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Polytope of Type {4,90}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,90}*1440
if this polytope has a name.
Group : SmallGroup(1440,4575)
Rank : 3
Schlafli Type : {4,90}
Number of vertices, edges, etc : 8, 360, 180
Order of s0s1s2 : 90
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,45}*720, {4,90}*720b, {4,90}*720c
   3-fold quotients : {4,30}*480
   4-fold quotients : {4,45}*360, {2,90}*360
   5-fold quotients : {4,18}*288
   6-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   8-fold quotients : {2,45}*180
   10-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {4,15}*120, {2,30}*120
   15-fold quotients : {4,6}*96
   20-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {2,15}*60
   30-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   36-fold quotients : {2,10}*40
   40-fold quotients : {2,9}*36
   60-fold quotients : {4,3}*24, {2,6}*24
   72-fold quotients : {2,5}*20
   120-fold quotients : {2,3}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,363)(  2,364)(  3,361)(  4,362)(  5,367)(  6,368)(  7,365)(  8,366)
(  9,371)( 10,372)( 11,369)( 12,370)( 13,375)( 14,376)( 15,373)( 16,374)
( 17,379)( 18,380)( 19,377)( 20,378)( 21,383)( 22,384)( 23,381)( 24,382)
( 25,387)( 26,388)( 27,385)( 28,386)( 29,391)( 30,392)( 31,389)( 32,390)
( 33,395)( 34,396)( 35,393)( 36,394)( 37,399)( 38,400)( 39,397)( 40,398)
( 41,403)( 42,404)( 43,401)( 44,402)( 45,407)( 46,408)( 47,405)( 48,406)
( 49,411)( 50,412)( 51,409)( 52,410)( 53,415)( 54,416)( 55,413)( 56,414)
( 57,419)( 58,420)( 59,417)( 60,418)( 61,423)( 62,424)( 63,421)( 64,422)
( 65,427)( 66,428)( 67,425)( 68,426)( 69,431)( 70,432)( 71,429)( 72,430)
( 73,435)( 74,436)( 75,433)( 76,434)( 77,439)( 78,440)( 79,437)( 80,438)
( 81,443)( 82,444)( 83,441)( 84,442)( 85,447)( 86,448)( 87,445)( 88,446)
( 89,451)( 90,452)( 91,449)( 92,450)( 93,455)( 94,456)( 95,453)( 96,454)
( 97,459)( 98,460)( 99,457)(100,458)(101,463)(102,464)(103,461)(104,462)
(105,467)(106,468)(107,465)(108,466)(109,471)(110,472)(111,469)(112,470)
(113,475)(114,476)(115,473)(116,474)(117,479)(118,480)(119,477)(120,478)
(121,483)(122,484)(123,481)(124,482)(125,487)(126,488)(127,485)(128,486)
(129,491)(130,492)(131,489)(132,490)(133,495)(134,496)(135,493)(136,494)
(137,499)(138,500)(139,497)(140,498)(141,503)(142,504)(143,501)(144,502)
(145,507)(146,508)(147,505)(148,506)(149,511)(150,512)(151,509)(152,510)
(153,515)(154,516)(155,513)(156,514)(157,519)(158,520)(159,517)(160,518)
(161,523)(162,524)(163,521)(164,522)(165,527)(166,528)(167,525)(168,526)
(169,531)(170,532)(171,529)(172,530)(173,535)(174,536)(175,533)(176,534)
(177,539)(178,540)(179,537)(180,538)(181,543)(182,544)(183,541)(184,542)
(185,547)(186,548)(187,545)(188,546)(189,551)(190,552)(191,549)(192,550)
(193,555)(194,556)(195,553)(196,554)(197,559)(198,560)(199,557)(200,558)
(201,563)(202,564)(203,561)(204,562)(205,567)(206,568)(207,565)(208,566)
(209,571)(210,572)(211,569)(212,570)(213,575)(214,576)(215,573)(216,574)
