Polytope of Type {44,12}

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