Polytope of Type {2,4,4,28}

s0 := (1,2);;
s1 := (  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)(  8, 64)(  9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)( 58,114)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)(140,196)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)(169,225)(170,226)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,312)(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)(281,337)(282,338)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)(361,417)(362,418)(363,419)(364,420)(365,421)(366,422)(367,423)(368,424)(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)(377,433)(378,434)(379,435)(380,436)(381,437)(382,438)(383,439)(384,440)(385,441)(386,442)(387,443)(388,444)(389,445)(390,446)(391,447)(392,448)(393,449)(394,450);;
s2 := ( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71, 99)( 72,100)( 73,101)( 74,102)( 75,103)( 76,104)( 77,105)( 78,106)( 79,107)( 80,108)( 81,109)( 82,110)( 83,111)( 84,112)( 85,113)( 86,114)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)(128,142)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(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)(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)(194,208)(195,209)(196,210)(197,211)(198,212)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)(254,282)(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)(350,392)(351,393)(352,394)(353,367)(354,368)(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(365,379)(366,380)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(407,421)(408,422)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(435,449)(436,450);;
s3 := (  3,115)(  4,121)(  5,120)(  6,119)(  7,118)(  8,117)(  9,116)( 10,122)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)( 17,129)( 18,135)( 19,134)( 20,133)( 21,132)( 22,131)( 23,130)( 24,136)( 25,142)( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,143)( 32,149)( 33,148)( 34,147)( 35,146)( 36,145)( 37,144)( 38,150)( 39,156)( 40,155)( 41,154)( 42,153)( 43,152)( 44,151)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)( 50,159)( 51,158)( 52,164)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,171)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,178)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,185)( 74,191)( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,192)( 81,198)( 82,197)( 83,196)( 84,195)( 85,194)( 86,193)( 87,199)( 88,205)( 89,204)( 90,203)( 91,202)( 92,201)( 93,200)( 94,206)( 95,212)( 96,211)( 97,210)( 98,209)( 99,208)(100,207)(101,213)(102,219)(103,218)(104,217)(105,216)(106,215)(107,214)(108,220)(109,226)(110,225)(111,224)(112,223)(113,222)(114,221)(227,339)(228,345)(229,344)(230,343)(231,342)(232,341)(233,340)(234,346)(235,352)(236,351)(237,350)(238,349)(239,348)(240,347)(241,353)(242,359)(243,358)(244,357)(245,356)(246,355)(247,354)(248,360)(249,366)(250,365)(251,364)(252,363)(253,362)(254,361)(255,367)(256,373)(257,372)(258,371)(259,370)(260,369)(261,368)(262,374)(263,380)(264,379)(265,378)(266,377)(267,376)(268,375)(269,381)(270,387)(271,386)(272,385)(273,384)(274,383)(275,382)(276,388)(277,394)(278,393)(279,392)(280,391)(281,390)(282,389)(283,395)(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)(290,402)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,409)(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)(304,416)(305,422)(306,421)(307,420)(308,419)(309,418)(310,417)(311,423)(312,429)(313,428)(314,427)(315,426)(316,425)(317,424)(318,430)(319,436)(320,435)(321,434)(322,433)(323,432)(324,431)(325,437)(326,443)(327,442)(328,441)(329,440)(330,439)(331,438)(332,444)(333,450)(334,449)(335,448)(336,447)(337,446)(338,445);;