(217,579)(218,580)(219,577)(220,578)(221,583)(222,584)(223,581)(224,582)
(225,587)(226,588)(227,585)(228,586)(229,591)(230,592)(231,589)(232,590)
(233,595)(234,596)(235,593)(236,594)(237,599)(238,600)(239,597)(240,598)
(241,603)(242,604)(243,601)(244,602)(245,607)(246,608)(247,605)(248,606)
(249,611)(250,612)(251,609)(252,610)(253,615)(254,616)(255,613)(256,614)
(257,619)(258,620)(259,617)(260,618)(261,623)(262,624)(263,621)(264,622)
(265,627)(266,628)(267,625)(268,626)(269,631)(270,632)(271,629)(272,630)
(273,635)(274,636)(275,633)(276,634)(277,639)(278,640)(279,637)(280,638)
(281,643)(282,644)(283,641)(284,642)(285,647)(286,648)(287,645)(288,646)
(289,651)(290,652)(291,649)(292,650)(293,655)(294,656)(295,653)(296,654)
(297,659)(298,660)(299,657)(300,658)(301,663)(302,664)(303,661)(304,662)
(305,667)(306,668)(307,665)(308,666)(309,671)(310,672)(311,669)(312,670)
(313,675)(314,676)(315,673)(316,674)(317,679)(318,680)(319,677)(320,678)
(321,683)(322,684)(323,681)(324,682)(325,687)(326,688)(327,685)(328,686)
(329,691)(330,692)(331,689)(332,690)(333,695)(334,696)(335,693)(336,694)
(337,699)(338,700)(339,697)(340,698)(341,703)(342,704)(343,701)(344,702)
(345,707)(346,708)(347,705)(348,706)(349,711)(350,712)(351,709)(352,710)
(353,715)(354,716)(355,713)(356,714)(357,719)(358,720)(359,717)(360,718);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 49)( 14, 50)( 15, 52)
( 16, 51)( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)( 23, 56)
( 24, 55)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)
( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 61,129)( 62,130)( 63,132)
( 64,131)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)
( 72,123)( 73,177)( 74,178)( 75,180)( 76,179)( 77,173)( 78,174)( 79,176)
( 80,175)( 81,169)( 82,170)( 83,172)( 84,171)( 85,165)( 86,166)( 87,168)
( 88,167)( 89,161)( 90,162)( 91,164)( 92,163)( 93,157)( 94,158)( 95,160)
( 96,159)( 97,153)( 98,154)( 99,156)(100,155)(101,149)(102,150)(103,152)
(104,151)(105,145)(106,146)(107,148)(108,147)(109,141)(110,142)(111,144)
(112,143)(113,137)(114,138)(115,140)(116,139)(117,133)(118,134)(119,136)
(120,135)(183,184)(185,189)(186,190)(187,192)(188,191)(193,229)(194,230)
(195,232)(196,231)(197,237)(198,238)(199,240)(200,239)(201,233)(202,234)
(203,236)(204,235)(205,217)(206,218)(207,220)(208,219)(209,225)(210,226)
(211,228)(212,227)(213,221)(214,222)(215,224)(216,223)(241,309)(242,310)
(243,312)(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)(250,302)
(251,304)(252,303)(253,357)(254,358)(255,360)(256,359)(257,353)(258,354)
(259,356)(260,355)(261,349)(262,350)(263,352)(264,351)(265,345)(266,346)
(267,348)(268,347)(269,341)(270,342)(271,344)(272,343)(273,337)(274,338)
(275,340)(276,339)(277,333)(278,334)(279,336)(280,335)(281,329)(282,330)
(283,332)(284,331)(285,325)(286,326)(287,328)(288,327)(289,321)(290,322)
(291,324)(292,323)(293,317)(294,318)(295,320)(296,319)(297,313)(298,314)
(299,316)(300,315)(363,364)(365,369)(366,370)(367,372)(368,371)(373,409)
