225,335)(226,336)(227,333)(228,334)(229,339)(230,340)(231,337)(232,338)(233,343)(234,344)(235,341)(236,342)(237,347)(238,348)(239,345)(240,346)(241,351)(242,352)(243,349)(244,350)(245,355)(246,356)(247,353)(248,354)(249,359)(250,360)(251,357)(252,358)(253,363)(254,364)(255,361)(256,362)(257,367)(258,368)(259,365)(260,366)(261,371)(262,372)(263,369)(264,370)(265,375)(266,376)(267,373)(268,374)(269,379)(270,380)(271,377)(272,378)(273,383)(274,384)(275,381)(276,382)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,399)(290,400)(291,397)(292,398)(293,403)(294,404)(295,401)(296,402)(297,407)(298,408)(299,405)(300,406)(301,411)(302,412)(303,409)(304,410)(305,415)(306,416)(307,413)(308,414)(309,419)(310,420)(311,417)(312,418)(313,423)(314,424)(315,421)(316,422)(317,427)(318,428)(319,425)(320,426)(321,431)(322,432)(323,429)(324,430);
s1 := Sym(432)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 77)( 46, 78)( 47, 80)( 48, 79)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 97)( 62, 98)( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)( 72,103)(111,112)(113,117)(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)(137,141)(138,142)(139,144)(140,143)(145,181)(146,182)(147,184)(148,183)(149,189)(150,190)(151,192)(152,191)(153,185)(154,186)(155,188)(156,187)(157,193)(158,194)(159,196)(160,195)(161,201)(162,202)(163,204)(164,203)(165,197)(166,198)(167,200)(168,199)(169,205)(170,206)(171,208)(172,207)(173,213)(174,214)(175,216)(176,215)(177,209)(178,210)(179,212)(180,211)(217,325)(218,326)(219,328)(220,327)(221,333)(222,334)(223,336)(224,335)(225,329)(226,330)(227,332)(228,331)(229,337)(230,338)(231,340)(232,339)(233,345)(234,346)(235,348)(236,347)(237,341)(238,342)(239,344)(240,343)(241,349)(242,350)(243,352)(244,351)(245,357)(246,358)(247,360)(248,359)(249,353)(250,354)(251,356)(252,355)(253,397)(254,398)(255,400)(256,399)(257,405)(258,406)(259,408)(260,407)(261,401)(262,402)(263,404)(264,403)(265,409)(266,410)(267,412)(268,411)(269,417)(270,418)(271,420)(272,419)(273,413)(274,414)(275,416)(276,415)(277,421)(278,422)(279,424)(280,423)(281,429)(282,430)(283,432)(284,431)(285,425)(286,426)(287,428)(288,427)(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)(296,371)(297,365)(298,366)(299,368)(300,367)(301,373)(302,374)(303,376)(304,375)(305,381)(306,382)(307,384)(308,383)(309,377)(310,378)(311,380)(312,379)(313,385)(314,386)(315,388)(316,387)(317,393)(318,394)(319,396)(320,395)(321,389)(322,390)(323,392)(324,391);
s2 := 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)( 13,269)( 14,272)( 15,271)( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,273)( 22,276)( 23,275)( 24,274)( 25,285)( 26,288)( 27,287)( 28,286)( 29,281)( 30,284)( 31,283)( 32,282)( 33,277)( 34,280)( 35,279)( 36,278)( 37,217)( 38,220)( 39,219)( 40,218)( 41,225)( 42,228)( 43,227)( 44,226)( 45,221)( 46,224)( 47,223)( 48,222)( 49,233)( 50,236)( 51,235)( 52,234)( 53,229)( 54,232)( 55,231)( 56,230)( 57,237)( 58,240)( 59,239)( 60,238)( 61,249)( 62,252)( 63,251)( 64,250)( 65,245)( 66,248)( 67,247)( 68,246)( 69,241)( 70,244)( 71,243)( 72,242)( 73,289)( 74,292)( 75,291)( 76,290)( 77,297)( 78,300)( 79,299)( 80,298)( 81,293)( 82,296)( 83,295)( 84,294)( 85,305)( 86,308)( 87,307)( 88,306)( 89,301)( 90,304)( 91,303)( 92,302)( 93,309)( 94,312)( 95,311)( 