Polytope of Type {4,36,6}

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

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

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