(374,410)(375,412)(376,411)(377,417)(378,418)(379,420)(380,419)(381,413)
(382,414)(383,416)(384,415)(385,397)(386,398)(387,400)(388,399)(389,405)
(390,406)(391,408)(392,407)(393,401)(394,402)(395,404)(396,403)(421,489)
(422,490)(423,492)(424,491)(425,485)(426,486)(427,488)(428,487)(429,481)
(430,482)(431,484)(432,483)(433,537)(434,538)(435,540)(436,539)(437,533)
(438,534)(439,536)(440,535)(441,529)(442,530)(443,532)(444,531)(445,525)
(446,526)(447,528)(448,527)(449,521)(450,522)(451,524)(452,523)(453,517)
(454,518)(455,520)(456,519)(457,513)(458,514)(459,516)(460,515)(461,509)
(462,510)(463,512)(464,511)(465,505)(466,506)(467,508)(468,507)(469,501)
(470,502)(471,504)(472,503)(473,497)(474,498)(475,500)(476,499)(477,493)
(478,494)(479,496)(480,495)(543,544)(545,549)(546,550)(547,552)(548,551)
(553,589)(554,590)(555,592)(556,591)(557,597)(558,598)(559,600)(560,599)
(561,593)(562,594)(563,596)(564,595)(565,577)(566,578)(567,580)(568,579)
(569,585)(570,586)(571,588)(572,587)(573,581)(574,582)(575,584)(576,583)
(601,669)(602,670)(603,672)(604,671)(605,665)(606,666)(607,668)(608,667)
(609,661)(610,662)(611,664)(612,663)(613,717)(614,718)(615,720)(616,719)
(617,713)(618,714)(619,716)(620,715)(621,709)(622,710)(623,712)(624,711)
(625,705)(626,706)(627,708)(628,707)(629,701)(630,702)(631,704)(632,703)
(633,697)(634,698)(635,700)(636,699)(637,693)(638,694)(639,696)(640,695)
(641,689)(642,690)(643,692)(644,691)(645,685)(646,686)(647,688)(648,687)
(649,681)(650,682)(651,684)(652,683)(653,677)(654,678)(655,680)(656,679)
(657,673)(658,674)(659,676)(660,675);;
s2 := (  1,253)(  2,256)(  3,255)(  4,254)(  5,261)(  6,264)(  7,263)(  8,262)
(  9,257)( 10,260)( 11,259)( 12,258)( 13,241)( 14,244)( 15,243)( 16,242)
( 17,249)( 18,252)( 19,251)( 20,250)( 21,245)( 22,248)( 23,247)( 24,246)
( 25,289)( 26,292)( 27,291)( 28,290)( 29,297)( 30,300)( 31,299)( 32,298)
( 33,293)( 34,296)( 35,295)( 36,294)( 37,277)( 38,280)( 39,279)( 40,278)
( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)
( 49,265)( 50,268)( 51,267)( 52,266)( 53,273)( 54,276)( 55,275)( 56,274)
( 57,269)( 58,272)( 59,271)( 60,270)( 61,193)( 62,196)( 63,195)( 64,194)
( 65,201)( 66,204)( 67,203)( 68,202)( 69,197)( 70,200)( 71,199)( 72,198)
( 73,181)( 74,184)( 75,183)( 76,182)( 77,189)( 78,192)( 79,191)( 80,190)
( 81,185)( 82,188)( 83,187)( 84,186)( 85,229)( 86,232)( 87,231)( 88,230)
( 89,237)( 90,240)( 91,239)( 92,238)( 93,233)( 94,236)( 95,235)( 96,234)
( 97,217)( 98,220)( 99,219)(100,218)(101,225)(102,228)(103,227)(104,226)
(105,221)(106,224)(107,223)(108,222)(109,205)(110,208)(111,207)(112,206)
(113,213)(114,216)(115,215)(116,214)(117,209)(118,212)(119,211)(120,210)
(121,321)(122,324)(123,323)(124,322)(125,317)(126,320)(127,319)(128,318)
(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)(136,310)
(137,305)(138,308)(139,307)(140,306)(141,301)(142,304)(143,303)(144,302)
(145,357)(146,360)(147,359)(148,358)(149,353)(150,356)(151,355)(152,354)
(153,349)(154,352)(155,351)(156,350)(157,345)(158,348)(159,347)(160,346)