96,310)( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)(104,318)(105,313)(106,316)(107,315)(108,314)(109,361)(110,364)(111,363)(112,362)(113,369)(114,372)(115,371)(116,370)(117,365)(118,368)(119,367)(120,366)(121,377)(122,380)(123,379)(124,378)(125,373)(126,376)(127,375)(128,374)(129,381)(130,384)(131,383)(132,382)(133,393)(134,396)(135,395)(136,394)(137,389)(138,392)(139,391)(140,390)(141,385)(142,388)(143,387)(144,386)(145,325)(146,328)(147,327)(148,326)(149,333)(150,336)(151,335)(152,334)(153,329)(154,332)(155,331)(156,330)(157,341)(158,344)(159,343)(160,342)(161,337)(162,340)(163,339)(164,338)(165,345)(166,348)(167,347)(168,346)(169,357)(170,360)(171,359)(172,358)(173,353)(174,356)(175,355)(176,354)(177,349)(178,352)(179,351)(180,350)(181,397)(182,400)(183,399)(184,398)(185,405)(186,408)(187,407)(188,406)(189,401)(190,404)(191,403)(192,402)(193,413)(194,416)(195,415)(196,414)(197,409)(198,412)(199,411)(200,410)(201,417)(202,420)(203,419)(204,418)(205,429)(206,432)(207,431)(208,430)(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)(216,422);
s3 := Sym(432)!(  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 89)( 82, 90)( 83, 91)( 84, 92)(101,105)(102,106)(103,107)(104,108)(109,121)(110,122)(111,123)(112,124)(113,129)(114,130)(115,131)(116,132)(117,125)(118,126)(119,127)(120,128)(137,141)(138,142)(139,143)(140,144)(145,157)(146,158)(147,159)(148,160)(149,165)(150,166)(151,167)(152,168)(153,161)(154,162)(155,163)(156,164)(173,177)(174,178)(175,179)(176,180)(181,193)(182,194)(183,195)(184,196)(185,201)(186,202)(187,203)(188,204)(189,197)(190,198)(191,199)(192,200)(209,213)(210,214)(211,215)(212,216)(217,229)(218,230)(219,231)(220,232)(221,237)(222,238)(223,239)(224,240)(225,233)(226,234)(227,235)(228,236)(245,249)(246,250)(247,251)(248,252)(253,265)(254,266)(255,267)(256,268)(257,273)(258,274)(259,275)(260,276)(261,269)(262,270)(263,271)(264,272)(281,285)(282,286)(283,287)(284,288)(289,301)(290,302)(291,303)(292,304)(293,309)(294,310)(295,311)(296,312)(297,305)(298,306)(299,307)(300,308)(317,321)(318,322)(319,323)(320,324)(325,337)(326,338)(327,339)(328,340)(329,345)(330,346)(331,347)(332,348)(333,341)(334,342)(335,343)(336,344)(353,357)(354,358)(355,359)(356,360)(361,373)(362,374)(363,375)(364,376)(365,381)(366,382)(367,383)(368,384)(369,377)(370,378)(371,379)(372,380)(389,393)(390,394)(391,395)(392,396)(397,409)(398,410)(399,411)(400,412)(401,417)(402,418)(403,419)(404,420)(405,413)(406,414)(407,415)(408,416)(425,429)(426,430)(427,431)(428,432);
s4 := Sym(432)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212)(221,225)(222,226)(223,227)(224,228)(229,241)(230,242)(231,243)(232,244)(233,249)(234,250)(235,251)(236,252)(237,245)(238,246)(239,247)(240,248)(257,261)(258,262)(259,263)(260,264)(265,277)(266,278)(267,279)(268,280)(269,285)(270,286)(271,287)(272,288)(273,281)(274,282)(275,283)(276,284)(293,297)(294,298)(295,299)(296,300)(301,313)(302,314)(303,315)(304,316)(305,321)(306,322)(307,323)(308,324)(309,317)(310,318)(311,319)(312,320)(329,333)(330,334)(331,335)(332,336)(337,349)(338,350)(339,351)(340,352)(341,357)(342,358)(343,359)(344,360)(345,353)(346,354)(347,355)(348,356)(365,369)(366,370)(367,371)(368,372)(373,385)(374,386)(375,387)(376,388)(377,393)(378,394)(379,395)(380,396)(381,389)(382,390)(383,391)(384,392)(401,405)(402,406)(403,407)(404,408)(409,421)(410,422)(411,423)(412,424)(413,429)(414,430)(415,431)(416,432)(417,425)(418,426)(419,427)(420,428);
poly := sub<Sym(432)|s0,s1,s2,s3,s4>;

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;