Polytope of Type {720}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {720}*1440
Also Known As : 720-gon, {720}. if this polytope has another name.
Group : SmallGroup(1440,160)
Rank : 2
Schlafli Type : {720}
Number of vertices, edges, etc : 720, 720
Order of s₀s₁ : 720
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {360}*720
   3-fold quotients : {240}*480
   4-fold quotients : {180}*360
   5-fold quotients : {144}*288
   6-fold quotients : {120}*240
   8-fold quotients : {90}*180
   9-fold quotients : {80}*160
   10-fold quotients : {72}*144
   12-fold quotients : {60}*120
   15-fold quotients : {48}*96
   16-fold quotients : {45}*90
   18-fold quotients : {40}*80
   20-fold quotients : {36}*72
   24-fold quotients : {30}*60
   30-fold quotients : {24}*48
   36-fold quotients : {20}*40
   40-fold quotients : {18}*36
   45-fold quotients : {16}*32
   48-fold quotients : {15}*30
   60-fold quotients : {12}*24
   72-fold quotients : {10}*20
   80-fold quotients : {9}*18
   90-fold quotients : {8}*16
   120-fold quotients : {6}*12
   144-fold quotients : {5}*10
   180-fold quotients : {4}*8
   240-fold quotients : {3}*6
   360-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 13)(  5, 15)(  6, 14)(  7, 10)(  8, 12)(  9, 11)( 16, 33)
( 17, 32)( 18, 31)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)
( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 47, 48)( 49, 58)
( 50, 60)( 51, 59)( 52, 55)( 53, 57)( 54, 56)( 61, 78)( 62, 77)( 63, 76)
( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)
( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 91,136)( 92,138)( 93,137)( 94,148)
( 95,150)( 96,149)( 97,145)( 98,147)( 99,146)(100,142)(101,144)(102,143)
(103,139)(104,141)(105,140)(106,168)(107,167)(108,166)(109,180)(110,179)
(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)
(119,170)(120,169)(121,153)(122,152)(123,151)(124,165)(125,164)(126,163)
(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)
(135,154)(181,271)(182,273)(183,272)(184,283)(185,285)(186,284)(187,280)
(188,282)(189,281)(190,277)(191,279)(192,278)(193,274)(194,276)(195,275)
(196,303)(197,302)(198,301)(199,315)(200,314)(201,313)(202,312)(203,311)
(204,310)(205,309)(206,308)(207,307)(208,306)(209,305)(210,304)(211,288)
(212,287)(213,286)(214,300)(215,299)(216,298)(217,297)(218,296)(219,295)
(220,294)(221,293)(222,292)(223,291)(224,290)(225,289)(226,316)(227,318)
(228,317)(229,328)(230,330)(231,329)(232,325)(233,327)(234,326)(235,322)
(236,324)(237,323)(238,319)(239,321)(240,320)(241,348)(242,347)(243,346)
(244,360)(245,359)(246,358)(247,357)(248,356)(249,355)(250,354)(251,353)
(252,352)(253,351)(254,350)(255,349)(256,333)(257,332)(258,331)(259,345)
(260,344)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)(267,337)
(268,336)(269,335)(270,334)(361,541)(362,543)(363,542)(364,553)(365,555)
(366,554)(367,550)(368,552)(369,551)(370,547)(371,549)(372,548)(373,544)
(374,546)(375,545)(376,573)(377,572)(378,571)(379,585)(380,584)(381,583)
(382,582)(383,581)(384,580)(385,579)(386,578)(387,577)(388,576)(389,575)
(390,574)(391,558)(392,557)(393,556)(394,570)(395,569)(396,568)(397,567)
(398,566)(399,565)(400,564)(401,563)(402,562)(403,561)(404,560)(405,559)
(406,586)(407,588)(408,587)(409,598)(410,600)(411,599)(412,595)(413,597)
(414,596)(415,592)(416,594)(417,593)(418,589)(419,591)(420,590)(421,618)
(422,617)(423,616)(424,630)(425,629)(426,628)(427,627)(428,626)(429,625)
(430,624)(431,623)(432,622)(433,621)(434,620)(435,619)(436,603)(437,602)
(438,601)(439,615)(440,614)(441,613)(442,612)(443,611)(444,610)(445,609)
(446,608)(447,607)(448,606)(449,605)(450,604)(451,676)(452,678)(453,677)
(454,688)(455,690)(456,689)(457,685)(458,687)(459,686)(460,682)(461,684)
(462,683)(463,679)(464,681)(465,680)(466,708)(467,707)(468,706)(469,720)
(470,719)(471,718)(472,717)(473,716)(474,715)(475,714)(476,713)(477,712)
(478,711)(479,710)(480,709)(481,693)(482,692)(483,691)(484,705)(485,704)
(486,703)(487,702)(488,701)(489,700)(490,699)(491,698)(492,697)(493,696)
(494,695)(495,694)(496,631)(497,633)(498,632)(499,643)(500,645)(501,644)
(502,640)(503,642)(504,641)(505,637)(506,639)(507,638)(508,634)(509,636)
(510,635)(511,663)(512,662)(513,661)(514,675)(515,674)(516,673)(517,672)
(518,671)(519,670)(520,669)(521,668)(522,667)(523,666)(524,665)(525,664)
(526,648)(527,647)(528,646)(529,660)(530,659)(531,658)(532,657)(533,656)
(534,655)(535,654)(536,653)(537,652)(538,651)(539,650)(540,649);;
s1 := (  1,379)(  2,381)(  3,380)(  4,376)(  5,378)(  6,377)(  7,388)(  8,390)
(  9,389)( 10,385)( 11,387)( 12,386)( 13,382)( 14,384)( 15,383)( 16,364)
( 17,366)( 18,365)( 19,361)( 20,363)( 21,362)( 22,373)( 23,375)( 24,374)
( 25,370)( 26,372)( 27,371)( 28,367)( 29,369)( 30,368)( 31,396)( 32,395)
( 33,394)( 34,393)( 35,392)( 36,391)( 37,405)( 38,404)( 39,403)( 40,402)
( 41,401)( 42,400)( 43,399)( 44,398)( 45,397)( 46,424)( 47,426)( 48,425)
( 49,421)( 50,423)( 51,422)( 52,433)( 53,435)( 54,434)( 55,430)( 56,432)
( 57,431)( 58,427)( 59,429)( 60,428)( 61,409)( 62,411)( 63,410)( 64,406)
( 65,408)( 66,407)( 67,418)( 68,420)( 69,419)( 70,415)( 71,417)( 72,416)
( 73,412)( 74,414)( 75,413)( 76,441)( 77,440)( 78,439)( 79,438)( 80,437)
( 81,436)( 82,450)( 83,449)( 84,448)( 85,447)( 86,446)( 87,445)( 88,444)
( 89,443)( 90,442)( 91,514)( 92,516)( 93,515)( 94,511)( 95,513)( 96,512)
( 97,523)( 98,525)( 99,524)(100,520)(101,522)(102,521)(103,517)(104,519)
(105,518)(106,499)(107,501)(108,500)(109,496)(110,498)(111,497)(112,508)
(113,510)(114,509)(115,505)(116,507)(117,506)(118,502)(119,504)(120,503)
(121,531)(122,530)(123,529)(124,528)(125,527)(126,526)(127,540)(128,539)
(129,538)(130,537)(131,536)(132,535)(133,534)(134,533)(135,532)(136,469)
(137,471)(138,470)(139,466)(140,468)(141,467)(142,478)(143,480)(144,479)
(145,475)(146,477)(147,476)(148,472)(149,474)(150,473)(151,454)(152,456)
(153,455)(154,451)(155,453)(156,452)(157,463)(158,465)(159,464)(160,460)
(161,462)(162,461)(163,457)(164,459)(165,458)(166,486)(167,485)(168,484)
(169,483)(170,482)(171,481)(172,495)(173,494)(174,493)(175,492)(176,491)
(177,490)(178,489)(179,488)(180,487)(181,649)(182,651)(183,650)(184,646)
(185,648)(186,647)(187,658)(188,660)(189,659)(190,655)(191,657)(192,656)
(193,652)(194,654)(195,653)(196,634)(197,636)(198,635)(199,631)(200,633)
(201,632)(202,643)(203,645)(204,644)(205,640)(206,642)(207,641)(208,637)
(209,639)(210,638)(211,666)(212,665)(213,664)(214,663)(215,662)(216,661)
(217,675)(218,674)(219,673)(220,672)(221,671)(222,670)(223,669)(224,668)
(225,667)(226,694)(227,696)(228,695)(229,691)(230,693)(231,692)(232,703)
(233,705)(234,704)(235,700)(236,702)(237,701)(238,697)(239,699)(240,698)
(241,679)(242,681)(243,680)(244,676)(245,678)(246,677)(247,688)(248,690)
(249,689)(250,685)(251,687)(252,686)(253,682)(254,684)(255,683)(256,711)
(257,710)(258,709)(259,708)(260,707)(261,706)(262,720)(263,719)(264,718)
(265,717)(266,716)(267,715)(268,714)(269,713)(270,712)(271,559)(272,561)
(273,560)(274,556)(275,558)(276,557)(277,568)(278,570)(279,569)(280,565)
(281,567)(282,566)(283,562)(284,564)(285,563)(286,544)(287,546)(288,545)
(289,541)(290,543)(291,542)(292,553)(293,555)(294,554)(295,550)(296,552)
(297,551)(298,547)(299,549)(300,548)(301,576)(302,575)(303,574)(304,573)
(305,572)(306,571)(307,585)(308,584)(309,583)(310,582)(311,581)(312,580)
(313,579)(314,578)(315,577)(316,604)(317,606)(318,605)(319,601)(320,603)
(321,602)(322,613)(323,615)(324,614)(325,610)(326,612)(327,611)(328,607)
(329,609)(330,608)(331,589)(332,591)(333,590)(334,586)(335,588)(336,587)
(337,598)(338,600)(339,599)(340,595)(341,597)(342,596)(343,592)(344,594)
(345,593)(346,621)(347,620)(348,619)(349,618)(350,617)(351,616)(352,630)
(353,629)(354,628)(355,627)(356,626)(357,625)(358,624)(359,623)(360,622);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(720)!(  2,  3)(  4, 13)(  5, 15)(  6, 14)(  7, 10)(  8, 12)(  9, 11)
( 16, 33)( 17, 32)( 18, 31)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 47, 48)
( 49, 58)( 50, 60)( 51, 59)( 52, 55)( 53, 57)( 54, 56)( 61, 78)( 62, 77)
( 63, 76)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)
( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 91,136)( 92,138)( 93,137)
( 94,148)( 95,150)( 96,149)( 97,145)( 98,147)( 99,146)(100,142)(101,144)
(102,143)(103,139)(104,141)(105,140)(106,168)(107,167)(108,166)(109,180)
(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)(117,172)
(118,171)(119,170)(120,169)(121,153)(122,152)(123,151)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)
(134,155)(135,154)(181,271)(182,273)(183,272)(184,283)(185,285)(186,284)
(187,280)(188,282)(189,281)(190,277)(191,279)(192,278)(193,274)(194,276)
(195,275)(196,303)(197,302)(198,301)(199,315)(200,314)(201,313)(202,312)
(203,311)(204,310)(205,309)(206,308)(207,307)(208,306)(209,305)(210,304)
(211,288)(212,287)(213,286)(214,300)(215,299)(216,298)(217,297)(218,296)
(219,295)(220,294)(221,293)(222,292)(223,291)(224,290)(225,289)(226,316)
(227,318)(228,317)(229,328)(230,330)(231,329)(232,325)(233,327)(234,326)
(235,322)(236,324)(237,323)(238,319)(239,321)(240,320)(241,348)(242,347)
(243,346)(244,360)(245,359)(246,358)(247,357)(248,356)(249,355)(250,354)
(251,353)(252,352)(253,351)(254,350)(255,349)(256,333)(257,332)(258,331)
(259,345)(260,344)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)
(267,337)(268,336)(269,335)(270,334)(361,541)(362,543)(363,542)(364,553)
(365,555)(366,554)(367,550)(368,552)(369,551)(370,547)(371,549)(372,548)
(373,544)(374,546)(375,545)(376,573)(377,572)(378,571)(379,585)(380,584)
(381,583)(382,582)(383,581)(384,580)(385,579)(386,578)(387,577)(388,576)
(389,575)(390,574)(391,558)(392,557)(393,556)(394,570)(395,569)(396,568)
(397,567)(398,566)(399,565)(400,564)(401,563)(402,562)(403,561)(404,560)
(405,559)(406,586)(407,588)(408,587)(409,598)(410,600)(411,599)(412,595)
(413,597)(414,596)(415,592)(416,594)(417,593)(418,589)(419,591)(420,590)
(421,618)(422,617)(423,616)(424,630)(425,629)(426,628)(427,627)(428,626)
(429,625)(430,624)(431,623)(432,622)(433,621)(434,620)(435,619)(436,603)
(437,602)(438,601)(439,615)(440,614)(441,613)(442,612)(443,611)(444,610)
(445,609)(446,608)(447,607)(448,606)(449,605)(450,604)(451,676)(452,678)
(453,677)(454,688)(455,690)(456,689)(457,685)(458,687)(459,686)(460,682)
(461,684)(462,683)(463,679)(464,681)(465,680)(466,708)(467,707)(468,706)
(469,720)(470,719)(471,718)(472,717)(473,716)(474,715)(475,714)(476,713)
(477,712)(478,711)(479,710)(480,709)(481,693)(482,692)(483,691)(484,705)
(485,704)(486,703)(487,702)(488,701)(489,700)(490,699)(491,698)(492,697)
(493,696)(494,695)(495,694)(496,631)(497,633)(498,632)(499,643)(500,645)
(501,644)(502,640)(503,642)(504,641)(505,637)(506,639)(507,638)(508,634)
(509,636)(510,635)(511,663)(512,662)(513,661)(514,675)(515,674)(516,673)
(517,672)(518,671)(519,670)(520,669)(521,668)(522,667)(523,666)(524,665)
(525,664)(526,648)(527,647)(528,646)(529,660)(530,659)(531,658)(532,657)
(533,656)(534,655)(535,654)(536,653)(537,652)(538,651)(539,650)(540,649);
s1 := Sym(720)!(  1,379)(  2,381)(  3,380)(  4,376)(  5,378)(  6,377)(  7,388)
(  8,390)(  9,389)( 10,385)( 11,387)( 12,386)( 13,382)( 14,384)( 15,383)
( 16,364)( 17,366)( 18,365)( 19,361)( 20,363)( 21,362)( 22,373)( 23,375)
( 24,374)( 25,370)( 26,372)( 27,371)( 28,367)( 29,369)( 30,368)( 31,396)
( 32,395)( 33,394)( 34,393)( 35,392)( 36,391)( 37,405)( 38,404)( 39,403)
( 40,402)( 41,401)( 42,400)( 43,399)( 44,398)( 45,397)( 46,424)( 47,426)
( 48,425)( 49,421)( 50,423)( 51,422)( 52,433)( 53,435)( 54,434)( 55,430)