(161,341)(162,344)(163,343)(164,342)(165,337)(166,340)(167,339)(168,338)
(169,333)(170,336)(171,335)(172,334)(173,329)(174,332)(175,331)(176,330)
(177,325)(178,328)(179,327)(180,326)(361,613)(362,616)(363,615)(364,614)
(365,621)(366,624)(367,623)(368,622)(369,617)(370,620)(371,619)(372,618)
(373,601)(374,604)(375,603)(376,602)(377,609)(378,612)(379,611)(380,610)
(381,605)(382,608)(383,607)(384,606)(385,649)(386,652)(387,651)(388,650)
(389,657)(390,660)(391,659)(392,658)(393,653)(394,656)(395,655)(396,654)
(397,637)(398,640)(399,639)(400,638)(401,645)(402,648)(403,647)(404,646)
(405,641)(406,644)(407,643)(408,642)(409,625)(410,628)(411,627)(412,626)
(413,633)(414,636)(415,635)(416,634)(417,629)(418,632)(419,631)(420,630)
(421,553)(422,556)(423,555)(424,554)(425,561)(426,564)(427,563)(428,562)
(429,557)(430,560)(431,559)(432,558)(433,541)(434,544)(435,543)(436,542)
(437,549)(438,552)(439,551)(440,550)(441,545)(442,548)(443,547)(444,546)
(445,589)(446,592)(447,591)(448,590)(449,597)(450,600)(451,599)(452,598)
(453,593)(454,596)(455,595)(456,594)(457,577)(458,580)(459,579)(460,578)
(461,585)(462,588)(463,587)(464,586)(465,581)(466,584)(467,583)(468,582)
(469,565)(470,568)(471,567)(472,566)(473,573)(474,576)(475,575)(476,574)
(477,569)(478,572)(479,571)(480,570)(481,681)(482,684)(483,683)(484,682)
(485,677)(486,680)(487,679)(488,678)(489,673)(490,676)(491,675)(492,674)
(493,669)(494,672)(495,671)(496,670)(497,665)(498,668)(499,667)(500,666)
(501,661)(502,664)(503,663)(504,662)(505,717)(506,720)(507,719)(508,718)
(509,713)(510,716)(511,715)(512,714)(513,709)(514,712)(515,711)(516,710)
(517,705)(518,708)(519,707)(520,706)(521,701)(522,704)(523,703)(524,702)
(525,697)(526,700)(527,699)(528,698)(529,693)(530,696)(531,695)(532,694)
(533,689)(534,692)(535,691)(536,690)(537,685)(538,688)(539,687)(540,686);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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*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(720)!(  1,363)(  2,364)(  3,361)(  4,362)(  5,367)(  6,368)(  7,365)
(  8,366)(  9,371)( 10,372)( 11,369)( 12,370)( 13,375)( 14,376)( 15,373)
( 16,374)( 17,379)( 18,380)( 19,377)( 20,378)( 21,383)( 22,384)( 23,381)
( 24,382)( 25,387)( 26,388)( 27,385)( 28,386)( 29,391)( 30,392)( 31,389)
( 32,390)( 33,395)( 34,396)( 35,393)( 36,394)( 37,399)( 38,400)( 39,397)
( 40,398)( 41,403)( 42,404)( 43,401)( 44,402)( 45,407)( 46,408)( 47,405)
( 48,406)( 49,411)( 50,412)( 51,409)( 52,410)( 53,415)( 54,416)( 55,413)
( 56,414)( 57,419)( 58,420)( 59,417)( 60,418)( 61,423)( 62,424)( 63,421)
( 64,422)( 65,427)( 66,428)( 67,425)( 68,426)( 69,431)( 70,432)( 71,429)
( 72,430)( 73,435)( 74,436)( 75,433)( 76,434)( 77,439)( 78,440)( 79,437)
( 80,438)( 81,443)( 82,444)( 83,441)( 84,442)( 85,447)( 86,448)( 87,445)
( 88,446)( 89,451)( 90,452)( 91,449)( 92,450)( 93,455)( 94,456)( 95,453)
( 96,454)( 97,459)( 98,460)( 99,457)(100,458)(101,463)(102,464)(103,461)
(104,462)(105,467)(106,468)(107,465)(108,466)(109,471)(110,472)(111,469)
