Polytope of Type {5,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,4,6}*1920
Also Known As : {{5,4|4},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {5,4,6}
Number of vertices, edges, etc : 40, 80, 96, 6
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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) :
3-fold quotients : {5,4,2}*640
6-fold quotients : {5,4,2}*320
16-fold quotients : {5,2,6}*120
32-fold quotients : {5,2,3}*60
48-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)( 26, 77)
( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)( 42, 61)
( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 83, 84)( 87, 88)
( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,145)( 98,146)( 99,148)(100,147)
(101,149)(102,150)(103,152)(104,151)(105,158)(106,157)(107,159)(108,160)
(109,154)(110,153)(111,155)(112,156)(113,129)(114,130)(115,132)(116,131)
(117,133)(118,134)(119,136)(120,135)(121,142)(122,141)(123,143)(124,144)
(125,138)(126,137)(127,139)(128,140)(163,164)(167,168)(169,174)(170,173)
(171,175)(172,176)(177,225)(178,226)(179,228)(180,227)(181,229)(182,230)
(183,232)(184,231)(185,238)(186,237)(187,239)(188,240)(189,234)(190,233)
(191,235)(192,236)(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)
(199,216)(200,215)(201,222)(202,221)(203,223)(204,224)(205,218)(206,217)
(207,219)(208,220)(243,244)(247,248)(249,254)(250,253)(251,255)(252,256)
(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)
(265,318)(266,317)(267,319)(268,320)(269,314)(270,313)(271,315)(272,316)
(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)
(281,302)(282,301)(283,303)(284,304)(285,298)(286,297)(287,299)(288,300)
(323,324)(327,328)(329,334)(330,333)(331,335)(332,336)(337,385)(338,386)
(339,388)(340,387)(341,389)(342,390)(343,392)(344,391)(345,398)(346,397)
(347,399)(348,400)(349,394)(350,393)(351,395)(352,396)(353,369)(354,370)
(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)(361,382)(362,381)
(363,383)(364,384)(365,378)(366,377)(367,379)(368,380)(403,404)(407,408)
(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)
(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)
(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)
(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)
(445,458)(446,457)(447,459)(448,460);;
s1 := ( 1, 17)( 2, 32)( 3, 22)( 4, 27)( 5, 30)( 6, 19)( 7, 25)( 8, 24)
( 9, 23)( 10, 26)( 11, 20)( 12, 29)( 13, 28)( 14, 21)( 15, 31)( 16, 18)
( 33, 65)( 34, 80)( 35, 70)( 36, 75)( 37, 78)( 38, 67)( 39, 73)( 40, 72)
( 41, 71)( 42, 74)( 43, 68)( 44, 77)( 45, 76)( 46, 69)( 47, 79)( 48, 66)
( 50, 64)( 51, 54)( 52, 59)( 53, 62)( 55, 57)( 60, 61)( 81, 97)( 82,112)
( 83,102)( 84,107)( 85,110)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,106)
( 91,100)( 92,109)( 93,108)( 94,101)( 95,111)( 96, 98)(113,145)(114,160)
(115,150)(116,155)(117,158)(118,147)(119,153)(120,152)(121,151)(122,154)
(123,148)(124,157)(125,156)(126,149)(127,159)(128,146)(130,144)(131,134)
(132,139)(133,142)(135,137)(140,141)(161,177)(162,192)(163,182)(164,187)
(165,190)(166,179)(167,185)(168,184)(169,183)(170,186)(171,180)(172,189)
(173,188)(174,181)(175,191)(176,178)(193,225)(194,240)(195,230)(196,235)
(197,238)(198,227)(199,233)(200,232)(201,231)(202,234)(203,228)(204,237)
(205,236)(206,229)(207,239)(208,226)(210,224)(211,214)(212,219)(213,222)
(215,217)(220,221)(241,257)(242,272)(243,262)(244,267)(245,270)(246,259)
(247,265)(248,264)(249,263)(250,266)(251,260)(252,269)(253,268)(254,261)
(255,271)(256,258)(273,305)(274,320)(275,310)(276,315)(277,318)(278,307)
(279,313)(280,312)(281,311)(282,314)(283,308)(284,317)(285,316)(286,309)
(287,319)(288,306)(290,304)(291,294)(292,299)(293,302)(295,297)(300,301)
(321,337)(322,352)(323,342)(324,347)(325,350)(326,339)(327,345)(328,344)
(329,343)(330,346)(331,340)(332,349)(333,348)(334,341)(335,351)(336,338)
(353,385)(354,400)(355,390)(356,395)(357,398)(358,387)(359,393)(360,392)
(361,391)(362,394)(363,388)(364,397)(365,396)(366,389)(367,399)(368,386)
(370,384)(371,374)(372,379)(373,382)(375,377)(380,381)(401,417)(402,432)
(403,422)(404,427)(405,430)(406,419)(407,425)(408,424)(409,423)(410,426)
(411,420)(412,429)(413,428)(414,421)(415,431)(416,418)(433,465)(434,480)
(435,470)(436,475)(437,478)(438,467)(439,473)(440,472)(441,471)(442,474)
(443,468)(444,477)(445,476)(446,469)(447,479)(448,466)(450,464)(451,454)
(452,459)(453,462)(455,457)(460,461);;
s2 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 13)( 10, 14)( 11, 15)( 12, 16)
( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)
( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)
( 81,165)( 82,166)( 83,167)( 84,168)( 85,161)( 86,162)( 87,163)( 88,164)
( 89,173)( 90,174)( 91,175)( 92,176)( 93,169)( 94,170)( 95,171)( 96,172)
( 97,181)( 98,182)( 99,183)(100,184)(101,177)(102,178)(103,179)(104,180)
(105,189)(106,190)(107,191)(108,192)(109,185)(110,186)(111,187)(112,188)
(113,197)(114,198)(115,199)(116,200)(117,193)(118,194)(119,195)(120,196)
(121,205)(122,206)(123,207)(124,208)(125,201)(126,202)(127,203)(128,204)
(129,213)(130,214)(131,215)(132,216)(133,209)(134,210)(135,211)(136,212)
(137,221)(138,222)(139,223)(140,224)(141,217)(142,218)(143,219)(144,220)
(145,229)(146,230)(147,231)(148,232)(149,225)(150,226)(151,227)(152,228)
(153,237)(154,238)(155,239)(156,240)(157,233)(158,234)(159,235)(160,236)
(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)
(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)
(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)
(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)
(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)
(321,405)(322,406)(323,407)(324,408)(325,401)(326,402)(327,403)(328,404)
(329,413)(330,414)(331,415)(332,416)(333,409)(334,410)(335,411)(336,412)
(337,421)(338,422)(339,423)(340,424)(341,417)(342,418)(343,419)(344,420)
(345,429)(346,430)(347,431)(348,432)(349,425)(350,426)(351,427)(352,428)
(353,437)(354,438)(355,439)(356,440)(357,433)(358,434)(359,435)(360,436)
(361,445)(362,446)(363,447)(364,448)(365,441)(366,442)(367,443)(368,444)
(369,453)(370,454)(371,455)(372,456)(373,449)(374,450)(375,451)(376,452)
(377,461)(378,462)(379,463)(380,464)(381,457)(382,458)(383,459)(384,460)
(385,469)(386,470)(387,471)(388,472)(389,465)(390,466)(391,467)(392,468)
(393,477)(394,478)(395,479)(396,480)(397,473)(398,474)(399,475)(400,476);;
s3 := ( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)( 8,328)
( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)( 16,336)
( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)( 24,344)
( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)( 32,352)
( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)( 40,360)
( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)( 48,368)
( 49,369)( 50,370)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)( 56,376)
( 57,377)( 58,378)( 59,379)( 60,380)( 61,381)( 62,382)( 63,383)( 64,384)
( 65,385)( 66,386)( 67,387)( 68,388)( 69,389)( 70,390)( 71,391)( 72,392)
( 73,393)( 74,394)( 75,395)( 76,396)( 77,397)( 78,398)( 79,399)( 80,400)
( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)
( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)( 96,256)
( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)(104,264)
(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)(112,272)
(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)
(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)(128,288)
(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)(136,296)
(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)(144,304)
(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)(152,312)
