Polytope of Type {12,60}

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

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

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