Polytope of Type {630}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {630}*1260
Also Known As : 630-gon, {630}. if this polytope has another name.
Group : SmallGroup(1260,39)
Rank : 2
Schlafli Type : {630}
Number of vertices, edges, etc : 630, 630
Order of s₀s₁ : 630
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 : {315}*630
   3-fold quotients : {210}*420
   5-fold quotients : {126}*252
   6-fold quotients : {105}*210
   7-fold quotients : {90}*180
   9-fold quotients : {70}*140
   10-fold quotients : {63}*126
   14-fold quotients : {45}*90
   15-fold quotients : {42}*84
   18-fold quotients : {35}*70
   21-fold quotients : {30}*60
   30-fold quotients : {21}*42
   35-fold quotients : {18}*36
   42-fold quotients : {15}*30
   45-fold quotients : {14}*28
   63-fold quotients : {10}*20
   70-fold quotients : {9}*18
   90-fold quotients : {7}*14
   105-fold quotients : {6}*12
   126-fold quotients : {5}*10
   210-fold quotients : {3}*6
   315-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope