Polytope of Type {8,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 4
Schlafli Type : {8,30,4}
Number of vertices, edges, etc : 8, 120, 60, 4
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {4,30,4}*960b
4-fold quotients : {2,30,4}*480b
5-fold quotients : {8,6,4}*384b
8-fold quotients : {2,15,4}*240
10-fold quotients : {4,6,4}*192b
20-fold quotients : {2,6,4}*96c
40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)
(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)
(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)
(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)
(161,221)(162,222)(163,223)(164,224)(165,225)(166,226)(167,227)(168,228)
(169,229)(170,230)(171,231)(172,232)(173,233)(174,234)(175,235)(176,236)
(177,237)(178,238)(179,239)(180,240)(241,361)(242,362)(243,363)(244,364)
(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)
(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)
(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)
(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)
(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)(284,404)
(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)(292,412)
(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)(300,420)
(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)
(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)(316,436)
(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)
(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)
(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)
(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)(348,468)
(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)(356,476)
(357,477)(358,478)(359,479)(360,480);;
s1 := ( 1,241)( 2,242)( 3,244)( 4,243)( 5,257)( 6,258)( 7,260)( 8,259)
( 9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)( 16,251)
( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)( 24,283)
( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)( 32,295)
( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)( 40,287)
( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)( 48,279)
( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)( 56,271)
( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)( 64,303)
( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)( 72,315)
( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)( 80,307)
( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)( 88,359)
( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)( 96,351)
( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)(104,323)
(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)(112,335)
(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)(120,327)
(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)(128,439)
(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)(136,431)
(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)(144,463)
(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)(152,475)
(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)(160,467)
(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)(168,459)
(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)(176,451)
(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)(184,363)
(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)(192,375)
(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)(200,367)
(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)(208,419)
(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)(216,411)
(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)(224,383)
(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)(232,395)
(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)(240,387);;
s2 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)
(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)
(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)
(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)
(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)
(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)
(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)
(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)(244,266)
(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)(252,278)
(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)(260,270)
(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)(292,298)
(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)
(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)(343,347)
(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)(362,388)
(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)(370,400)
(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)(378,392)
(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)(410,420)
(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)(425,441)
(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)(433,453)
(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)(461,465)
(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)(474,476);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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(480)!(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)
(128,188)(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)
(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)
(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)
(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)
(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,226)(167,227)
(168,228)(169,229)(170,230)(171,231)(172,232)(173,233)(174,234)(175,235)
(176,236)(177,237)(178,238)(179,239)(180,240)(241,361)(242,362)(243,363)
(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)
(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)
(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)
(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)
(276,396)(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)
(284,404)(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)
(292,412)(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)
(300,420)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)
(308,428)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)
(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)
(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)
(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)
(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)
(348,468)(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)
(356,476)(357,477)(358,478)(359,479)(360,480);
s1 := Sym(480)!( 1,241)( 2,242)( 3,244)( 4,243)( 5,257)( 6,258)( 7,260)
( 8,259)( 9,253)( 10,254)( 11,256)( 12,255)( 13,249)( 14,250)( 15,252)
( 16,251)( 17,245)( 18,246)( 19,248)( 20,247)( 21,281)( 22,282)( 23,284)
( 24,283)( 25,297)( 26,298)( 27,300)( 28,299)( 29,293)( 30,294)( 31,296)
( 32,295)( 33,289)( 34,290)( 35,292)( 36,291)( 37,285)( 38,286)( 39,288)
( 40,287)( 41,261)( 42,262)( 43,264)( 44,263)( 45,277)( 46,278)( 47,280)
( 48,279)( 49,273)( 50,274)( 51,276)( 52,275)( 53,269)( 54,270)( 55,272)
( 56,271)( 57,265)( 58,266)( 59,268)( 60,267)( 61,301)( 62,302)( 63,304)
( 64,303)( 65,317)( 66,318)( 67,320)( 68,319)( 69,313)( 70,314)( 71,316)
( 72,315)( 73,309)( 74,310)( 75,312)( 76,311)( 77,305)( 78,306)( 79,308)
( 80,307)( 81,341)( 82,342)( 83,344)( 84,343)( 85,357)( 86,358)( 87,360)
( 88,359)( 89,353)( 90,354)( 91,356)( 92,355)( 93,349)( 94,350)( 95,352)
( 96,351)( 97,345)( 98,346)( 99,348)(100,347)(101,321)(102,322)(103,324)
(104,323)(105,337)(106,338)(107,340)(108,339)(109,333)(110,334)(111,336)
(112,335)(113,329)(114,330)(115,332)(116,331)(117,325)(118,326)(119,328)
(120,327)(121,421)(122,422)(123,424)(124,423)(125,437)(126,438)(127,440)
(128,439)(129,433)(130,434)(131,436)(132,435)(133,429)(134,430)(135,432)
(136,431)(137,425)(138,426)(139,428)(140,427)(141,461)(142,462)(143,464)
(144,463)(145,477)(146,478)(147,480)(148,479)(149,473)(150,474)(151,476)
(152,475)(153,469)(154,470)(155,472)(156,471)(157,465)(158,466)(159,468)
(160,467)(161,441)(162,442)(163,444)(164,443)(165,457)(166,458)(167,460)
(168,459)(169,453)(170,454)(171,456)(172,455)(173,449)(174,450)(175,452)
(176,451)(177,445)(178,446)(179,448)(180,447)(181,361)(182,362)(183,364)
(184,363)(185,377)(186,378)(187,380)(188,379)(189,373)(190,374)(191,376)
(192,375)(193,369)(194,370)(195,372)(196,371)(197,365)(198,366)(199,368)
(200,367)(201,401)(202,402)(203,404)(204,403)(205,417)(206,418)(207,420)
(208,419)(209,413)(210,414)(211,416)(212,415)(213,409)(214,410)(215,412)
(216,411)(217,405)(218,406)(219,408)(220,407)(221,381)(222,382)(223,384)
(224,383)(225,397)(226,398)(227,400)(228,399)(229,393)(230,394)(231,396)
(232,395)(233,389)(234,390)(235,392)(236,391)(237,385)(238,386)(239,388)
(240,387);
s2 := Sym(480)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)
(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)
(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)
(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)
(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)
(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)
(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)
(229,237)(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)
(244,266)(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)
(252,278)(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)
(260,270)(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)
(292,298)(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)
(307,323)(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)
(315,335)(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)
(343,347)(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)
(362,388)(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)
(370,400)(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)
(378,392)(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)
(410,420)(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)
(425,441)(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)
(433,453)(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)
(461,465)(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)
(474,476);
s3 := Sym(480)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480);
poly := sub<Sym(480)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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 >;
References : None.
to this polytope