(112,470)(113,475)(114,476)(115,473)(116,474)(117,479)(118,480)(119,477)
(120,478)(121,483)(122,484)(123,481)(124,482)(125,487)(126,488)(127,485)
(128,486)(129,491)(130,492)(131,489)(132,490)(133,495)(134,496)(135,493)
(136,494)(137,499)(138,500)(139,497)(140,498)(141,503)(142,504)(143,501)
(144,502)(145,507)(146,508)(147,505)(148,506)(149,511)(150,512)(151,509)
(152,510)(153,515)(154,516)(155,513)(156,514)(157,519)(158,520)(159,517)
(160,518)(161,523)(162,524)(163,521)(164,522)(165,527)(166,528)(167,525)
(168,526)(169,531)(170,532)(171,529)(172,530)(173,535)(174,536)(175,533)
(176,534)(177,539)(178,540)(179,537)(180,538)(181,543)(182,544)(183,541)
(184,542)(185,547)(186,548)(187,545)(188,546)(189,551)(190,552)(191,549)
(192,550)(193,555)(194,556)(195,553)(196,554)(197,559)(198,560)(199,557)
(200,558)(201,563)(202,564)(203,561)(204,562)(205,567)(206,568)(207,565)
(208,566)(209,571)(210,572)(211,569)(212,570)(213,575)(214,576)(215,573)
(216,574)(217,579)(218,580)(219,577)(220,578)(221,583)(222,584)(223,581)
(224,582)(225,587)(226,588)(227,585)(228,586)(229,591)(230,592)(231,589)
(232,590)(233,595)(234,596)(235,593)(236,594)(237,599)(238,600)(239,597)
(240,598)(241,603)(242,604)(243,601)(244,602)(245,607)(246,608)(247,605)
(248,606)(249,611)(250,612)(251,609)(252,610)(253,615)(254,616)(255,613)
(256,614)(257,619)(258,620)(259,617)(260,618)(261,623)(262,624)(263,621)
(264,622)(265,627)(266,628)(267,625)(268,626)(269,631)(270,632)(271,629)
(272,630)(273,635)(274,636)(275,633)(276,634)(277,639)(278,640)(279,637)
(280,638)(281,643)(282,644)(283,641)(284,642)(285,647)(286,648)(287,645)
(288,646)(289,651)(290,652)(291,649)(292,650)(293,655)(294,656)(295,653)
(296,654)(297,659)(298,660)(299,657)(300,658)(301,663)(302,664)(303,661)
(304,662)(305,667)(306,668)(307,665)(308,666)(309,671)(310,672)(311,669)
(312,670)(313,675)(314,676)(315,673)(316,674)(317,679)(318,680)(319,677)
(320,678)(321,683)(322,684)(323,681)(324,682)(325,687)(326,688)(327,685)
(328,686)(329,691)(330,692)(331,689)(332,690)(333,695)(334,696)(335,693)
(336,694)(337,699)(338,700)(339,697)(340,698)(341,703)(342,704)(343,701)
(344,702)(345,707)(346,708)(347,705)(348,706)(349,711)(350,712)(351,709)
(352,710)(353,715)(354,716)(355,713)(356,714)(357,719)(358,720)(359,717)
(360,718);
s1 := Sym(720)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 49)( 14, 50)
( 15, 52)( 16, 51)( 17, 57)( 18, 58)( 19, 60)( 20, 59)( 21, 53)( 22, 54)
( 23, 56)( 24, 55)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)
( 31, 48)( 32, 47)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 61,129)( 62,130)
( 63,132)( 64,131)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)
( 71,124)( 72,123)( 73,177)( 74,178)( 75,180)( 76,179)( 77,173)( 78,174)
( 79,176)( 80,175)( 81,169)( 82,170)( 83,172)( 84,171)( 85,165)( 86,166)
( 87,168)( 88,167)( 89,161)( 90,162)( 91,164)( 92,163)( 93,157)( 94,158)
( 95,160)( 96,159)( 97,153)( 98,154)( 99,156)(100,155)(101,149)(102,150)
(103,152)(104,151)(105,145)(106,146)(107,148)(108,147)(109,141)(110,142)
