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Polytope of Type {8,45}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,45}*1440
if this polytope has a name.
Group : SmallGroup(1440,1528)
Rank : 3
Schlafli Type : {8,45}
Number of vertices, edges, etc : 16, 360, 90
Order of s0s1s2 : 180
Order of s0s1s2s1 : 8
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
   3-fold quotients : {8,15}*480
   4-fold quotients : {4,45}*360
   5-fold quotients : {8,9}*288
   6-fold quotients : {4,15}*240
   8-fold quotients : {2,45}*180
   10-fold quotients : {4,9}*144
   12-fold quotients : {4,15}*120
   15-fold quotients : {8,3}*96
   20-fold quotients : {4,9}*72
   24-fold quotients : {2,15}*60
   30-fold quotients : {4,3}*48
   40-fold quotients : {2,9}*36
   60-fold quotients : {4,3}*24
   72-fold quotients : {2,5}*20
   120-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,365)(  2,366)(  3,368)(  4,367)(  5,362)(  6,361)(  7,363)(  8,364)
(  9,373)( 10,374)( 11,376)( 12,375)( 13,370)( 14,369)( 15,371)( 16,372)
( 17,381)( 18,382)( 19,384)( 20,383)( 21,378)( 22,377)( 23,379)( 24,380)
( 25,389)( 26,390)( 27,392)( 28,391)( 29,386)( 30,385)( 31,387)( 32,388)
( 33,397)( 34,398)( 35,400)( 36,399)( 37,394)( 38,393)( 39,395)( 40,396)
( 41,405)( 42,406)( 43,408)( 44,407)( 45,402)( 46,401)( 47,403)( 48,404)
( 49,413)( 50,414)( 51,416)( 52,415)( 53,410)( 54,409)( 55,411)( 56,412)
( 57,421)( 58,422)( 59,424)( 60,423)( 61,418)( 62,417)( 63,419)( 64,420)
( 65,429)( 66,430)( 67,432)( 68,431)( 69,426)( 70,425)( 71,427)( 72,428)
( 73,437)( 74,438)( 75,440)( 76,439)( 77,434)( 78,433)( 79,435)( 80,436)
( 81,445)( 82,446)( 83,448)( 84,447)( 85,442)( 86,441)( 87,443)( 88,444)
( 89,453)( 90,454)( 91,456)( 92,455)( 93,450)( 94,449)( 95,451)( 96,452)
( 97,461)( 98,462)( 99,464)(100,463)(101,458)(102,457)(103,459)(104,460)
(105,469)(106,470)(107,472)(108,471)(109,466)(110,465)(111,467)(112,468)
(113,477)(114,478)(115,480)(116,479)(117,474)(118,473)(119,475)(120,476)
(121,485)(122,486)(123,488)(124,487)(125,482)(126,481)(127,483)(128,484)
(129,493)(130,494)(131,496)(132,495)(133,490)(134,489)(135,491)(136,492)
(137,501)(138,502)(139,504)(140,503)(141,498)(142,497)(143,499)(144,500)
(145,509)(146,510)(147,512)(148,511)(149,506)(150,505)(151,507)(152,508)
(153,517)(154,518)(155,520)(156,519)(157,514)(158,513)(159,515)(160,516)
(161,525)(162,526)(163,528)(164,527)(165,522)(166,521)(167,523)(168,524)
(169,533)(170,534)(171,536)(172,535)(173,530)(174,529)(175,531)(176,532)
(177,541)(178,542)(179,544)(180,543)(181,538)(182,537)(183,539)(184,540)
(185,549)(186,550)(187,552)(188,551)(189,546)(190,545)(191,547)(192,548)
(193,557)(194,558)(195,560)(196,559)(197,554)(198,553)(199,555)(200,556)
(201,565)(202,566)(203,568)(204,567)(205,562)(206,561)(207,563)(208,564)
(209,573)(210,574)(211,576)(212,575)(213,570)(214,569)(215,571)(216,572)
(217,581)(218,582)(219,584)(220,583)(221,578)(222,577)(223,579)(224,580)
