Polytope of Type {36,6,4}

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

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