Polytope of Type {30,24}

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