Polytope of Type {10,60}

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

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