(225,589)(226,590)(227,592)(228,591)(229,586)(230,585)(231,587)(232,588)
(233,597)(234,598)(235,600)(236,599)(237,594)(238,593)(239,595)(240,596)
(241,605)(242,606)(243,608)(244,607)(245,602)(246,601)(247,603)(248,604)
(249,613)(250,614)(251,616)(252,615)(253,610)(254,609)(255,611)(256,612)
(257,621)(258,622)(259,624)(260,623)(261,618)(262,617)(263,619)(264,620)
(265,629)(266,630)(267,632)(268,631)(269,626)(270,625)(271,627)(272,628)
(273,637)(274,638)(275,640)(276,639)(277,634)(278,633)(279,635)(280,636)
(281,645)(282,646)(283,648)(284,647)(285,642)(286,641)(287,643)(288,644)
(289,653)(290,654)(291,656)(292,655)(293,650)(294,649)(295,651)(296,652)
(297,661)(298,662)(299,664)(300,663)(301,658)(302,657)(303,659)(304,660)
(305,669)(306,670)(307,672)(308,671)(309,666)(310,665)(311,667)(312,668)
(313,677)(314,678)(315,680)(316,679)(317,674)(318,673)(319,675)(320,676)
(321,685)(322,686)(323,688)(324,687)(325,682)(326,681)(327,683)(328,684)
(329,693)(330,694)(331,696)(332,695)(333,690)(334,689)(335,691)(336,692)
(337,701)(338,702)(339,704)(340,703)(341,698)(342,697)(343,699)(344,700)
(345,709)(346,710)(347,712)(348,711)(349,706)(350,705)(351,707)(352,708)
(353,717)(354,718)(355,720)(356,719)(357,714)(358,713)(359,715)(360,716);;
s1 := (  3,  4)(  5,  7)(  6,  8)(  9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,103)
( 30,104)( 31,101)( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)( 37,119)
( 38,120)( 39,117)( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)( 45,111)
( 46,112)( 47,109)( 48,110)( 49, 73)( 50, 74)( 51, 76)( 52, 75)( 53, 79)
( 54, 80)( 55, 77)( 56, 78)( 57, 89)( 58, 90)( 59, 92)( 60, 91)( 61, 95)
( 62, 96)( 63, 93)( 64, 94)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 87)
( 70, 88)( 71, 85)( 72, 86)(121,257)(122,258)(123,260)(124,259)(125,263)
(126,264)(127,261)(128,262)(129,249)(130,250)(131,252)(132,251)(133,255)
(134,256)(135,253)(136,254)(137,241)(138,242)(139,244)(140,243)(141,247)
(142,248)(143,245)(144,246)(145,353)(146,354)(147,356)(148,355)(149,359)
(150,360)(151,357)(152,358)(153,345)(154,346)(155,348)(156,347)(157,351)
(158,352)(159,349)(160,350)(161,337)(162,338)(163,340)(164,339)(165,343)
(166,344)(167,341)(168,342)(169,329)(170,330)(171,332)(172,331)(173,335)
(174,336)(175,333)(176,334)(177,321)(178,322)(179,324)(180,323)(181,327)
(182,328)(183,325)(184,326)(185,313)(186,314)(187,316)(188,315)(189,319)
(190,320)(191,317)(192,318)(193,305)(194,306)(195,308)(196,307)(197,311)
(198,312)(199,309)(200,310)(201,297)(202,298)(203,300)(204,299)(205,303)
(206,304)(207,301)(208,302)(209,289)(210,290)(211,292)(212,291)(213,295)
(214,296)(215,293)(216,294)(217,281)(218,282)(219,284)(220,283)(221,287)
(222,288)(223,285)(224,286)(225,273)(226,274)(227,276)(228,275)(229,279)
(230,280)(231,277)(232,278)(233,265)(234,266)(235,268)(236,267)(237,271)
(238,272)(239,269)(240,270)(361,362)(365,368)(366,367)(369,378)(370,377)
(371,379)(372,380)(373,384)(374,383)(375,382)(376,381)(385,458)(386,457)
(387,459)(388,460)(389,464)(390,463)(391,462)(392,461)(393,474)(394,473)
(395,475)(396,476)(397,480)(398,479)(399,478)(400,477)(401,466)(402,465)
(403,467)(404,468)(405,472)(406,471)(407,470)(408,469)(409,434)(410,433)
(411,435)(412,436)(413,440)(414,439)(415,438)(416,437)(417,450)(418,449)
(419,451)(420,452)(421,456)(422,455)(423,454)(424,453)(425,442)(426,441)
(427,443)(428,444)(429,448)(430,447)(431,446)(432,445)(481,618)(482,617)
(483,619)(484,620)(485,624)(486,623)(487,622)(488,621)(489,610)(490,609)
(491,611)(492,612)(493,616)(494,615)(495,614)(496,613)(497,602)(498,601)
(499,603)(500,604)(501,608)(502,607)(503,606)(504,605)(505,714)(506,713)
(507,715)(508,716)(509,720)(510,719)(511,718)(512,717)(513,706)(514,705)
(515,707)(516,708)(517,712)(518,711)(519,710)(520,709)(521,698)(522,697)
(523,699)(524,700)(525,704)(526,703)(527,702)(528,701)(529,690)(530,689)
(531,691)(532,692)(533,696)(534,695)(535,694)(536,693)(537,682)(538,681)
(539,683)(540,684)(541,688)(542,687)(543,686)(544,685)(545,674)(546,673)
(547,675)(548,676)(549,680)(550,679)(551,678)(552,677)(553,666)(554,665)
(555,667)(556,668)(557,672)(558,671)(559,670)(560,669)(561,658)(562,657)
(563,659)(564,660)(565,664)(566,663)(567,662)(568,661)(569,650)(570,649)
(571,651)(572,652)(573,656)(574,655)(575,654)(576,653)(577,642)(578,641)
(579,643)(580,644)(581,648)(582,647)(583,646)(584,645)(585,634)(586,633)
(587,635)(588,636)(589,640)(590,639)(591,638)(592,637)(593,626)(594,625)
(595,627)(596,628)(597,632)(598,631)(599,630)(600,629);;
s2 := (  1,145)(  2,146)(  3,151)(  4,152)(  5,150)(  6,149)(  7,147)(  8,148)
(  9,161)( 10,162)( 11,167)( 12,168)( 13,166)( 14,165)( 15,163)( 16,164)
( 17,153)( 18,154)( 19,159)( 20,160)( 21,158)( 22,157)( 23,155)( 24,156)
( 25,121)( 26,122)( 27,127)( 28,128)( 29,126)( 30,125)( 31,123)( 32,124)
( 33,137)( 34,138)( 35,143)( 36,144)( 37,142)( 38,141)( 39,139)( 40,140)
( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)( 48,132)
( 49,217)( 50,218)( 51,223)( 52,224)( 53,222)( 54,221)( 55,219)( 56,220)
( 57,233)( 58,234)( 59,239)( 60,240)( 61,238)( 62,237)( 63,235)( 64,236)
( 65,225)( 66,226)( 67,231)( 68,232)( 69,230)( 70,229)( 71,227)( 72,228)
( 73,193)( 74,194)( 75,199)( 76,200)( 77,198)( 78,197)( 79,195)( 80,196)
( 81,209)( 82,210)( 83,215)( 84,216)( 85,214)( 86,213)( 87,211)( 88,212)
( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)( 96,204)
( 97,169)( 98,170)( 99,175)(100,176)(101,174)(102,173)(103,171)(104,172)
(105,185)(106,186)(107,191)(108,192)(109,190)(110,189)(111,187)(112,188)
(113,177)(114,178)(115,183)(116,184)(117,182)(118,181)(119,179)(120,180)
(241,281)(242,282)(243,287)(244,288)(245,286)(246,285)(247,283)(248,284)
(249,273)(250,274)(251,279)(252,280)(253,278)(254,277)(255,275)(256,276)
(257,265)(258,266)(259,271)(260,272)(261,270)(262,269)(263,267)(264,268)
(289,353)(290,354)(291,359)(292,360)(293,358)(294,357)(295,355)(296,356)
(297,345)(298,346)(299,351)(300,352)(301,350)(302,349)(303,347)(304,348)
(305,337)(306,338)(307,343)(308,344)(309,342)(310,341)(311,339)(312,340)
(313,329)(314,330)(315,335)(316,336)(317,334)(318,333)(319,331)(320,332)
(323,327)(324,328)(325,326)(361,506)(362,505)(363,512)(364,511)(365,509)
(366,510)(367,508)(368,507)(369,522)(370,521)(371,528)(372,527)(373,525)
(374,526)(375,524)(376,523)(377,514)(378,513)(379,520)(380,519)(381,517)
(382,518)(383,516)(384,515)(385,482)(386,481)(387,488)(388,487)(389,485)
(390,486)(391,484)(392,483)(393,498)(394,497)(395,504)(396,503)(397,501)
(398,502)(399,500)(400,499)(401,490)(402,489)(403,496)(404,495)(405,493)
(406,494)(407,492)(408,491)(409,578)(410,577)(411,584)(412,583)(413,581)
(414,582)(415,580)(416,579)(417,594)(418,593)(419,600)(420,599)(421,597)
(422,598)(423,596)(424,595)(425,586)(426,585)(427,592)(428,591)(429,589)
(430,590)(431,588)(432,587)(433,554)(434,553)(435,560)(436,559)(437,557)
(438,558)(439,556)(440,555)(441,570)(442,569)(443,576)(444,575)(445,573)
(446,574)(447,572)(448,571)(449,562)(450,561)(451,568)(452,567)(453,565)
(454,566)(455,564)(456,563)(457,530)(458,529)(459,536)(460,535)(461,533)
(462,534)(463,532)(464,531)(465,546)(466,545)(467,552)(468,551)(469,549)
(470,550)(471,548)(472,547)(473,538)(474,537)(475,544)(476,543)(477,541)
(478,542)(479,540)(480,539)(601,642)(602,641)(603,648)(604,647)(605,645)
(606,646)(607,644)(608,643)(609,634)(610,633)(611,640)(612,639)(613,637)
(614,638)(615,636)(616,635)(617,626)(618,625)(619,632)(620,631)(621,629)
(622,630)(623,628)(624,627)(649,714)(650,713)(651,720)(652,719)(653,717)
(654,718)(655,716)(656,715)(657,706)(658,705)(659,712)(660,711)(661,709)
(662,710)(663,708)(664,707)(665,698)(666,697)(667,704)(668,703)(669,701)
(670,702)(671,700)(672,699)(673,690)(674,689)(675,696)(676,695)(677,693)
(678,694)(679,692)(680,691)(681,682)(683,688)(684,687);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*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)!(  1,365)(  2,366)(  3,368)(  4,367)(  5,362)(  6,361)(  7,363)
(  8,364)(  9,373)( 10,374)( 11,376)( 12,375)( 13,370)( 14,369)( 15,371)
( 16,372)( 17,381)( 18,382)( 19,384)( 20,383)( 21,378)( 22,377)( 23,379)
( 24,380)( 25,389)( 26,390)( 27,392)( 28,391)( 29,386)( 30,385)( 31,387)
( 32,388)( 33,397)( 34,398)( 35,400)( 36,399)( 37,394)( 38,393)( 39,395)
( 40,396)( 41,405)( 42,406)( 43,408)( 44,407)( 45,402)( 46,401)( 47,403)
( 48,404)( 49,413)( 50,414)( 51,416)( 52,415)( 53,410)( 54,409)( 55,411)
( 56,412)( 57,421)( 58,422)( 59,424)( 60,423)( 61,418)( 62,417)( 63,419)
( 64,420)( 65,429)( 66,430)( 67,432)( 68,431)( 69,426)( 70,425)( 71,427)
( 72,428)( 73,437)( 74,438)( 75,440)( 76,439)( 77,434)( 78,433)( 79,435)
( 80,436)( 81,445)( 82,446)( 83,448)( 84,447)( 85,442)( 86,441)( 87,443)
( 88,444)( 89,453)( 90,454)( 91,456)( 92,455)( 93,450)( 94,449)( 95,451)
( 96,452)( 97,461)( 98,462)( 99,464)(100,463)(101,458)(102,457)(103,459)
(104,460)(105,469)(106,470)(107,472)(108,471)(109,466)(110,465)(111,467)
(112,468)(113,477)(114,478)(115,480)(116,479)(117,474)(118,473)(119,475)
