Polytope of Type {618}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {618}*1236
Also Known As : 618-gon, {618}. if this polytope has another name.
Group : SmallGroup(1236,14)
Rank : 2
Schlafli Type : {618}
Number of vertices, edges, etc : 618, 618
Order of s₀s₁ : 618
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 : {309}*618
   3-fold quotients : {206}*412
   6-fold quotients : {103}*206
   103-fold quotients : {6}*12
   206-fold quotients : {3}*6
   309-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope