Polytope of Type {4,6,36}

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