s4 := (  3,284)(  4,283)(  5,289)(  6,288)(  7,287)(  8,286)(  9,285)( 10,291)( 11,290)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)( 17,298)( 18,297)( 19,303)( 20,302)( 21,301)( 22,300)( 23,299)( 24,305)( 25,304)( 26,310)( 27,309)( 28,308)( 29,307)( 30,306)( 31,312)( 32,311)( 33,317)( 34,316)( 35,315)( 36,314)( 37,313)( 38,319)( 39,318)( 40,324)( 41,323)( 42,322)( 43,321)( 44,320)( 45,326)( 46,325)( 47,331)( 48,330)( 49,329)( 50,328)( 51,327)( 52,333)( 53,332)( 54,338)( 55,337)( 56,336)( 57,335)( 58,334)( 59,228)( 60,227)( 61,233)( 62,232)( 63,231)( 64,230)( 65,229)( 66,235)( 67,234)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)( 73,242)( 74,241)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,249)( 81,248)( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,256)( 88,255)( 89,261)( 90,260)( 91,259)( 92,258)( 93,257)( 94,263)( 95,262)( 96,268)( 97,267)( 98,266)( 99,265)(100,264)(101,270)(102,269)(103,275)(104,274)(105,273)(106,272)(107,271)(108,277)(109,276)(110,282)(111,281)(112,280)(113,279)(114,278)(115,403)(116,402)(117,408)(118,407)(119,406)(120,405)(121,404)(122,396)(123,395)(124,401)(125,400)(126,399)(127,398)(128,397)(129,417)(130,416)(131,422)(132,421)(133,420)(134,419)(135,418)(136,410)(137,409)(138,415)(139,414)(140,413)(141,412)(142,411)(143,431)(144,430)(145,436)(146,435)(147,434)(148,433)(149,432)(150,424)(151,423)(152,429)(153,428)(154,427)(155,426)(156,425)(157,445)(158,444)(159,450)(160,449)(161,448)(162,447)(163,446)(164,438)(165,437)(166,443)(167,442)(168,441)(169,440)(170,439)(171,347)(172,346)(173,352)(174,351)(175,350)(176,349)(177,348)(178,340)(179,339)(180,345)(181,344)(182,343)(183,342)(184,341)(185,361)(186,360)(187,366)(188,365)(189,364)(190,363)(191,362)(192,354)(193,353)(194,359)(195,358)(196,357)(197,356)(198,355)(199,375)(200,374)(201,380)(202,379)(203,378)(204,377)(205,376)(206,368)(207,367)(208,373)(209,372)(210,371)(211,370)(212,369)(213,389)(214,388)(215,394)(216,393)(217,392)(218,391)(219,390)(220,382)(221,381)(222,387)(223,386)(224,385)(225,384)(226,383);;
poly := Group([s0,s1,s2,s3,s4]);;

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

s0 := Sym(450)!(1,2);
s1 := Sym(450)!(  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)(  8, 64)(  9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)( 58,114)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)(137,193)(138,194)(139,195)(140,196)(141,197)(142,198)(143,199)(144,200)(145,201)(146,202)(147,203)(148,204)(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,211)(156,212)(157,213)(158,214)(159,215)(160,216)(161,217)(162,218)(163,219)(164,220)(165,221)(166,222)(167,223)(168,224)(169,225)(170,226)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)(249,305)(250,306)(251,307)(252,308)(253,309)(254,310)(255,311)(256,312)(257,313)(258,314)(259,315)(260,316)(261,317)(262,318)(263,319)(264,320)(265,321)(266,322)(267,323)(268,324)(269,325)(270,326)(271,327)(272,328)(273,329)(274,330)(275,331)(276,332)(277,333)(278,334)(279,335)(280,336)(281,337)(282,338)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)(361,417)(362,418)(363,419)(364,420)(365,421)(366,422)(367,423)(368,424)(369,425)(370,426)(371,427)(372,428)(373,429)(374,430)(375,431)(376,432)(377,433)(378,434)(379,435)(380,436)(381,437)(382,438)(383,439)(384,440)(385,441)(386,442)(387,443)(388,444)(389,445)(390,446)(391,447)(392,448)(393,449)(394,450);
s2 := Sym(450)!( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71, 99)( 72,100)( 73,101)( 74,102)( 75,103)( 76,104)( 77,105)( 78,106)( 79,107)( 80,108)( 81,109)( 82,110)( 83,111)( 84,112)( 85,113)( 86,114)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)(128,142)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(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)(185,199)(186,200)(187,201)(188,202)(189,203)(190,204)(191,205)(192,206)(193,207)(194,208)(195,209)(196,210)(197,211)(198,212)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)(254,282)(339,381)(340,382)(341,383)(342,384)(343,385)(344,386)(345,387)(346,388)(347,389)(348,390)(349,391)(350,392)(351,393)(352,394)(353,367)(354,368)(355,369)(356,370)(357,371)(358,372)(359,373)(360,374)(361,375)(362,376)(363,377)(364,378)(365,379)(366,380)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(407,421)(408,422)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448)(435,449)(436,450);
s3 := Sym(450)!(  3,115)(  4,121)(  5,120)(  6,119)(  7,118)(  8,117)(  9,116)( 10,122)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)( 17,129)( 18,135)( 19,134)( 20,133)( 21,132)( 22,131)( 23,130)( 24,136)( 25,142)( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,143)( 32,149)( 33,148)( 34,147)( 35,146)( 36,145)( 37,144)( 38,150)( 39,156)( 40,155)( 41,154)( 42,153)( 43,152)( 44,151)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)( 50,159)( 51,158)( 52,164)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)( 59,171)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,178)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,185)( 74,191)( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,192)( 81,198)( 82,197)( 83,196)( 84,195)( 85,194)( 86,193)( 87,199)( 88,205)( 89,204)( 90,203)( 91,202)( 92,201)( 93,200)( 94,206)( 95,212)( 96,211)( 97,210)( 98,209)( 99,208)(100,207)(101,213)(102,219)(103,218)(104,217)(105,216)(106,215)(107,214)(108,220)(109,226)(110,225)(111,224)(112,223)(113,222)(114,221)(227,339)(228,345)(229,344)(230,343)(231,342)(232,341)(233,340)(234,346)(235,352)(236,351)(237,350)(238,349)(239,348)(240,347)(241,353)(242,359)(243,358)(244,357)(245,356)(246,355)(247,354)(248,360)(249,366)(250,365)(251,364)(252,363)(253,362)(254,361)(255,367)(256,373)(257,372)(258,371)(259,370)(260,369)(261,368)(262,374)(263,380)(264,379)(265,378)(266,377)(267,376)(268,375)(269,381)(270,387)(271,386)(272,385)(273,384)(274,383)(275,382)(276,388)(277,394)(278,393)(279,392)(280,391)(281,390)(282,389)(283,395)(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)(290,402)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,409)(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)(304,416)(305,422)(306,421)(307,420)(308,419)(309,418)(310,417)(311,423)(312,429)(313,428)(314,427)(315,426)(316,425)(317,424)(318,430)(319,436)(320,435)(321,434)(322,433)(323,432)(324,431)(325,437)(326,443)(327,442)(328,441)(329,440)(330,439)(331,438)(332,444)(333,450)(334,449)(335,448)(336,447)(337,446)(338,445);
s4 := Sym(450)!(  3,284)(  4,283)(  5,289)(  6,288)(  7,287)(  8,286)(  9,285)( 10,291)( 11,290)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)( 17,298)( 18,297)( 19,303)( 20,302)( 21,301)( 22,300)( 23,299)( 24,305)( 25,304)( 26,310)( 27,309)( 28,308)( 29,307)( 30,306)( 31,312)( 32,311)( 33,317)( 34,316)( 35,315)( 36,314)( 37,313)( 38,319)( 39,318)( 40,324)( 41,323)( 42,322)( 43,321)( 44,320)( 45,326)( 46,325)( 47,331)( 48,330)( 49,329)( 50,328)( 51,327)( 52,333)( 53,332)( 54,338)( 55,337)( 56,336)( 57,335)( 58,334)( 59,228)( 60,227)( 61,233)( 62,232)( 63,231)( 64,230)( 65,229)( 66,235)( 67,234)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)( 73,242)( 74,241)( 75,247)( 76,246)( 77,245)( 78,244)( 79,243)( 80,249)( 81,248)( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,256)( 88,255)( 89,261)( 90,260)( 91,259)( 92,258)( 93,257)( 94,263)( 95,262)( 96,268)( 97,267)( 98,266)( 99,265)(100,264)(101,270)(102,269)(103,275)(104,274)(105,273)(106,272)(107,271)(108,277)(109,276)(110,282)(111,281)(112,280)(113,279)(114,278)(115,403)(116,402)(117,408)(118,407)(119,406)(120,405)(121,404)(122,396)(123,395)(124,401)(125,400)(126,399)(127,398)(128,397)(129,417)(130,416)(131,422)(132,421)(133,420)(134,419)(135,418)(136,410)(137,409)(138,415)(139,414)(140,413)(141,412)(142,411)(143,431)(144,430)(145,436)(146,435)(147,434)(148,433)(149,432)(150,424)(151,423)(152,429)(153,428)(154,427)(155,426)(156,425)(157,445)(158,444)(159,450)(160,449)(161,448)(162,447)(163,446)(164,438)(165,437)(166,443)(167,442)(168,441)(169,440)(170,439)(171,347)(172,346)(173,352)(174,351)(175,350)(176,349)(177,348)(178,340)(179,339)(180,345)(181,344)(182,343)(183,342)(184,341)(185,361)(186,360)(187,366)(188,365)(189,364)(190,363)(191,362)(192,354)(193,353)(194,359)(195,358)(196,357)(197,356)(198,355)(199,375)(200,374)(201,380)(202,379)(203,378)(204,377)(205,376)(206,368)(207,367)(208,373)(209,372)(210,371)(211,370)(212,369)(213,389)(214,388)(215,394)(216,393)(217,392)(218,391)(219,390)(220,382)(221,381)(222,387)(223,386)(224,385)(225,384)(226,383);
poly := sub<Sym(450)|s0,s1,s2,s3,s4>;

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;