Polytope of Type {606}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {606}*1212
Also Known As : 606-gon, {606}. if this polytope has another name.
Group : SmallGroup(1212,11)
Rank : 2
Schlafli Type : {606}
Number of vertices, edges, etc : 606, 606
Order of s₀s₁ : 606
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 : {303}*606
   3-fold quotients : {202}*404
   6-fold quotients : {101}*202
   101-fold quotients : {6}*12
   202-fold quotients : {3}*6
   303-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope