Polytope of Type {2,4,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30,4}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240412)
Rank : 5
Schlafli Type : {2,4,30,4}
Number of vertices, edges, etc : 2, 4, 60, 60, 4
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,15,4}*960
5-fold quotients : {2,4,6,4}*384f
10-fold quotients : {2,4,3,4}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)( 9,257)( 10,258)
( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)( 17,249)( 18,250)
( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)( 26,274)
( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)( 33,265)( 34,266)
( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)( 42,290)
( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)( 49,281)( 50,282)
( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)( 58,306)
( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)( 65,297)( 66,298)
( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)( 74,322)
( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)( 81,313)( 82,314)
( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)( 90,338)
( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)( 97,329)( 98,330)
( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)(106,354)
(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)(113,345)(114,346)
(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)(122,370)
(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)(129,361)(130,362)
(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)(137,385)(138,386)
(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)(145,377)(146,378)
(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)(153,401)(154,402)
(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)(161,393)(162,394)
(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)(169,417)(170,418)
(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)(177,409)(178,410)
(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)(186,434)
(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)(193,425)(194,426)
(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)(202,450)
(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)(209,441)(210,442)
(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,465)(218,466)
(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)(225,457)(226,458)
(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)(233,481)(234,482)
(235,467)(236,468)(237,469)(238,470)(239,471)(240,472)(241,473)(242,474);;
s2 := ( 3, 83)( 4, 86)( 5, 85)( 6, 84)( 7, 91)( 8, 94)( 9, 93)( 10, 92)
( 11, 87)( 12, 90)( 13, 89)( 14, 88)( 15, 95)( 16, 98)( 17, 97)( 18, 96)
( 19,147)( 20,150)( 21,149)( 22,148)( 23,155)( 24,158)( 25,157)( 26,156)
( 27,151)( 28,154)( 29,153)( 30,152)( 31,159)( 32,162)( 33,161)( 34,160)
( 35,131)( 36,134)( 37,133)( 38,132)( 39,139)( 40,142)( 41,141)( 42,140)
( 43,135)( 44,138)( 45,137)( 46,136)( 47,143)( 48,146)( 49,145)( 50,144)
( 51,115)( 52,118)( 53,117)( 54,116)( 55,123)( 56,126)( 57,125)( 58,124)
( 59,119)( 60,122)( 61,121)( 62,120)( 63,127)( 64,130)( 65,129)( 66,128)
( 67, 99)( 68,102)( 69,101)( 70,100)( 71,107)( 72,110)( 73,109)( 74,108)
( 75,103)( 76,106)( 77,105)( 78,104)( 79,111)( 80,114)( 81,113)( 82,112)
(164,166)(167,171)(168,174)(169,173)(170,172)(176,178)(179,227)(180,230)
(181,229)(182,228)(183,235)(184,238)(185,237)(186,236)(187,231)(188,234)
(189,233)(190,232)(191,239)(192,242)(193,241)(194,240)(195,211)(196,214)
(197,213)(198,212)(199,219)(200,222)(201,221)(202,220)(203,215)(204,218)
(205,217)(206,216)(207,223)(208,226)(209,225)(210,224)(243,323)(244,326)
(245,325)(246,324)(247,331)(248,334)(249,333)(250,332)(251,327)(252,330)
(253,329)(254,328)(255,335)(256,338)(257,337)(258,336)(259,387)(260,390)
(261,389)(262,388)(263,395)(264,398)(265,397)(266,396)(267,391)(268,394)
(269,393)(270,392)(271,399)(272,402)(273,401)(274,400)(275,371)(276,374)
(277,373)(278,372)(279,379)(280,382)(281,381)(282,380)(283,375)(284,378)
(285,377)(286,376)(287,383)(288,386)(289,385)(290,384)(291,355)(292,358)
(293,357)(294,356)(295,363)(296,366)(297,365)(298,364)(299,359)(300,362)
(301,361)(302,360)(303,367)(304,370)(305,369)(306,368)(307,339)(308,342)
(309,341)(310,340)(311,347)(312,350)(313,349)(314,348)(315,343)(316,346)
(317,345)(318,344)(319,351)(320,354)(321,353)(322,352)(404,406)(407,411)
(408,414)(409,413)(410,412)(416,418)(419,467)(420,470)(421,469)(422,468)
(423,475)(424,478)(425,477)(426,476)(427,471)(428,474)(429,473)(430,472)
(431,479)(432,482)(433,481)(434,480)(435,451)(436,454)(437,453)(438,452)
(439,459)(440,462)(441,461)(442,460)(443,455)(444,458)(445,457)(446,456)
(447,463)(448,466)(449,465)(450,464);;
s3 := ( 3,259)( 4,260)( 5,262)( 6,261)( 7,271)( 8,272)( 9,274)( 10,273)
( 11,267)( 12,268)( 13,270)( 14,269)( 15,263)( 16,264)( 17,266)( 18,265)
( 19,243)( 20,244)( 21,246)( 22,245)( 23,255)( 24,256)( 25,258)( 26,257)
( 27,251)( 28,252)( 29,254)( 30,253)( 31,247)( 32,248)( 33,250)( 34,249)
( 35,307)( 36,308)( 37,310)( 38,309)( 39,319)( 40,320)( 41,322)( 42,321)
( 43,315)( 44,316)( 45,318)( 46,317)( 47,311)( 48,312)( 49,314)( 50,313)
( 51,291)( 52,292)( 53,294)( 54,293)( 55,303)( 56,304)( 57,306)( 58,305)
( 59,299)( 60,300)( 61,302)( 62,301)( 63,295)( 64,296)( 65,298)( 66,297)
( 67,275)( 68,276)( 69,278)( 70,277)( 71,287)( 72,288)( 73,290)( 74,289)
( 75,283)( 76,284)( 77,286)( 78,285)( 79,279)( 80,280)( 81,282)( 82,281)
( 83,419)( 84,420)( 85,422)( 86,421)( 87,431)( 88,432)( 89,434)( 90,433)
( 91,427)( 92,428)( 93,430)( 94,429)( 95,423)( 96,424)( 97,426)( 98,425)
( 99,403)(100,404)(101,406)(102,405)(103,415)(104,416)(105,418)(106,417)
(107,411)(108,412)(109,414)(110,413)(111,407)(112,408)(113,410)(114,409)
(115,467)(116,468)(117,470)(118,469)(119,479)(120,480)(121,482)(122,481)
(123,475)(124,476)(125,478)(126,477)(127,471)(128,472)(129,474)(130,473)
(131,451)(132,452)(133,454)(134,453)(135,463)(136,464)(137,466)(138,465)
(139,459)(140,460)(141,462)(142,461)(143,455)(144,456)(145,458)(146,457)
(147,435)(148,436)(149,438)(150,437)(151,447)(152,448)(153,450)(154,449)
(155,443)(156,444)(157,446)(158,445)(159,439)(160,440)(161,442)(162,441)
(163,339)(164,340)(165,342)(166,341)(167,351)(168,352)(169,354)(170,353)
(171,347)(172,348)(173,350)(174,349)(175,343)(176,344)(177,346)(178,345)
(179,323)(180,324)(181,326)(182,325)(183,335)(184,336)(185,338)(186,337)
(187,331)(188,332)(189,334)(190,333)(191,327)(192,328)(193,330)(194,329)
(195,387)(196,388)(197,390)(198,389)(199,399)(200,400)(201,402)(202,401)
(203,395)(204,396)(205,398)(206,397)(207,391)(208,392)(209,394)(210,393)
(211,371)(212,372)(213,374)(214,373)(215,383)(216,384)(217,386)(218,385)
(219,379)(220,380)(221,382)(222,381)(223,375)(224,376)(225,378)(226,377)
(227,355)(228,356)(229,358)(230,357)(231,367)(232,368)(233,370)(234,369)
(235,363)(236,364)(237,366)(238,365)(239,359)(240,360)(241,362)(242,361);;
s4 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)
(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)
(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)
(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)
(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)
(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)(224,226)
(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)(240,242)
(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)(256,258)
(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)(272,274)
(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)(288,290)
(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)(304,306)
(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)(320,322)
(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)(336,338)
(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)(352,354)
(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)(368,370)
(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)(384,386)
(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)(400,402)
(403,405)(404,406)(407,409)(408,410)(411,413)(412,414)(415,417)(416,418)
(419,421)(420,422)(423,425)(424,426)(427,429)(428,430)(431,433)(432,434)
(435,437)(436,438)(439,441)(440,442)(443,445)(444,446)(447,449)(448,450)
(451,453)(452,454)(455,457)(456,458)(459,461)(460,462)(463,465)(464,466)
(467,469)(468,470)(471,473)(472,474)(475,477)(476,478)(479,481)(480,482);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
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, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(482)!(1,2);
s1 := Sym(482)!( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)( 9,257)
( 10,258)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)( 17,249)
( 18,250)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)
( 26,274)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)( 33,265)
( 34,266)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)
( 42,290)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)( 49,281)
( 50,282)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)
( 58,306)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)( 65,297)
( 66,298)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)
( 74,322)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)( 81,313)
( 82,314)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)
( 90,338)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)( 97,329)
( 98,330)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)
(106,354)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)(113,345)
(114,346)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)
(122,370)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)(129,361)
(130,362)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)(137,385)
(138,386)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)(145,377)
(146,378)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)(153,401)
(154,402)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)(161,393)
(162,394)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)(169,417)
(170,418)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)(177,409)
(178,410)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,433)
(186,434)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)(193,425)
(194,426)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,449)
(202,450)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)(209,441)
(210,442)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,465)
(218,466)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)(225,457)
(226,458)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)(233,481)
(234,482)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472)(241,473)
(242,474);
s2 := Sym(482)!( 3, 83)( 4, 86)( 5, 85)( 6, 84)( 7, 91)( 8, 94)( 9, 93)
( 10, 92)( 11, 87)( 12, 90)( 13, 89)( 14, 88)( 15, 95)( 16, 98)( 17, 97)
( 18, 96)( 19,147)( 20,150)( 21,149)( 22,148)( 23,155)( 24,158)( 25,157)
( 26,156)( 27,151)( 28,154)( 29,153)( 30,152)( 31,159)( 32,162)( 33,161)
( 34,160)( 35,131)( 36,134)( 37,133)( 38,132)( 39,139)( 40,142)( 41,141)
( 42,140)( 43,135)( 44,138)( 45,137)( 46,136)( 47,143)( 48,146)( 49,145)
( 50,144)( 51,115)( 52,118)( 53,117)( 54,116)( 55,123)( 56,126)( 57,125)
( 58,124)( 59,119)( 60,122)( 61,121)( 62,120)( 63,127)( 64,130)( 65,129)
( 66,128)( 67, 99)( 68,102)( 69,101)( 70,100)( 71,107)( 72,110)( 73,109)
( 74,108)( 75,103)( 76,106)( 77,105)( 78,104)( 79,111)( 80,114)( 81,113)
( 82,112)(164,166)(167,171)(168,174)(169,173)(170,172)(176,178)(179,227)
(180,230)(181,229)(182,228)(183,235)(184,238)(185,237)(186,236)(187,231)
(188,234)(189,233)(190,232)(191,239)(192,242)(193,241)(194,240)(195,211)
(196,214)(197,213)(198,212)(199,219)(200,222)(201,221)(202,220)(203,215)
(204,218)(205,217)(206,216)(207,223)(208,226)(209,225)(210,224)(243,323)
(244,326)(245,325)(246,324)(247,331)(248,334)(249,333)(250,332)(251,327)
(252,330)(253,329)(254,328)(255,335)(256,338)(257,337)(258,336)(259,387)
(260,390)(261,389)(262,388)(263,395)(264,398)(265,397)(266,396)(267,391)
(268,394)(269,393)(270,392)(271,399)(272,402)(273,401)(274,400)(275,371)
(276,374)(277,373)(278,372)(279,379)(280,382)(281,381)(282,380)(283,375)
(284,378)(285,377)(286,376)(287,383)(288,386)(289,385)(290,384)(291,355)
(292,358)(293,357)(294,356)(295,363)(296,366)(297,365)(298,364)(299,359)
(300,362)(301,361)(302,360)(303,367)(304,370)(305,369)(306,368)(307,339)
(308,342)(309,341)(310,340)(311,347)(312,350)(313,349)(314,348)(315,343)
(316,346)(317,345)(318,344)(319,351)(320,354)(321,353)(322,352)(404,406)
(407,411)(408,414)(409,413)(410,412)(416,418)(419,467)(420,470)(421,469)
(422,468)(423,475)(424,478)(425,477)(426,476)(427,471)(428,474)(429,473)
(430,472)(431,479)(432,482)(433,481)(434,480)(435,451)(436,454)(437,453)
(438,452)(439,459)(440,462)(441,461)(442,460)(443,455)(444,458)(445,457)
(446,456)(447,463)(448,466)(449,465)(450,464);
s3 := Sym(482)!( 3,259)( 4,260)( 5,262)( 6,261)( 7,271)( 8,272)( 9,274)
( 10,273)( 11,267)( 12,268)( 13,270)( 14,269)( 15,263)( 16,264)( 17,266)
( 18,265)( 19,243)( 20,244)( 21,246)( 22,245)( 23,255)( 24,256)( 25,258)
( 26,257)( 27,251)( 28,252)( 29,254)( 30,253)( 31,247)( 32,248)( 33,250)
( 34,249)( 35,307)( 36,308)( 37,310)( 38,309)( 39,319)( 40,320)( 41,322)
( 42,321)( 43,315)( 44,316)( 45,318)( 46,317)( 47,311)( 48,312)( 49,314)
( 50,313)( 51,291)( 52,292)( 53,294)( 54,293)( 55,303)( 56,304)( 57,306)
( 58,305)( 59,299)( 60,300)( 61,302)( 62,301)( 63,295)( 64,296)( 65,298)
( 66,297)( 67,275)( 68,276)( 69,278)( 70,277)( 71,287)( 72,288)( 73,290)
( 74,289)( 75,283)( 76,284)( 77,286)( 78,285)( 79,279)( 80,280)( 81,282)
( 82,281)( 83,419)( 84,420)( 85,422)( 86,421)( 87,431)( 88,432)( 89,434)
( 90,433)( 91,427)( 92,428)( 93,430)( 94,429)( 95,423)( 96,424)( 97,426)
( 98,425)( 99,403)(100,404)(101,406)(102,405)(103,415)(104,416)(105,418)
(106,417)(107,411)(108,412)(109,414)(110,413)(111,407)(112,408)(113,410)
(114,409)(115,467)(116,468)(117,470)(118,469)(119,479)(120,480)(121,482)
(122,481)(123,475)(124,476)(125,478)(126,477)(127,471)(128,472)(129,474)
(130,473)(131,451)(132,452)(133,454)(134,453)(135,463)(136,464)(137,466)
(138,465)(139,459)(140,460)(141,462)(142,461)(143,455)(144,456)(145,458)
(146,457)(147,435)(148,436)(149,438)(150,437)(151,447)(152,448)(153,450)
(154,449)(155,443)(156,444)(157,446)(158,445)(159,439)(160,440)(161,442)
(162,441)(163,339)(164,340)(165,342)(166,341)(167,351)(168,352)(169,354)
(170,353)(171,347)(172,348)(173,350)(174,349)(175,343)(176,344)(177,346)
(178,345)(179,323)(180,324)(181,326)(182,325)(183,335)(184,336)(185,338)
(186,337)(187,331)(188,332)(189,334)(190,333)(191,327)(192,328)(193,330)
(194,329)(195,387)(196,388)(197,390)(198,389)(199,399)(200,400)(201,402)
(202,401)(203,395)(204,396)(205,398)(206,397)(207,391)(208,392)(209,394)
(210,393)(211,371)(212,372)(213,374)(214,373)(215,383)(216,384)(217,386)
(218,385)(219,379)(220,380)(221,382)(222,381)(223,375)(224,376)(225,378)
(226,377)(227,355)(228,356)(229,358)(230,357)(231,367)(232,368)(233,370)
(234,369)(235,363)(236,364)(237,366)(238,365)(239,359)(240,360)(241,362)
(242,361);
s4 := Sym(482)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)
(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)
(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)
(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)
(208,210)(211,213)(212,214)(215,217)(216,218)(219,221)(220,222)(223,225)
(224,226)(227,229)(228,230)(231,233)(232,234)(235,237)(236,238)(239,241)
(240,242)(243,245)(244,246)(247,249)(248,250)(251,253)(252,254)(255,257)
(256,258)(259,261)(260,262)(263,265)(264,266)(267,269)(268,270)(271,273)
(272,274)(275,277)(276,278)(279,281)(280,282)(283,285)(284,286)(287,289)
(288,290)(291,293)(292,294)(295,297)(296,298)(299,301)(300,302)(303,305)
(304,306)(307,309)(308,310)(311,313)(312,314)(315,317)(316,318)(319,321)
(320,322)(323,325)(324,326)(327,329)(328,330)(331,333)(332,334)(335,337)
(336,338)(339,341)(340,342)(343,345)(344,346)(347,349)(348,350)(351,353)
(352,354)(355,357)(356,358)(359,361)(360,362)(363,365)(364,366)(367,369)
(368,370)(371,373)(372,374)(375,377)(376,378)(379,381)(380,382)(383,385)
(384,386)(387,389)(388,390)(391,393)(392,394)(395,397)(396,398)(399,401)
(400,402)(403,405)(404,406)(407,409)(408,410)(411,413)(412,414)(415,417)
(416,418)(419,421)(420,422)(423,425)(424,426)(427,429)(428,430)(431,433)
(432,434)(435,437)(436,438)(439,441)(440,442)(443,445)(444,446)(447,449)
(448,450)(451,453)(452,454)(455,457)(456,458)(459,461)(460,462)(463,465)
(464,466)(467,469)(468,470)(471,473)(472,474)(475,477)(476,478)(479,481)
(480,482);
poly := sub<Sym(482)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
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,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1 >;
to this polytope