(111,144)(112,143)(113,137)(114,138)(115,140)(116,139)(117,133)(118,134)
(119,136)(120,135)(183,184)(185,189)(186,190)(187,192)(188,191)(193,229)
(194,230)(195,232)(196,231)(197,237)(198,238)(199,240)(200,239)(201,233)
(202,234)(203,236)(204,235)(205,217)(206,218)(207,220)(208,219)(209,225)
(210,226)(211,228)(212,227)(213,221)(214,222)(215,224)(216,223)(241,309)
(242,310)(243,312)(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)
(250,302)(251,304)(252,303)(253,357)(254,358)(255,360)(256,359)(257,353)
(258,354)(259,356)(260,355)(261,349)(262,350)(263,352)(264,351)(265,345)
(266,346)(267,348)(268,347)(269,341)(270,342)(271,344)(272,343)(273,337)
(274,338)(275,340)(276,339)(277,333)(278,334)(279,336)(280,335)(281,329)
(282,330)(283,332)(284,331)(285,325)(286,326)(287,328)(288,327)(289,321)
(290,322)(291,324)(292,323)(293,317)(294,318)(295,320)(296,319)(297,313)
(298,314)(299,316)(300,315)(363,364)(365,369)(366,370)(367,372)(368,371)
(373,409)(374,410)(375,412)(376,411)(377,417)(378,418)(379,420)(380,419)
(381,413)(382,414)(383,416)(384,415)(385,397)(386,398)(387,400)(388,399)
(389,405)(390,406)(391,408)(392,407)(393,401)(394,402)(395,404)(396,403)
(421,489)(422,490)(423,492)(424,491)(425,485)(426,486)(427,488)(428,487)
(429,481)(430,482)(431,484)(432,483)(433,537)(434,538)(435,540)(436,539)
(437,533)(438,534)(439,536)(440,535)(441,529)(442,530)(443,532)(444,531)
(445,525)(446,526)(447,528)(448,527)(449,521)(450,522)(451,524)(452,523)
(453,517)(454,518)(455,520)(456,519)(457,513)(458,514)(459,516)(460,515)
(461,509)(462,510)(463,512)(464,511)(465,505)(466,506)(467,508)(468,507)
(469,501)(470,502)(471,504)(472,503)(473,497)(474,498)(475,500)(476,499)
(477,493)(478,494)(479,496)(480,495)(543,544)(545,549)(546,550)(547,552)
(548,551)(553,589)(554,590)(555,592)(556,591)(557,597)(558,598)(559,600)
(560,599)(561,593)(562,594)(563,596)(564,595)(565,577)(566,578)(567,580)
(568,579)(569,585)(570,586)(571,588)(572,587)(573,581)(574,582)(575,584)
(576,583)(601,669)(602,670)(603,672)(604,671)(605,665)(606,666)(607,668)
(608,667)(609,661)(610,662)(611,664)(612,663)(613,717)(614,718)(615,720)
(616,719)(617,713)(618,714)(619,716)(620,715)(621,709)(622,710)(623,712)
(624,711)(625,705)(626,706)(627,708)(628,707)(629,701)(630,702)(631,704)
(632,703)(633,697)(634,698)(635,700)(636,699)(637,693)(638,694)(639,696)
(640,695)(641,689)(642,690)(643,692)(644,691)(645,685)(646,686)(647,688)
(648,687)(649,681)(650,682)(651,684)(652,683)(653,677)(654,678)(655,680)
(656,679)(657,673)(658,674)(659,676)(660,675);
s2 := Sym(720)!(  1,253)(  2,256)(  3,255)(  4,254)(  5,261)(  6,264)(  7,263)
(  8,262)(  9,257)( 10,260)( 11,259)( 12,258)( 13,241)( 14,244)( 15,243)
( 16,242)( 17,249)( 18,252)( 19,251)( 20,250)( 21,245)( 22,248)( 23,247)
( 24,246)( 25,289)( 26,292)( 27,291)( 28,290)( 29,297)( 30,300)( 31,299)
( 32,298)( 33,293)( 34,296)( 35,295)( 36,294)( 37,277)( 38,280)( 39,279)
( 40,278)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)
