Polytope of Type {14,44}

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

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