(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)(160,320)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 7, 8)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)
( 26, 77)( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)
( 42, 61)( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 83, 84)
( 87, 88)( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,145)( 98,146)( 99,148)
(100,147)(101,149)(102,150)(103,152)(104,151)(105,158)(106,157)(107,159)
(108,160)(109,154)(110,153)(111,155)(112,156)(113,129)(114,130)(115,132)
(116,131)(117,133)(118,134)(119,136)(120,135)(121,142)(122,141)(123,143)
(124,144)(125,138)(126,137)(127,139)(128,140)(163,164)(167,168)(169,174)
(170,173)(171,175)(172,176)(177,225)(178,226)(179,228)(180,227)(181,229)
(182,230)(183,232)(184,231)(185,238)(186,237)(187,239)(188,240)(189,234)
(190,233)(191,235)(192,236)(193,209)(194,210)(195,212)(196,211)(197,213)
(198,214)(199,216)(200,215)(201,222)(202,221)(203,223)(204,224)(205,218)
(206,217)(207,219)(208,220)(243,244)(247,248)(249,254)(250,253)(251,255)
(252,256)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)
(264,311)(265,318)(266,317)(267,319)(268,320)(269,314)(270,313)(271,315)
(272,316)(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)
(280,295)(281,302)(282,301)(283,303)(284,304)(285,298)(286,297)(287,299)
(288,300)(323,324)(327,328)(329,334)(330,333)(331,335)(332,336)(337,385)
(338,386)(339,388)(340,387)(341,389)(342,390)(343,392)(344,391)(345,398)
(346,397)(347,399)(348,400)(349,394)(350,393)(351,395)(352,396)(353,369)
(354,370)(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)(361,382)
(362,381)(363,383)(364,384)(365,378)(366,377)(367,379)(368,380)(403,404)
(407,408)(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)
(420,467)(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)
(428,480)(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)
(436,451)(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)
(444,464)(445,458)(446,457)(447,459)(448,460);
s1 := Sym(480)!( 1, 17)( 2, 32)( 3, 22)( 4, 27)( 5, 30)( 6, 19)( 7, 25)
( 8, 24)( 9, 23)( 10, 26)( 11, 20)( 12, 29)( 13, 28)( 14, 21)( 15, 31)
( 16, 18)( 33, 65)( 34, 80)( 35, 70)( 36, 75)( 37, 78)( 38, 67)( 39, 73)
( 40, 72)( 41, 71)( 42, 74)( 43, 68)( 44, 77)( 45, 76)( 46, 69)( 47, 79)
( 48, 66)( 50, 64)( 51, 54)( 52, 59)( 53, 62)( 55, 57)( 60, 61)( 81, 97)
( 82,112)( 83,102)( 84,107)( 85,110)( 86, 99)( 87,105)( 88,104)( 89,103)
( 90,106)( 91,100)( 92,109)( 93,108)( 94,101)( 95,111)( 96, 98)(113,145)
(114,160)(115,150)(116,155)(117,158)(118,147)(119,153)(120,152)(121,151)
(122,154)(123,148)(124,157)(125,156)(126,149)(127,159)(128,146)(130,144)
(131,134)(132,139)(133,142)(135,137)(140,141)(161,177)(162,192)(163,182)
(164,187)(165,190)(166,179)(167,185)(168,184)(169,183)(170,186)(171,180)
(172,189)(173,188)(174,181)(175,191)(176,178)(193,225)(194,240)(195,230)
(196,235)(197,238)(198,227)(199,233)(200,232)(201,231)(202,234)(203,228)
(204,237)(205,236)(206,229)(207,239)(208,226)(210,224)(211,214)(212,219)
(213,222)(215,217)(220,221)(241,257)(242,272)(243,262)(244,267)(245,270)
(246,259)(247,265)(248,264)(249,263)(250,266)(251,260)(252,269)(253,268)
(254,261)(255,271)(256,258)(273,305)(274,320)(275,310)(276,315)(277,318)
(278,307)(279,313)(280,312)(281,311)(282,314)(283,308)(284,317)(285,316)
(286,309)(287,319)(288,306)(290,304)(291,294)(292,299)(293,302)(295,297)
(300,301)(321,337)(322,352)(323,342)(324,347)(325,350)(326,339)(327,345)
(328,344)(329,343)(330,346)(331,340)(332,349)(333,348)(334,341)(335,351)
(336,338)(353,385)(354,400)(355,390)(356,395)(357,398)(358,387)(359,393)
(360,392)(361,391)(362,394)(363,388)(364,397)(365,396)(366,389)(367,399)
(368,386)(370,384)(371,374)(372,379)(373,382)(375,377)(380,381)(401,417)
(402,432)(403,422)(404,427)(405,430)(406,419)(407,425)(408,424)(409,423)
