Polytope of Type {14,54}

s0 := ( 10, 55)( 11, 56)( 12, 57)( 13, 58)( 14, 59)( 15, 60)( 16, 61)( 17, 62)( 18, 63)( 19, 46)( 20, 47)( 21, 48)( 22, 49)( 23, 50)( 24, 51)( 25, 52)( 26, 53)( 27, 54)( 28, 37)( 29, 38)( 30, 39)( 31, 40)( 32, 41)( 33, 42)( 34, 43)( 35, 44)( 36, 45)( 73,118)( 74,119)( 75,120)( 76,121)( 77,122)( 78,123)( 79,124)( 80,125)( 81,126)( 82,109)( 83,110)( 84,111)( 85,112)( 86,113)( 87,114)( 88,115)( 89,116)( 90,117)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189)(145,172)(146,173)(147,174)(148,175)(149,176)(150,177)(151,178)(152,179)(153,180)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,169)(161,170)(162,171)(199,244)(200,245)(201,246)(202,247)(203,248)(204,249)(205,250)(206,251)(207,252)(208,235)(209,236)(210,237)(211,238)(212,239)(213,240)(214,241)(215,242)(216,243)(217,226)(218,227)(219,228)(220,229)(221,230)(222,231)(223,232)(224,233)(225,234)(262,307)(263,308)(264,309)(265,310)(266,311)(267,312)(268,313)(269,314)(270,315)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)(277,304)(278,305)(279,306)(280,289)(281,290)(282,291)(283,292)(284,293)(285,294)(286,295)(287,296)(288,297)(325,370)(326,371)(327,372)(328,373)(329,374)(330,375)(331,376)(332,377)(333,378)(334,361)(335,362)(336,363)(337,364)(338,365)(339,366)(340,367)(341,368)(342,369)(343,352)(344,353)(345,354)(346,355)(347,356)(348,357)(349,358)(350,359)(351,360);;
s1 := (  1, 10)(  2, 12)(  3, 11)(  4, 17)(  5, 16)(  6, 18)(  7, 14)(  8, 13)(  9, 15)( 19, 55)( 20, 57)( 21, 56)( 22, 62)( 23, 61)( 24, 63)( 25, 59)( 26, 58)( 27, 60)( 28, 46)( 29, 48)( 30, 47)( 31, 53)( 32, 52)( 33, 54)( 34, 50)( 35, 49)( 36, 51)( 38, 39)( 40, 44)( 41, 43)( 42, 45)( 64,140)( 65,139)( 66,141)( 67,137)( 68,136)( 69,138)( 70,144)( 71,143)( 72,142)( 73,131)( 74,130)( 75,132)( 76,128)( 77,127)( 78,129)( 79,135)( 80,134)( 81,133)( 82,185)( 83,184)( 84,186)( 85,182)( 86,181)( 87,183)( 88,189)( 89,188)( 90,187)( 91,176)( 92,175)( 93,177)( 94,173)( 95,172)( 96,174)( 97,180)( 98,179)( 99,178)(100,167)(101,166)(102,168)(103,164)(104,163)(105,165)(106,171)(107,170)(108,169)(109,158)(110,157)(111,159)(112,155)(113,154)(114,156)(115,162)(116,161)(117,160)(118,149)(119,148)(120,150)(121,146)(122,145)(123,147)(124,153)(125,152)(126,151)(190,199)(191,201)(192,200)(193,206)(194,205)(195,207)(196,203)(197,202)(198,204)(208,244)(209,246)(210,245)(211,251)(212,250)(213,252)(214,248)(215,247)(216,249)(217,235)(218,237)(219,236)(220,242)(221,241)(222,243)(223,239)(224,238)(225,240)(227,228)(229,233)(230,232)(231,234)(253,329)(254,328)(255,330)(256,326)(257,325)(258,327)(259,333)(260,332)(261,331)(262,320)(263,319)(264,321)(265,317)(266,316)(267,318)(268,324)(269,323)(270,322)(271,374)(272,373)(273,375)(274,371)(275,370)(276,372)(277,378)(278,377)(279,376)(280,365)(281,364)(282,366)(283,362)(284,361)(285,363)(286,369)(287,368)(288,367)(289,356)(290,355)(291,357)(292,353)(293,352)(294,354)(295,360)(296,359)(297,358)(298,347)(299,346)(300,348)(301,344)(302,343)(303,345)(304,351)(305,350)(306,349)(307,338)(308,337)(309,339)(310,335)(311,334)(312,336)(313,342)(314,341)(315,340);;
