Polytope of Type {12,42}

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

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