(120,476)(121,485)(122,486)(123,488)(124,487)(125,482)(126,481)(127,483)
(128,484)(129,493)(130,494)(131,496)(132,495)(133,490)(134,489)(135,491)
(136,492)(137,501)(138,502)(139,504)(140,503)(141,498)(142,497)(143,499)
(144,500)(145,509)(146,510)(147,512)(148,511)(149,506)(150,505)(151,507)
(152,508)(153,517)(154,518)(155,520)(156,519)(157,514)(158,513)(159,515)
(160,516)(161,525)(162,526)(163,528)(164,527)(165,522)(166,521)(167,523)
(168,524)(169,533)(170,534)(171,536)(172,535)(173,530)(174,529)(175,531)
(176,532)(177,541)(178,542)(179,544)(180,543)(181,538)(182,537)(183,539)
(184,540)(185,549)(186,550)(187,552)(188,551)(189,546)(190,545)(191,547)
(192,548)(193,557)(194,558)(195,560)(196,559)(197,554)(198,553)(199,555)
(200,556)(201,565)(202,566)(203,568)(204,567)(205,562)(206,561)(207,563)
(208,564)(209,573)(210,574)(211,576)(212,575)(213,570)(214,569)(215,571)
(216,572)(217,581)(218,582)(219,584)(220,583)(221,578)(222,577)(223,579)
(224,580)(225,589)(226,590)(227,592)(228,591)(229,586)(230,585)(231,587)
(232,588)(233,597)(234,598)(235,600)(236,599)(237,594)(238,593)(239,595)
(240,596)(241,605)(242,606)(243,608)(244,607)(245,602)(246,601)(247,603)
(248,604)(249,613)(250,614)(251,616)(252,615)(253,610)(254,609)(255,611)
(256,612)(257,621)(258,622)(259,624)(260,623)(261,618)(262,617)(263,619)
(264,620)(265,629)(266,630)(267,632)(268,631)(269,626)(270,625)(271,627)
(272,628)(273,637)(274,638)(275,640)(276,639)(277,634)(278,633)(279,635)
(280,636)(281,645)(282,646)(283,648)(284,647)(285,642)(286,641)(287,643)
(288,644)(289,653)(290,654)(291,656)(292,655)(293,650)(294,649)(295,651)
(296,652)(297,661)(298,662)(299,664)(300,663)(301,658)(302,657)(303,659)
(304,660)(305,669)(306,670)(307,672)(308,671)(309,666)(310,665)(311,667)
(312,668)(313,677)(314,678)(315,680)(316,679)(317,674)(318,673)(319,675)
(320,676)(321,685)(322,686)(323,688)(324,687)(325,682)(326,681)(327,683)
(328,684)(329,693)(330,694)(331,696)(332,695)(333,690)(334,689)(335,691)
(336,692)(337,701)(338,702)(339,704)(340,703)(341,698)(342,697)(343,699)
(344,700)(345,709)(346,710)(347,712)(348,711)(349,706)(350,705)(351,707)
(352,708)(353,717)(354,718)(355,720)(356,719)(357,714)(358,713)(359,715)
(360,716);
s1 := Sym(720)!(  3,  4)(  5,  7)(  6,  8)(  9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 97)( 26, 98)( 27,100)( 28, 99)
( 29,103)( 30,104)( 31,101)( 32,102)( 33,113)( 34,114)( 35,116)( 36,115)
( 37,119)( 38,120)( 39,117)( 40,118)( 41,105)( 42,106)( 43,108)( 44,107)
( 45,111)( 46,112)( 47,109)( 48,110)( 49, 73)( 50, 74)( 51, 76)( 52, 75)
( 53, 79)( 54, 80)( 55, 77)( 56, 78)( 57, 89)( 58, 90)( 59, 92)( 60, 91)
( 61, 95)( 62, 96)( 63, 93)( 64, 94)( 65, 81)( 66, 82)( 67, 84)( 68, 83)
( 69, 87)( 70, 88)( 71, 85)( 72, 86)(121,257)(122,258)(123,260)(124,259)
(125,263)(126,264)(127,261)(128,262)(129,249)(130,250)(131,252)(132,251)
(133,255)(134,256)(135,253)(136,254)(137,241)(138,242)(139,244)(140,243)
(141,247)(142,248)(143,245)(144,246)(145,353)(146,354)(147,356)(148,355)
(149,359)(150,360)(151,357)(152,358)(153,345)(154,346)(155,348)(156,347)
(157,351)(158,352)(159,349)(160,350)(161,337)(162,338)(163,340)(164,339)
(165,343)(166,344)(167,341)(168,342)(169,329)(170,330)(171,332)(172,331)
(173,335)(174,336)(175,333)(176,334)(177,321)(178,322)(179,324)(180,323)
(181,327)(182,328)(183,325)(184,326)(185,313)(186,314)(187,316)(188,315)
(189,319)(190,320)(191,317)(192,318)(193,305)(194,306)(195,308)(196,307)
(197,311)(198,312)(199,309)(200,310)(201,297)(202,298)(203,300)(204,299)
(205,303)(206,304)(207,301)(208,302)(209,289)(210,290)(211,292)(212,291)
(213,295)(214,296)(215,293)(216,294)(217,281)(218,282)(219,284)(220,283)
(221,287)(222,288)(223,285)(224,286)(225,273)(226,274)(227,276)(228,275)
(229,279)(230,280)(231,277)(232,278)(233,265)(234,266)(235,268)(236,267)
(237,271)(238,272)(239,269)(240,270)(361,362)(365,368)(366,367)(369,378)
(370,377)(371,379)(372,380)(373,384)(374,383)(375,382)(376,381)(385,458)
(386,457)(387,459)(388,460)(389,464)(390,463)(391,462)(392,461)(393,474)
(394,473)(395,475)(396,476)(397,480)(398,479)(399,478)(400,477)(401,466)
(402,465)(403,467)(404,468)(405,472)(406,471)(407,470)(408,469)(409,434)
(410,433)(411,435)(412,436)(413,440)(414,439)(415,438)(416,437)(417,450)
(418,449)(419,451)(420,452)(421,456)(422,455)(423,454)(424,453)(425,442)
(426,441)(427,443)(428,444)(429,448)(430,447)(431,446)(432,445)(481,618)
(482,617)(483,619)(484,620)(485,624)(486,623)(487,622)(488,621)(489,610)
(490,609)(491,611)(492,612)(493,616)(494,615)(495,614)(496,613)(497,602)
(498,601)(499,603)(500,604)(501,608)(502,607)(503,606)(504,605)(505,714)
(506,713)(507,715)(508,716)(509,720)(510,719)(511,718)(512,717)(513,706)
(514,705)(515,707)(516,708)(517,712)(518,711)(519,710)(520,709)(521,698)
(522,697)(523,699)(524,700)(525,704)(526,703)(527,702)(528,701)(529,690)
(530,689)(531,691)(532,692)(533,696)(534,695)(535,694)(536,693)(537,682)
(538,681)(539,683)(540,684)(541,688)(542,687)(543,686)(544,685)(545,674)
(546,673)(547,675)(548,676)(549,680)(550,679)(551,678)(552,677)(553,666)
(554,665)(555,667)(556,668)(557,672)(558,671)(559,670)(560,669)(561,658)
(562,657)(563,659)(564,660)(565,664)(566,663)(567,662)(568,661)(569,650)
(570,649)(571,651)(572,652)(573,656)(574,655)(575,654)(576,653)(577,642)
(578,641)(579,643)(580,644)(581,648)(582,647)(583,646)(584,645)(585,634)
(586,633)(587,635)(588,636)(589,640)(590,639)(591,638)(592,637)(593,626)
(594,625)(595,627)(596,628)(597,632)(598,631)(599,630)(600,629);
s2 := Sym(720)!(  1,145)(  2,146)(  3,151)(  4,152)(  5,150)(  6,149)(  7,147)
(  8,148)(  9,161)( 10,162)( 11,167)( 12,168)( 13,166)( 14,165)( 15,163)
( 16,164)( 17,153)( 18,154)( 19,159)( 20,160)( 21,158)( 22,157)( 23,155)
( 24,156)( 25,121)( 26,122)( 27,127)( 28,128)( 29,126)( 30,125)( 31,123)
( 32,124)( 33,137)( 34,138)( 35,143)( 36,144)( 37,142)( 38,141)( 39,139)
( 40,140)( 41,129)( 42,130)( 43,135)( 44,136)( 45,134)( 46,133)( 47,131)
