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