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