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