Polytope of Type {6,120}

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