( 56,432)( 57,431)( 58,427)( 59,429)( 60,428)( 61,409)( 62,411)( 63,410)
( 64,406)( 65,408)( 66,407)( 67,418)( 68,420)( 69,419)( 70,415)( 71,417)
( 72,416)( 73,412)( 74,414)( 75,413)( 76,441)( 77,440)( 78,439)( 79,438)
( 80,437)( 81,436)( 82,450)( 83,449)( 84,448)( 85,447)( 86,446)( 87,445)
( 88,444)( 89,443)( 90,442)( 91,514)( 92,516)( 93,515)( 94,511)( 95,513)
( 96,512)( 97,523)( 98,525)( 99,524)(100,520)(101,522)(102,521)(103,517)
(104,519)(105,518)(106,499)(107,501)(108,500)(109,496)(110,498)(111,497)
(112,508)(113,510)(114,509)(115,505)(116,507)(117,506)(118,502)(119,504)
(120,503)(121,531)(122,530)(123,529)(124,528)(125,527)(126,526)(127,540)
(128,539)(129,538)(130,537)(131,536)(132,535)(133,534)(134,533)(135,532)
(136,469)(137,471)(138,470)(139,466)(140,468)(141,467)(142,478)(143,480)
(144,479)(145,475)(146,477)(147,476)(148,472)(149,474)(150,473)(151,454)
(152,456)(153,455)(154,451)(155,453)(156,452)(157,463)(158,465)(159,464)
(160,460)(161,462)(162,461)(163,457)(164,459)(165,458)(166,486)(167,485)
(168,484)(169,483)(170,482)(171,481)(172,495)(173,494)(174,493)(175,492)
(176,491)(177,490)(178,489)(179,488)(180,487)(181,649)(182,651)(183,650)
(184,646)(185,648)(186,647)(187,658)(188,660)(189,659)(190,655)(191,657)
(192,656)(193,652)(194,654)(195,653)(196,634)(197,636)(198,635)(199,631)
(200,633)(201,632)(202,643)(203,645)(204,644)(205,640)(206,642)(207,641)
(208,637)(209,639)(210,638)(211,666)(212,665)(213,664)(214,663)(215,662)
(216,661)(217,675)(218,674)(219,673)(220,672)(221,671)(222,670)(223,669)
(224,668)(225,667)(226,694)(227,696)(228,695)(229,691)(230,693)(231,692)
(232,703)(233,705)(234,704)(235,700)(236,702)(237,701)(238,697)(239,699)
(240,698)(241,679)(242,681)(243,680)(244,676)(245,678)(246,677)(247,688)
(248,690)(249,689)(250,685)(251,687)(252,686)(253,682)(254,684)(255,683)
(256,711)(257,710)(258,709)(259,708)(260,707)(261,706)(262,720)(263,719)
(264,718)(265,717)(266,716)(267,715)(268,714)(269,713)(270,712)(271,559)
(272,561)(273,560)(274,556)(275,558)(276,557)(277,568)(278,570)(279,569)
(280,565)(281,567)(282,566)(283,562)(284,564)(285,563)(286,544)(287,546)
(288,545)(289,541)(290,543)(291,542)(292,553)(293,555)(294,554)(295,550)
(296,552)(297,551)(298,547)(299,549)(300,548)(301,576)(302,575)(303,574)
(304,573)(305,572)(306,571)(307,585)(308,584)(309,583)(310,582)(311,581)
(312,580)(313,579)(314,578)(315,577)(316,604)(317,606)(318,605)(319,601)
(320,603)(321,602)(322,613)(323,615)(324,614)(325,610)(326,612)(327,611)
(328,607)(329,609)(330,608)(331,589)(332,591)(333,590)(334,586)(335,588)
(336,587)(337,598)(338,600)(339,599)(340,595)(341,597)(342,596)(343,592)
(344,594)(345,593)(346,621)(347,620)(348,619)(349,618)(350,617)(351,616)
(352,630)(353,629)(354,628)(355,627)(356,626)(357,625)(358,624)(359,623)
(360,622);
poly := sub<Sym(720)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope