Overview
- Group
- SmallGroup(1380,28)
- Rank
- 2
- Schläfli Type
- {690}
- Vertices, edges, …
- 690, 690
- Order of s0s1
- 690
- Also known as
- 690-gon, {690}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
10-fold
15-fold
23-fold
30-fold
46-fold
69-fold
115-fold
138-fold
230-fold
345-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)(116,231)(117,253)(118,252)(119,251)(120,250)(121,249)(122,248)(123,247)(124,246)(125,245)(126,244)(127,243)(128,242)(129,241)(130,240)(131,239)(132,238)(133,237)(134,236)(135,235)(136,234)(137,233)(138,232)(139,323)(140,345)(141,344)(142,343)(143,342)(144,341)(145,340)(146,339)(147,338)(148,337)(149,336)(150,335)(151,334)(152,333)(153,332)(154,331)(155,330)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)(162,300)(163,322)(164,321)(165,320)(166,319)(167,318)(168,317)(169,316)(170,315)(171,314)(172,313)(173,312)(174,311)(175,310)(176,309)(177,308)(178,307)(179,306)(180,305)(181,304)(182,303)(183,302)(184,301)(185,277)(186,299)(187,298)(188,297)(189,296)(190,295)(191,294)(192,293)(193,292)(194,291)(195,290)(196,289)(197,288)(198,287)(199,286)(200,285)(201,284)(202,283)(203,282)(204,281)(205,280)(206,279)(207,278)(208,254)(209,276)(210,275)(211,274)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)(222,263)(223,262)(224,261)(225,260)(226,259)(227,258)(228,257)(229,256)(230,255)(347,368)(348,367)(349,366)(350,365)(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)(357,358)(369,438)(370,460)(371,459)(372,458)(373,457)(374,456)(375,455)(376,454)(377,453)(378,452)(379,451)(380,450)(381,449)(382,448)(383,447)(384,446)(385,445)(386,444)(387,443)(388,442)(389,441)(390,440)(391,439)(392,415)(393,437)(394,436)(395,435)(396,434)(397,433)(398,432)(399,431)(400,430)(401,429)(402,428)(403,427)(404,426)(405,425)(406,424)(407,423)(408,422)(409,421)(410,420)(411,419)(412,418)(413,417)(414,416)(461,576)(462,598)(463,597)(464,596)(465,595)(466,594)(467,593)(468,592)(469,591)(470,590)(471,589)(472,588)(473,587)(474,586)(475,585)(476,584)(477,583)(478,582)(479,581)(480,580)(481,579)(482,578)(483,577)(484,668)(485,690)(486,689)(487,688)(488,687)(489,686)(490,685)(491,684)(492,683)(493,682)(494,681)(495,680)(496,679)(497,678)(498,677)(499,676)(500,675)(501,674)(502,673)(503,672)(504,671)(505,670)(506,669)(507,645)(508,667)(509,666)(510,665)(511,664)(512,663)(513,662)(514,661)(515,660)(516,659)(517,658)(518,657)(519,656)(520,655)(521,654)(522,653)(523,652)(524,651)(525,650)(526,649)(527,648)(528,647)(529,646)(530,622)(531,644)(532,643)(533,642)(534,641)(535,640)(536,639)(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)(543,632)(544,631)(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)(551,624)(552,623)(553,599)(554,621)(555,620)(556,619)(557,618)(558,617)(559,616)(560,615)(561,614)(562,613)(563,612)(564,611)(565,610)(566,609)(567,608)(568,607)(569,606)(570,605)(571,604)(572,603)(573,602)(574,601)(575,600);; s1 := ( 1,485)( 2,484)( 3,506)( 4,505)( 5,504)( 6,503)( 7,502)( 8,501)( 9,500)( 10,499)( 11,498)( 12,497)( 13,496)( 14,495)( 15,494)( 16,493)( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)( 24,462)( 25,461)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)( 32,477)( 33,476)( 34,475)( 35,474)( 36,473)( 37,472)( 38,471)( 39,470)( 40,469)( 41,468)( 42,467)( 43,466)( 44,465)( 45,464)( 46,463)( 47,554)( 48,553)( 49,575)( 50,574)( 51,573)( 52,572)( 53,571)( 54,570)( 55,569)( 56,568)( 57,567)( 58,566)( 59,565)( 60,564)( 61,563)( 62,562)( 63,561)( 64,560)( 65,559)( 66,558)( 67,557)( 68,556)( 69,555)( 70,531)( 71,530)( 72,552)( 73,551)( 74,550)( 75,549)( 76,548)( 77,547)( 78,546)( 79,545)( 80,544)( 81,543)( 82,542)( 83,541)( 84,540)( 85,539)( 86,538)( 87,537)( 88,536)( 89,535)( 90,534)( 91,533)( 92,532)( 93,508)( 94,507)( 95,529)( 96,528)( 97,527)( 98,526)( 99,525)(100,524)(101,523)(102,522)(103,521)(104,520)(105,519)(106,518)(107,517)(108,516)(109,515)(110,514)(111,513)(112,512)(113,511)(114,510)(115,509)(116,370)(117,369)(118,391)(119,390)(120,389)(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)(136,373)(137,372)(138,371)(139,347)(140,346)(141,368)(142,367)(143,366)(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)(161,348)(162,439)(163,438)(164,460)(165,459)(166,458)(167,457)(168,456)(169,455)(170,454)(171,453)(172,452)(173,451)(174,450)(175,449)(176,448)(177,447)(178,446)(179,445)(180,444)(181,443)(182,442)(183,441)(184,440)(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)(192,432)(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)(200,424)(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)(208,393)(209,392)(210,414)(211,413)(212,412)(213,411)(214,410)(215,409)(216,408)(217,407)(218,406)(219,405)(220,404)(221,403)(222,402)(223,401)(224,400)(225,399)(226,398)(227,397)(228,396)(229,395)(230,394)(231,600)(232,599)(233,621)(234,620)(235,619)(236,618)(237,617)(238,616)(239,615)(240,614)(241,613)(242,612)(243,611)(244,610)(245,609)(246,608)(247,607)(248,606)(249,605)(250,604)(251,603)(252,602)(253,601)(254,577)(255,576)(256,598)(257,597)(258,596)(259,595)(260,594)(261,593)(262,592)(263,591)(264,590)(265,589)(266,588)(267,587)(268,586)(269,585)(270,584)(271,583)(272,582)(273,581)(274,580)(275,579)(276,578)(277,669)(278,668)(279,690)(280,689)(281,688)(282,687)(283,686)(284,685)(285,684)(286,683)(287,682)(288,681)(289,680)(290,679)(291,678)(292,677)(293,676)(294,675)(295,674)(296,673)(297,672)(298,671)(299,670)(300,646)(301,645)(302,667)(303,666)(304,665)(305,664)(306,663)(307,662)(308,661)(309,660)(310,659)(311,658)(312,657)(313,656)(314,655)(315,654)(316,653)(317,652)(318,651)(319,650)(320,649)(321,648)(322,647)(323,623)(324,622)(325,644)(326,643)(327,642)(328,641)(329,640)(330,639)(331,638)(332,637)(333,636)(334,635)(335,634)(336,633)(337,632)(338,631)(339,630)(340,629)(341,628)(342,627)(343,626)(344,625)(345,624);; 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(690)!( 2, 23)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)(116,231)(117,253)(118,252)(119,251)(120,250)(121,249)(122,248)(123,247)(124,246)(125,245)(126,244)(127,243)(128,242)(129,241)(130,240)(131,239)(132,238)(133,237)(134,236)(135,235)(136,234)(137,233)(138,232)(139,323)(140,345)(141,344)(142,343)(143,342)(144,341)(145,340)(146,339)(147,338)(148,337)(149,336)(150,335)(151,334)(152,333)(153,332)(154,331)(155,330)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)(162,300)(163,322)(164,321)(165,320)(166,319)(167,318)(168,317)(169,316)(170,315)(171,314)(172,313)(173,312)(174,311)(175,310)(176,309)(177,308)(178,307)(179,306)(180,305)(181,304)(182,303)(183,302)(184,301)(185,277)(186,299)(187,298)(188,297)(189,296)(190,295)(191,294)(192,293)(193,292)(194,291)(195,290)(196,289)(197,288)(198,287)(199,286)(200,285)(201,284)(202,283)(203,282)(204,281)(205,280)(206,279)(207,278)(208,254)(209,276)(210,275)(211,274)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)(222,263)(223,262)(224,261)(225,260)(226,259)(227,258)(228,257)(229,256)(230,255)(347,368)(348,367)(349,366)(350,365)(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)(357,358)(369,438)(370,460)(371,459)(372,458)(373,457)(374,456)(375,455)(376,454)(377,453)(378,452)(379,451)(380,450)(381,449)(382,448)(383,447)(384,446)(385,445)(386,444)(387,443)(388,442)(389,441)(390,440)(391,439)(392,415)(393,437)(394,436)(395,435)(396,434)(397,433)(398,432)(399,431)(400,430)(401,429)(402,428)(403,427)(404,426)(405,425)(406,424)(407,423)(408,422)(409,421)(410,420)(411,419)(412,418)(413,417)(414,416)(461,576)(462,598)(463,597)(464,596)(465,595)(466,594)(467,593)(468,592)(469,591)(470,590)(471,589)(472,588)(473,587)(474,586)(475,585)(476,584)(477,583)(478,582)(479,581)(480,580)(481,579)(482,578)(483,577)(484,668)(485,690)(486,689)(487,688)(488,687)(489,686)(490,685)(491,684)(492,683)(493,682)(494,681)(495,680)(496,679)(497,678)(498,677)(499,676)(500,675)(501,674)(502,673)(503,672)(504,671)(505,670)(506,669)(507,645)(508,667)(509,666)(510,665)(511,664)(512,663)(513,662)(514,661)(515,660)(516,659)(517,658)(518,657)(519,656)(520,655)(521,654)(522,653)(523,652)(524,651)(525,650)(526,649)(527,648)(528,647)(529,646)(530,622)(531,644)(532,643)(533,642)(534,641)(535,640)(536,639)(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)(543,632)(544,631)(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)(551,624)(552,623)(553,599)(554,621)(555,620)(556,619)(557,618)(558,617)(559,616)(560,615)(561,614)(562,613)(563,612)(564,611)(565,610)(566,609)(567,608)(568,607)(569,606)(570,605)(571,604)(572,603)(573,602)(574,601)(575,600); s1 := Sym(690)!( 1,485)( 2,484)( 3,506)( 4,505)( 5,504)( 6,503)( 7,502)( 8,501)( 9,500)( 10,499)( 11,498)( 12,497)( 13,496)( 14,495)( 15,494)( 16,493)( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)( 24,462)( 25,461)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)( 32,477)( 33,476)( 34,475)( 35,474)( 36,473)( 37,472)( 38,471)( 39,470)( 40,469)( 41,468)( 42,467)( 43,466)( 44,465)( 45,464)( 46,463)( 47,554)( 48,553)( 49,575)( 50,574)( 51,573)( 52,572)( 53,571)( 54,570)( 55,569)( 56,568)( 57,567)( 58,566)( 59,565)( 60,564)( 61,563)( 62,562)( 63,561)( 64,560)( 65,559)( 66,558)( 67,557)( 68,556)( 69,555)( 70,531)( 71,530)( 72,552)( 73,551)( 74,550)( 75,549)( 76,548)( 77,547)( 78,546)( 79,545)( 80,544)( 81,543)( 82,542)( 83,541)( 84,540)( 85,539)( 86,538)( 87,537)( 88,536)( 89,535)( 90,534)( 91,533)( 92,532)( 93,508)( 94,507)( 95,529)( 96,528)( 97,527)( 98,526)( 99,525)(100,524)(101,523)(102,522)(103,521)(104,520)(105,519)(106,518)(107,517)(108,516)(109,515)(110,514)(111,513)(112,512)(113,511)(114,510)(115,509)(116,370)(117,369)(118,391)(119,390)(120,389)(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)(128,381)(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)(136,373)(137,372)(138,371)(139,347)(140,346)(141,368)(142,367)(143,366)(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)(161,348)(162,439)(163,438)(164,460)(165,459)(166,458)(167,457)(168,456)(169,455)(170,454)(171,453)(172,452)(173,451)(174,450)(175,449)(176,448)(177,447)(178,446)(179,445)(180,444)(181,443)(182,442)(183,441)(184,440)(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)(192,432)(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)(200,424)(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)(208,393)(209,392)(210,414)(211,413)(212,412)(213,411)(214,410)(215,409)(216,408)(217,407)(218,406)(219,405)(220,404)(221,403)(222,402)(223,401)(224,400)(225,399)(226,398)(227,397)(228,396)(229,395)(230,394)(231,600)(232,599)(233,621)(234,620)(235,619)(236,618)(237,617)(238,616)(239,615)(240,614)(241,613)(242,612)(243,611)(244,610)(245,609)(246,608)(247,607)(248,606)(249,605)(250,604)(251,603)(252,602)(253,601)(254,577)(255,576)(256,598)(257,597)(258,596)(259,595)(260,594)(261,593)(262,592)(263,591)(264,590)(265,589)(266,588)(267,587)(268,586)(269,585)(270,584)(271,583)(272,582)(273,581)(274,580)(275,579)(276,578)(277,669)(278,668)(279,690)(280,689)(281,688)(282,687)(283,686)(284,685)(285,684)(286,683)(287,682)(288,681)(289,680)(290,679)(291,678)(292,677)(293,676)(294,675)(295,674)(296,673)(297,672)(298,671)(299,670)(300,646)(301,645)(302,667)(303,666)(304,665)(305,664)(306,663)(307,662)(308,661)(309,660)(310,659)(311,658)(312,657)(313,656)(314,655)(315,654)(316,653)(317,652)(318,651)(319,650)(320,649)(321,648)(322,647)(323,623)(324,622)(325,644)(326,643)(327,642)(328,641)(329,640)(330,639)(331,638)(332,637)(333,636)(334,635)(335,634)(336,633)(337,632)(338,631)(339,630)(340,629)(341,628)(342,627)(343,626)(344,625)(345,624); poly := sub<Sym(690)|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 >;
References
None.
to this polytope.