( 48,132)( 49,217)( 50,218)( 51,223)( 52,224)( 53,222)( 54,221)( 55,219)
( 56,220)( 57,233)( 58,234)( 59,239)( 60,240)( 61,238)( 62,237)( 63,235)
( 64,236)( 65,225)( 66,226)( 67,231)( 68,232)( 69,230)( 70,229)( 71,227)
( 72,228)( 73,193)( 74,194)( 75,199)( 76,200)( 77,198)( 78,197)( 79,195)
( 80,196)( 81,209)( 82,210)( 83,215)( 84,216)( 85,214)( 86,213)( 87,211)
( 88,212)( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)
( 96,204)( 97,169)( 98,170)( 99,175)(100,176)(101,174)(102,173)(103,171)
(104,172)(105,185)(106,186)(107,191)(108,192)(109,190)(110,189)(111,187)
(112,188)(113,177)(114,178)(115,183)(116,184)(117,182)(118,181)(119,179)
(120,180)(241,281)(242,282)(243,287)(244,288)(245,286)(246,285)(247,283)
(248,284)(249,273)(250,274)(251,279)(252,280)(253,278)(254,277)(255,275)
(256,276)(257,265)(258,266)(259,271)(260,272)(261,270)(262,269)(263,267)
(264,268)(289,353)(290,354)(291,359)(292,360)(293,358)(294,357)(295,355)
(296,356)(297,345)(298,346)(299,351)(300,352)(301,350)(302,349)(303,347)
(304,348)(305,337)(306,338)(307,343)(308,344)(309,342)(310,341)(311,339)
(312,340)(313,329)(314,330)(315,335)(316,336)(317,334)(318,333)(319,331)
(320,332)(323,327)(324,328)(325,326)(361,506)(362,505)(363,512)(364,511)
(365,509)(366,510)(367,508)(368,507)(369,522)(370,521)(371,528)(372,527)
(373,525)(374,526)(375,524)(376,523)(377,514)(378,513)(379,520)(380,519)
(381,517)(382,518)(383,516)(384,515)(385,482)(386,481)(387,488)(388,487)
(389,485)(390,486)(391,484)(392,483)(393,498)(394,497)(395,504)(396,503)
(397,501)(398,502)(399,500)(400,499)(401,490)(402,489)(403,496)(404,495)
(405,493)(406,494)(407,492)(408,491)(409,578)(410,577)(411,584)(412,583)
(413,581)(414,582)(415,580)(416,579)(417,594)(418,593)(419,600)(420,599)
(421,597)(422,598)(423,596)(424,595)(425,586)(426,585)(427,592)(428,591)
(429,589)(430,590)(431,588)(432,587)(433,554)(434,553)(435,560)(436,559)
(437,557)(438,558)(439,556)(440,555)(441,570)(442,569)(443,576)(444,575)
(445,573)(446,574)(447,572)(448,571)(449,562)(450,561)(451,568)(452,567)
(453,565)(454,566)(455,564)(456,563)(457,530)(458,529)(459,536)(460,535)
(461,533)(462,534)(463,532)(464,531)(465,546)(466,545)(467,552)(468,551)
(469,549)(470,550)(471,548)(472,547)(473,538)(474,537)(475,544)(476,543)
(477,541)(478,542)(479,540)(480,539)(601,642)(602,641)(603,648)(604,647)
(605,645)(606,646)(607,644)(608,643)(609,634)(610,633)(611,640)(612,639)
(613,637)(614,638)(615,636)(616,635)(617,626)(618,625)(619,632)(620,631)
(621,629)(622,630)(623,628)(624,627)(649,714)(650,713)(651,720)(652,719)
(653,717)(654,718)(655,716)(656,715)(657,706)(658,705)(659,712)(660,711)
(661,709)(662,710)(663,708)(664,707)(665,698)(666,697)(667,704)(668,703)
(669,701)(670,702)(671,700)(672,699)(673,690)(674,689)(675,696)(676,695)
(677,693)(678,694)(679,692)(680,691)(681,682)(683,688)(684,687);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*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