(410,426)(411,420)(412,429)(413,428)(414,421)(415,431)(416,418)(433,465)
(434,480)(435,470)(436,475)(437,478)(438,467)(439,473)(440,472)(441,471)
(442,474)(443,468)(444,477)(445,476)(446,469)(447,479)(448,466)(450,464)
(451,454)(452,459)(453,462)(455,457)(460,461);
s2 := Sym(480)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 13)( 10, 14)( 11, 15)
( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)
( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)
( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)
( 76, 80)( 81,165)( 82,166)( 83,167)( 84,168)( 85,161)( 86,162)( 87,163)
( 88,164)( 89,173)( 90,174)( 91,175)( 92,176)( 93,169)( 94,170)( 95,171)
( 96,172)( 97,181)( 98,182)( 99,183)(100,184)(101,177)(102,178)(103,179)
(104,180)(105,189)(106,190)(107,191)(108,192)(109,185)(110,186)(111,187)
(112,188)(113,197)(114,198)(115,199)(116,200)(117,193)(118,194)(119,195)
(120,196)(121,205)(122,206)(123,207)(124,208)(125,201)(126,202)(127,203)
(128,204)(129,213)(130,214)(131,215)(132,216)(133,209)(134,210)(135,211)
(136,212)(137,221)(138,222)(139,223)(140,224)(141,217)(142,218)(143,219)
(144,220)(145,229)(146,230)(147,231)(148,232)(149,225)(150,226)(151,227)
(152,228)(153,237)(154,238)(155,239)(156,240)(157,233)(158,234)(159,235)
(160,236)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)
(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)
(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)
(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)
(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)
(316,320)(321,405)(322,406)(323,407)(324,408)(325,401)(326,402)(327,403)
(328,404)(329,413)(330,414)(331,415)(332,416)(333,409)(334,410)(335,411)
(336,412)(337,421)(338,422)(339,423)(340,424)(341,417)(342,418)(343,419)
(344,420)(345,429)(346,430)(347,431)(348,432)(349,425)(350,426)(351,427)
(352,428)(353,437)(354,438)(355,439)(356,440)(357,433)(358,434)(359,435)
(360,436)(361,445)(362,446)(363,447)(364,448)(365,441)(366,442)(367,443)
(368,444)(369,453)(370,454)(371,455)(372,456)(373,449)(374,450)(375,451)
(376,452)(377,461)(378,462)(379,463)(380,464)(381,457)(382,458)(383,459)
(384,460)(385,469)(386,470)(387,471)(388,472)(389,465)(390,466)(391,467)
(392,468)(393,477)(394,478)(395,479)(396,480)(397,473)(398,474)(399,475)
(400,476);
s3 := Sym(480)!( 1,321)( 2,322)( 3,323)( 4,324)( 5,325)( 6,326)( 7,327)
( 8,328)( 9,329)( 10,330)( 11,331)( 12,332)( 13,333)( 14,334)( 15,335)
( 16,336)( 17,337)( 18,338)( 19,339)( 20,340)( 21,341)( 22,342)( 23,343)
( 24,344)( 25,345)( 26,346)( 27,347)( 28,348)( 29,349)( 30,350)( 31,351)
( 32,352)( 33,353)( 34,354)( 35,355)( 36,356)( 37,357)( 38,358)( 39,359)
( 40,360)( 41,361)( 42,362)( 43,363)( 44,364)( 45,365)( 46,366)( 47,367)
( 48,368)( 49,369)( 50,370)( 51,371)( 52,372)( 53,373)( 54,374)( 55,375)
( 56,376)( 57,377)( 58,378)( 59,379)( 60,380)( 61,381)( 62,382)( 63,383)
( 64,384)( 65,385)( 66,386)( 67,387)( 68,388)( 69,389)( 70,390)( 71,391)
( 72,392)( 73,393)( 74,394)( 75,395)( 76,396)( 77,397)( 78,398)( 79,399)
( 80,400)( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)
( 88,248)( 89,249)( 90,250)( 91,251)( 92,252)( 93,253)( 94,254)( 95,255)
( 96,256)( 97,257)( 98,258)( 99,259)(100,260)(101,261)(102,262)(103,263)
(104,264)(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,271)
(112,272)(113,273)(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)
(120,280)(121,281)(122,282)(123,283)(124,284)(125,285)(126,286)(127,287)
(128,288)(129,289)(130,290)(131,291)(132,292)(133,293)(134,294)(135,295)
(136,296)(137,297)(138,298)(139,299)(140,300)(141,301)(142,302)(143,303)
(144,304)(145,305)(146,306)(147,307)(148,308)(149,309)(150,310)(151,311)
(152,312)(153,313)(154,314)(155,315)(156,316)(157,317)(158,318)(159,319)
(160,320)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
to this polytope