Polytope of Type {4,10,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 4
Schlafli Type : {4,10,6}
Number of vertices, edges, etc : 16, 80, 120, 6
Order of s0s1s2s3 : 30
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) :
3-fold quotients : {4,10,2}*640a
6-fold quotients : {4,5,2}*320
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 := ( 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);;
s2 := ( 1, 49)( 2, 58)( 3, 59)( 4, 52)( 5, 56)( 6, 63)( 7, 62)( 8, 53)
( 9, 57)( 10, 50)( 11, 51)( 12, 60)( 13, 64)( 14, 55)( 15, 54)( 16, 61)
( 17, 33)( 18, 42)( 19, 43)( 20, 36)( 21, 40)( 22, 47)( 23, 46)( 24, 37)
( 25, 41)( 26, 34)( 27, 35)( 28, 44)( 29, 48)( 30, 39)( 31, 38)( 32, 45)
( 66, 74)( 67, 75)( 69, 72)( 70, 79)( 71, 78)( 77, 80)( 81,209)( 82,218)
( 83,219)( 84,212)( 85,216)( 86,223)( 87,222)( 88,213)( 89,217)( 90,210)
( 91,211)( 92,220)( 93,224)( 94,215)( 95,214)( 96,221)( 97,193)( 98,202)
( 99,203)(100,196)(101,200)(102,207)(103,206)(104,197)(105,201)(106,194)
(107,195)(108,204)(109,208)(110,199)(111,198)(112,205)(113,177)(114,186)
(115,187)(116,180)(117,184)(118,191)(119,190)(120,181)(121,185)(122,178)
(123,179)(124,188)(125,192)(126,183)(127,182)(128,189)(129,161)(130,170)
(131,171)(132,164)(133,168)(134,175)(135,174)(136,165)(137,169)(138,162)
(139,163)(140,172)(141,176)(142,167)(143,166)(144,173)(145,225)(146,234)
(147,235)(148,228)(149,232)(150,239)(151,238)(152,229)(153,233)(154,226)
(155,227)(156,236)(157,240)(158,231)(159,230)(160,237)(241,289)(242,298)
(243,299)(244,292)(245,296)(246,303)(247,302)(248,293)(249,297)(250,290)
(251,291)(252,300)(253,304)(254,295)(255,294)(256,301)(257,273)(258,282)
(259,283)(260,276)(261,280)(262,287)(263,286)(264,277)(265,281)(266,274)
(267,275)(268,284)(269,288)(270,279)(271,278)(272,285)(306,314)(307,315)
(309,312)(310,319)(311,318)(317,320)(321,449)(322,458)(323,459)(324,452)
(325,456)(326,463)(327,462)(328,453)(329,457)(330,450)(331,451)(332,460)
(333,464)(334,455)(335,454)(336,461)(337,433)(338,442)(339,443)(340,436)
(341,440)(342,447)(343,446)(344,437)(345,441)(346,434)(347,435)(348,444)
(349,448)(350,439)(351,438)(352,445)(353,417)(354,426)(355,427)(356,420)
(357,424)(358,431)(359,430)(360,421)(361,425)(362,418)(363,419)(364,428)
(365,432)(366,423)(367,422)(368,429)(369,401)(370,410)(371,411)(372,404)
(373,408)(374,415)(375,414)(376,405)(377,409)(378,402)(379,403)(380,412)
(381,416)(382,407)(383,406)(384,413)(385,465)(386,474)(387,475)(388,468)
(389,472)(390,479)(391,478)(392,469)(393,473)(394,466)(395,467)(396,476)
(397,480)(398,471)(399,470)(400,477);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, 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,
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*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)!( 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(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);
s2 := Sym(480)!( 1, 49)( 2, 58)( 3, 59)( 4, 52)( 5, 56)( 6, 63)( 7, 62)
( 8, 53)( 9, 57)( 10, 50)( 11, 51)( 12, 60)( 13, 64)( 14, 55)( 15, 54)
( 16, 61)( 17, 33)( 18, 42)( 19, 43)( 20, 36)( 21, 40)( 22, 47)( 23, 46)
( 24, 37)( 25, 41)( 26, 34)( 27, 35)( 28, 44)( 29, 48)( 30, 39)( 31, 38)
( 32, 45)( 66, 74)( 67, 75)( 69, 72)( 70, 79)( 71, 78)( 77, 80)( 81,209)
( 82,218)( 83,219)( 84,212)( 85,216)( 86,223)( 87,222)( 88,213)( 89,217)
( 90,210)( 91,211)( 92,220)( 93,224)( 94,215)( 95,214)( 96,221)( 97,193)
( 98,202)( 99,203)(100,196)(101,200)(102,207)(103,206)(104,197)(105,201)
(106,194)(107,195)(108,204)(109,208)(110,199)(111,198)(112,205)(113,177)
(114,186)(115,187)(116,180)(117,184)(118,191)(119,190)(120,181)(121,185)
(122,178)(123,179)(124,188)(125,192)(126,183)(127,182)(128,189)(129,161)
(130,170)(131,171)(132,164)(133,168)(134,175)(135,174)(136,165)(137,169)
(138,162)(139,163)(140,172)(141,176)(142,167)(143,166)(144,173)(145,225)
(146,234)(147,235)(148,228)(149,232)(150,239)(151,238)(152,229)(153,233)
(154,226)(155,227)(156,236)(157,240)(158,231)(159,230)(160,237)(241,289)
(242,298)(243,299)(244,292)(245,296)(246,303)(247,302)(248,293)(249,297)
(250,290)(251,291)(252,300)(253,304)(254,295)(255,294)(256,301)(257,273)
(258,282)(259,283)(260,276)(261,280)(262,287)(263,286)(264,277)(265,281)
(266,274)(267,275)(268,284)(269,288)(270,279)(271,278)(272,285)(306,314)
(307,315)(309,312)(310,319)(311,318)(317,320)(321,449)(322,458)(323,459)
(324,452)(325,456)(326,463)(327,462)(328,453)(329,457)(330,450)(331,451)
(332,460)(333,464)(334,455)(335,454)(336,461)(337,433)(338,442)(339,443)
(340,436)(341,440)(342,447)(343,446)(344,437)(345,441)(346,434)(347,435)
(348,444)(349,448)(350,439)(351,438)(352,445)(353,417)(354,426)(355,427)
(356,420)(357,424)(358,431)(359,430)(360,421)(361,425)(362,418)(363,419)
(364,428)(365,432)(366,423)(367,422)(368,429)(369,401)(370,410)(371,411)
(372,404)(373,408)(374,415)(375,414)(376,405)(377,409)(378,402)(379,403)
(380,412)(381,416)(382,407)(383,406)(384,413)(385,465)(386,474)(387,475)
(388,468)(389,472)(390,479)(391,478)(392,469)(393,473)(394,466)(395,467)
(396,476)(397,480)(398,471)(399,470)(400,477);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
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,
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*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