Polytope of Type {4,24,6}

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)(162,250)(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)(170,230)(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)(178,234)(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)(194,278)(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)(202,282)(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)(210,274)(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);;
s2 := (  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)( 80,266)( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)( 88,258)( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)( 96,262)( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)(104,278)(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)(112,234)(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)(120,238)(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)(128,218)(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)(136,246)(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)(144,250);;
s3 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)(212,216)(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)(236,240)(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)(260,264)(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)(284,288);;
poly := Group([s0,s1,s2,s3]);;

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(288)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288);
s1 := Sym(288)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)(162,250)(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)(170,230)(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)(178,234)(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)(194,278)(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)(202,282)(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)(210,274)(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);
s2 := Sym(288)!(  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)( 80,266)( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)( 88,258)( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)( 96,262)( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)(104,278)(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)(112,234)(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)(120,238)(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)(128,218)(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)(136,246)(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)(144,250);
s3 := Sym(288)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)(164,168)(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)(188,192)(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)(212,216)(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)(236,240)(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)(260,264)(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)(284,288);
poly := sub<Sym(288)|s0,s1,s2,s3>;

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;