( 48,282)( 49,265)( 50,268)( 51,267)( 52,266)( 53,273)( 54,276)( 55,275)
( 56,274)( 57,269)( 58,272)( 59,271)( 60,270)( 61,193)( 62,196)( 63,195)
( 64,194)( 65,201)( 66,204)( 67,203)( 68,202)( 69,197)( 70,200)( 71,199)
( 72,198)( 73,181)( 74,184)( 75,183)( 76,182)( 77,189)( 78,192)( 79,191)
( 80,190)( 81,185)( 82,188)( 83,187)( 84,186)( 85,229)( 86,232)( 87,231)
( 88,230)( 89,237)( 90,240)( 91,239)( 92,238)( 93,233)( 94,236)( 95,235)
( 96,234)( 97,217)( 98,220)( 99,219)(100,218)(101,225)(102,228)(103,227)
(104,226)(105,221)(106,224)(107,223)(108,222)(109,205)(110,208)(111,207)
(112,206)(113,213)(114,216)(115,215)(116,214)(117,209)(118,212)(119,211)
(120,210)(121,321)(122,324)(123,323)(124,322)(125,317)(126,320)(127,319)
(128,318)(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)
(136,310)(137,305)(138,308)(139,307)(140,306)(141,301)(142,304)(143,303)
(144,302)(145,357)(146,360)(147,359)(148,358)(149,353)(150,356)(151,355)
(152,354)(153,349)(154,352)(155,351)(156,350)(157,345)(158,348)(159,347)
(160,346)(161,341)(162,344)(163,343)(164,342)(165,337)(166,340)(167,339)
(168,338)(169,333)(170,336)(171,335)(172,334)(173,329)(174,332)(175,331)
(176,330)(177,325)(178,328)(179,327)(180,326)(361,613)(362,616)(363,615)
(364,614)(365,621)(366,624)(367,623)(368,622)(369,617)(370,620)(371,619)
(372,618)(373,601)(374,604)(375,603)(376,602)(377,609)(378,612)(379,611)
(380,610)(381,605)(382,608)(383,607)(384,606)(385,649)(386,652)(387,651)
(388,650)(389,657)(390,660)(391,659)(392,658)(393,653)(394,656)(395,655)
(396,654)(397,637)(398,640)(399,639)(400,638)(401,645)(402,648)(403,647)
(404,646)(405,641)(406,644)(407,643)(408,642)(409,625)(410,628)(411,627)
(412,626)(413,633)(414,636)(415,635)(416,634)(417,629)(418,632)(419,631)
(420,630)(421,553)(422,556)(423,555)(424,554)(425,561)(426,564)(427,563)
(428,562)(429,557)(430,560)(431,559)(432,558)(433,541)(434,544)(435,543)
(436,542)(437,549)(438,552)(439,551)(440,550)(441,545)(442,548)(443,547)
(444,546)(445,589)(446,592)(447,591)(448,590)(449,597)(450,600)(451,599)
(452,598)(453,593)(454,596)(455,595)(456,594)(457,577)(458,580)(459,579)
(460,578)(461,585)(462,588)(463,587)(464,586)(465,581)(466,584)(467,583)
(468,582)(469,565)(470,568)(471,567)(472,566)(473,573)(474,576)(475,575)
(476,574)(477,569)(478,572)(479,571)(480,570)(481,681)(482,684)(483,683)
(484,682)(485,677)(486,680)(487,679)(488,678)(489,673)(490,676)(491,675)
(492,674)(493,669)(494,672)(495,671)(496,670)(497,665)(498,668)(499,667)
(500,666)(501,661)(502,664)(503,663)(504,662)(505,717)(506,720)(507,719)
(508,718)(509,713)(510,716)(511,715)(512,714)(513,709)(514,712)(515,711)
(516,710)(517,705)(518,708)(519,707)(520,706)(521,701)(522,704)(523,703)
(524,702)(525,697)(526,700)(527,699)(528,698)(529,693)(530,696)(531,695)
(532,694)(533,689)(534,692)(535,691)(536,690)(537,685)(538,688)(539,687)
(540,686);
poly := sub<Sym(720)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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*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