s2 := (  1,253)(  2,255)(  3,254)(  4,260)(  5,259)(  6,261)(  7,257)(  8,256)(  9,258)( 10,262)( 11,264)( 12,263)( 13,269)( 14,268)( 15,270)( 16,266)( 17,265)( 18,267)( 19,271)( 20,273)( 21,272)( 22,278)( 23,277)( 24,279)( 25,275)( 26,274)( 27,276)( 28,280)( 29,282)( 30,281)( 31,287)( 32,286)( 33,288)( 34,284)( 35,283)( 36,285)( 37,289)( 38,291)( 39,290)( 40,296)( 41,295)( 42,297)( 43,293)( 44,292)( 45,294)( 46,298)( 47,300)( 48,299)( 49,305)( 50,304)( 51,306)( 52,302)( 53,301)( 54,303)( 55,307)( 56,309)( 57,308)( 58,314)( 59,313)( 60,315)( 61,311)( 62,310)( 63,312)( 64,190)( 65,192)( 66,191)( 67,197)( 68,196)( 69,198)( 70,194)( 71,193)( 72,195)( 73,199)( 74,201)( 75,200)( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,208)( 83,210)( 84,209)( 85,215)( 86,214)( 87,216)( 88,212)( 89,211)( 90,213)( 91,217)( 92,219)( 93,218)( 94,224)( 95,223)( 96,225)( 97,221)( 98,220)( 99,222)(100,226)(101,228)(102,227)(103,233)(104,232)(105,234)(106,230)(107,229)(108,231)(109,235)(110,237)(111,236)(112,242)(113,241)(114,243)(115,239)(116,238)(117,240)(118,244)(119,246)(120,245)(121,251)(122,250)(123,252)(124,248)(125,247)(126,249)(127,320)(128,319)(129,321)(130,317)(131,316)(132,318)(133,324)(134,323)(135,322)(136,329)(137,328)(138,330)(139,326)(140,325)(141,327)(142,333)(143,332)(144,331)(145,338)(146,337)(147,339)(148,335)(149,334)(150,336)(151,342)(152,341)(153,340)(154,347)(155,346)(156,348)(157,344)(158,343)(159,345)(160,351)(161,350)(162,349)(163,356)(164,355)(165,357)(166,353)(167,352)(168,354)(169,360)(170,359)(171,358)(172,365)(173,364)(174,366)(175,362)(176,361)(177,363)(178,369)(179,368)(180,367)(181,374)(182,373)(183,375)(184,371)(185,370)(186,372)(187,378)(188,377)(189,376);;
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*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(378)!( 10, 55)( 11, 56)( 12, 57)( 13, 58)( 14, 59)( 15, 60)( 16, 61)( 17, 62)( 18, 63)( 19, 46)( 20, 47)( 21, 48)( 22, 49)( 23, 50)( 24, 51)( 25, 52)( 26, 53)( 27, 54)( 28, 37)( 29, 38)( 30, 39)( 31, 40)( 32, 41)( 33, 42)( 34, 43)( 35, 44)( 36, 45)( 73,118)( 74,119)( 75,120)( 76,121)( 77,122)( 78,123)( 79,124)( 80,125)( 81,126)( 82,109)( 83,110)( 84,111)( 85,112)( 86,113)( 87,114)( 88,115)( 89,116)( 90,117)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(136,181)(137,182)(138,183)(139,184)(140,185)(141,186)(142,187)(143,188)(144,189)(145,172)(146,173)(147,174)(148,175)(149,176)(150,177)(151,178)(152,179)(153,180)(154,163)(155,164)(156,165)(157,166)(158,167)(159,168)(160,169)(161,170)(162,171)(199,244)(200,245)(201,246)(202,247)(203,248)(204,249)(205,250)(206,251)(207,252)(208,235)(209,236)(210,237)(211,238)(212,239)(213,240)(214,241)(215,242)(216,243)(217,226)(218,227)(219,228)(220,229)(221,230)(222,231)(223,232)(224,233)(225,234)(262,307)(263,308)(264,309)(265,310)(266,311)(267,312)(268,313)(269,314)(270,315)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)(277,304)(278,305)(279,306)(280,289)(281,290)(282,291)(283,292)(284,293)(285,294)(286,295)(287,296)(288,297)(325,370)(326,371)(327,372)(328,373)(329,374)(330,375)(331,376)(332,377)(333,378)(334,361)(335,362)(336,363)(337,364)(338,365)(339,366)(340,367)(341,368)(342,369)(343,352)(344,353)(345,354)(346,355)(347,356)(348,357)(349,358)(350,359)(351,360);
s1 := Sym(378)!(  1, 10)(  2, 12)(  3, 11)(  4, 17)(  5, 16)(  6, 18)(  7, 14)(  8, 13)(  9, 15)( 19, 55)( 20, 57)( 21, 56)( 22, 62)( 23, 61)( 24, 63)( 25, 59)( 26, 58)( 27, 60)( 28, 46)( 29, 48)( 30, 47)( 31, 53)( 32, 52)( 33, 54)( 34, 50)( 35, 49)( 36, 51)( 38, 39)( 40, 44)( 41, 43)( 42, 45)( 64,140)( 65,139)( 66,141)( 67,137)( 68,136)( 69,138)( 70,144)( 71,143)( 72,142)( 73,131)( 74,130)( 75,132)( 76,128)( 77,127)( 78,129)( 79,135)( 80,134)( 81,133)( 82,185)( 83,184)( 84,186)( 85,182)( 86,181)( 87,183)( 88,189)( 89,188)( 90,187)( 91,176)( 92,175)( 93,177)( 94,173)( 95,172)( 96,174)( 97,180)( 98,179)( 99,178)(100,167)(101,166)(102,168)(103,164)(104,163)(105,165)(106,171)(107,170)(108,169)(109,158)(110,157)(111,159)(112,155)(113,154)(114,156)(115,162)(116,161)(117,160)(118,149)(119,148)(120,150)(121,146)(122,145)(123,147)(124,153)(125,152)(126,151)(190,199)(191,201)(192,200)(193,206)(194,205)(195,207)(196,203)(197,202)(198,204)(208,244)(209,246)(210,245)(211,251)(212,250)(213,252)(214,248)(215,247)(216,249)(217,235)(218,237)(219,236)(220,242)(221,241)(222,243)(223,239)(224,238)(225,240)(227,228)(229,233)(230,232)(231,234)(253,329)(254,328)(255,330)(256,326)(257,325)(258,327)(259,333)(260,332)(261,331)(262,320)(263,319)(264,321)(265,317)(266,316)(267,318)(268,324)(269,323)(270,322)(271,374)(272,373)(273,375)(274,371)(275,370)(276,372)(277,378)(278,377)(279,376)(280,365)(281,364)(282,366)(283,362)(284,361)(285,363)(286,369)(287,368)(288,367)(289,356)(290,355)(291,357)(292,353)(293,352)(294,354)(295,360)(296,359)(297,358)(298,347)(299,346)(300,348)(301,344)(302,343)(303,345)(304,351)(305,350)(306,349)(307,338)(308,337)(309,339)(310,335)(311,334)(312,336)(313,342)(314,341)(315,340);
s2 := Sym(378)!(  1,253)(  2,255)(  3,254)(  4,260)(  5,259)(  6,261)(  7,257)(  8,256)(  9,258)( 10,262)( 11,264)( 12,263)( 13,269)( 14,268)( 15,270)( 16,266)( 17,265)( 18,267)( 19,271)( 20,273)( 21,272)( 22,278)( 23,277)( 24,279)( 25,275)( 26,274)( 27,276)( 28,280)( 29,282)( 30,281)( 31,287)( 32,286)( 33,288)( 34,284)( 35,283)( 36,285)( 37,289)( 38,291)( 39,290)( 40,296)( 41,295)( 42,297)( 43,293)( 44,292)( 45,294)( 46,298)( 47,300)( 48,299)( 49,305)( 50,304)( 51,306)( 52,302)( 53,301)( 54,303)( 55,307)( 56,309)( 57,308)( 58,314)( 59,313)( 60,315)( 61,311)( 62,310)( 63,312)( 64,190)( 65,192)( 66,191)( 67,197)( 68,196)( 69,198)( 70,194)( 71,193)( 72,195)( 73,199)( 74,201)( 75,200)( 76,206)( 77,205)( 78,207)( 79,203)( 80,202)( 81,204)( 82,208)( 83,210)( 84,209)( 85,215)( 86,214)( 87,216)( 88,212)( 89,211)( 90,213)( 91,217)( 92,219)( 93,218)( 94,224)( 95,223)( 96,225)( 97,221)( 98,220)( 99,222)(100,226)(101,228)(102,227)(103,233)(104,232)(105,234)(106,230)(107,229)(108,231)(109,235)(110,237)(111,236)(112,242)(113,241)(114,243)(115,239)(116,238)(117,240)(118,244)(119,246)(120,245)(121,251)(122,250)(123,252)(124,248)(125,247)(126,249)(127,320)(128,319)(129,321)(130,317)(131,316)(132,318)(133,324)(134,323)(135,322)(136,329)(137,328)(138,330)(139,326)(140,325)(141,327)(142,333)(143,332)(144,331)(145,338)(146,337)(147,339)(148,335)(149,334)(150,336)(151,342)(152,341)(153,340)(154,347)(155,346)(156,348)(157,344)(158,343)(159,345)(160,351)(161,350)(162,349)(163,356)(164,355)(165,357)(166,353)(167,352)(168,354)(169,360)(170,359)(171,358)(172,365)(173,364)(174,366)(175,362)(176,361)(177,363)(178,369)(179,368)(180,367)(181,374)(182,373)(183,375)(184,371)(185,370)(186,372)(187,378)(188,377)(189,376);
poly := sub<Sym(378)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;