Polytope of Type {594}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {594}*1188
Also Known As : 594-gon, {594}. if this polytope has another name.
Group : SmallGroup(1188,9)
Rank : 2
Schlafli Type : {594}
Number of vertices, edges, etc : 594, 594
Order of s₀s₁ : 594
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 : {297}*594
   3-fold quotients : {198}*396
   6-fold quotients : {99}*198
   9-fold quotients : {66}*132
   11-fold quotients : {54}*108
   18-fold quotients : {33}*66
   22-fold quotients : {27}*54
   27-fold quotients : {22}*44
   33-fold quotients : {18}*36
   54-fold quotients : {11}*22
   66-fold quotients : {9}*18
   99-fold quotients : {6}*12
   198-fold quotients : {3}*6
   297-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope