Overview
- Group
- SmallGroup(1856,968)
- Rank
- 3
- Schläfli Type
- {58,16}
- Vertices, edges, …
- 58, 464, 16
- Order of s0s1s2
- 464
- Order of s0s1s2s1
- 2
- Also known as
- {58,16|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
29-fold
58-fold
116-fold
232-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 := ( 1,233)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)( 8,255)( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)( 16,247)( 17,246)( 18,245)( 19,244)( 20,243) ( 21,242)( 22,241)( 23,240)( 24,239)( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)( 32,289)( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)( 40,281)( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)( 48,273)( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)( 56,265)( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)( 64,315)( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)( 72,307)( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,320)( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)( 96,341)( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)(104,333)(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)(112,325)(113,324)(114,323)(115,322)(116,321)(117,349)(118,377)(119,376)(120,375)(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)(128,367)(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)(136,359)(137,358)(138,357)(139,356)(140,355)(141,354)(142,353)(143,352)(144,351)(145,350)(146,378)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)(153,400)(154,399)(155,398)(156,397)(157,396)(158,395)(159,394)(160,393)(161,392)(162,391)(163,390)(164,389)(165,388)(166,387)(167,386)(168,385)(169,384)(170,383)(171,382)(172,381)(173,380)(174,379)(175,407)(176,435)(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)(184,427)(185,426)(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)(192,419)(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)(200,411)(201,410)(202,409)(203,408)(204,436)(205,464)(206,463)(207,462)(208,461)(209,460)(210,459)(211,458)(212,457)(213,456)(214,455)(215,454)(216,453)(217,452)(218,451)(219,450)(220,449)(221,448)(222,447)(223,446)(224,445)(225,444)(226,443)(227,442)(228,441)(229,440)(230,439)(231,438)(232,437)(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)(472,719)(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)(480,711)(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)(488,703)(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)(496,753)(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)(504,745)(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)(512,737)(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)(520,729)(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)(528,779)(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)(536,771)(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)(544,763)(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)(552,784)(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)(560,805)(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)(568,797)(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)(576,789)(577,788)(578,787)(579,786)(580,785)(581,813)(582,841)(583,840)(584,839)(585,838)(586,837)(587,836)(588,835)(589,834)(590,833)(591,832)(592,831)(593,830)(594,829)(595,828)(596,827)(597,826)(598,825)(599,824)(600,823)(601,822)(602,821)(603,820)(604,819)(605,818)(606,817)(607,816)(608,815)(609,814)(610,842)(611,870)(612,869)(613,868)(614,867)(615,866)(616,865)(617,864)(618,863)(619,862)(620,861)(621,860)(622,859)(623,858)(624,857)(625,856)(626,855)(627,854)(628,853)(629,852)(630,851)(631,850)(632,849)(633,848)(634,847)(635,846)(636,845)(637,844)(638,843)(639,871)(640,899)(641,898)(642,897)(643,896)(644,895)(645,894)(646,893)(647,892)(648,891)(649,890)(650,889)(651,888)(652,887)(653,886)(654,885)(655,884)(656,883)(657,882)(658,881)(659,880)(660,879)(661,878)(662,877)(663,876)(664,875)(665,874)(666,873)(667,872)(668,900)(669,928)(670,927)(671,926)(672,925)(673,924)(674,923)(675,922)(676,921)(677,920)(678,919)(679,918)(680,917)(681,916)(682,915)(683,914)(684,913)(685,912)(686,911)(687,910)(688,909)(689,908)(690,907)(691,906)(692,905)(693,904)(694,903)(695,902)(696,901);; s1 := ( 1,234)( 2,233)( 3,261)( 4,260)( 5,259)( 6,258)( 7,257)( 8,256)( 9,255)( 10,254)( 11,253)( 12,252)( 13,251)( 14,250)( 15,249)( 16,248)( 17,247)( 18,246)( 19,245)( 20,244) ( 21,243)( 22,242)( 23,241)( 24,240)( 25,239)( 26,238)( 27,237)( 28,236)( 29,235)( 30,263)( 31,262)( 32,290)( 33,289)( 34,288)( 35,287)( 36,286)( 37,285)( 38,284)( 39,283)( 40,282)( 41,281)( 42,280)( 43,279)( 44,278)( 45,277)( 46,276)( 47,275)( 48,274)( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)( 56,266)( 57,265)( 58,264)( 59,321)( 60,320)( 61,348)( 62,347)( 63,346)( 64,345)( 65,344)( 66,343)( 67,342)( 68,341)( 69,340)( 70,339)( 71,338)( 72,337)( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,331)( 79,330)( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,324)( 86,323)( 87,322)( 88,292)( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)(112,297)(113,296)(114,295)(115,294)(116,293)(117,408)(118,407)(119,435)(120,434)(121,433)(122,432)(123,431)(124,430)(125,429)(126,428)(127,427)(128,426)(129,425)(130,424)(131,423)(132,422)(133,421)(134,420)(135,419)(136,418)(137,417)(138,416)(139,415)(140,414)(141,413)(142,412)(143,411)(144,410)(145,409)(146,437)(147,436)(148,464)(149,463)(150,462)(151,461)(152,460)(153,459)(154,458)(155,457)(156,456)(157,455)(158,454)(159,453)(160,452)(161,451)(162,450)(163,449)(164,448)(165,447)(166,446)(167,445)(168,444)(169,443)(170,442)(171,441)(172,440)(173,439)(174,438)(175,350)(176,349)(177,377)(178,376)(179,375)(180,374)(181,373)(182,372)(183,371)(184,370)(185,369)(186,368)(187,367)(188,366)(189,365)(190,364)(191,363)(192,362)(193,361)(194,360)(195,359)(196,358)(197,357)(198,356)(199,355)(200,354)(201,353)(202,352)(203,351)(204,379)(205,378)(206,406)(207,405)(208,404)(209,403)(210,402)(211,401)(212,400)(213,399)(214,398)(215,397)(216,396)(217,395)(218,394)(219,393)(220,392)(221,391)(222,390)(223,389)(224,388)(225,387)(226,386)(227,385)(228,384)(229,383)(230,382)(231,381)(232,380)(465,814)(466,813)(467,841)(468,840)(469,839)(470,838)(471,837)(472,836)(473,835)(474,834)(475,833)(476,832)(477,831)(478,830)(479,829)(480,828)(481,827)(482,826)(483,825)(484,824)(485,823)(486,822)(487,821)(488,820)(489,819)(490,818)(491,817)(492,816)(493,815)(494,843)(495,842)(496,870)(497,869)(498,868)(499,867)(500,866)(501,865)(502,864)(503,863)(504,862)(505,861)(506,860)(507,859)(508,858)(509,857)(510,856)(511,855)(512,854)(513,853)(514,852)(515,851)(516,850)(517,849)(518,848)(519,847)(520,846)(521,845)(522,844)(523,901)(524,900)(525,928)(526,927)(527,926)(528,925)(529,924)(530,923)(531,922)(532,921)(533,920)(534,919)(535,918)(536,917)(537,916)(538,915)(539,914)(540,913)(541,912)(542,911)(543,910)(544,909)(545,908)(546,907)(547,906)(548,905)(549,904)(550,903)(551,902)(552,872)(553,871)(554,899)(555,898)(556,897)(557,896)(558,895)(559,894)(560,893)(561,892)(562,891)(563,890)(564,889)(565,888)(566,887)(567,886)(568,885)(569,884)(570,883)(571,882)(572,881)(573,880)(574,879)(575,878)(576,877)(577,876)(578,875)(579,874)(580,873)(581,698)(582,697)(583,725)(584,724)(585,723)(586,722)(587,721)(588,720)(589,719)(590,718)(591,717)(592,716)(593,715)(594,714)(595,713)(596,712)(597,711)(598,710)(599,709)(600,708)(601,707)(602,706)(603,705)(604,704)(605,703)(606,702)(607,701)(608,700)(609,699)(610,727)(611,726)(612,754)(613,753)(614,752)(615,751)(616,750)(617,749)(618,748)(619,747)(620,746)(621,745)(622,744)(623,743)(624,742)(625,741)(626,740)(627,739)(628,738)(629,737)(630,736)(631,735)(632,734)(633,733)(634,732)(635,731)(636,730)(637,729)(638,728)(639,785)(640,784)(641,812)(642,811)(643,810)(644,809)(645,808)(646,807)(647,806)(648,805)(649,804)(650,803)(651,802)(652,801)(653,800)(654,799)(655,798)(656,797)(657,796)(658,795)(659,794)(660,793)(661,792)(662,791)(663,790)(664,789)(665,788)(666,787)(667,786)(668,756)(669,755)(670,783)(671,782)(672,781)(673,780)(674,779)(675,778)(676,777)(677,776)(678,775)(679,774)(680,773)(681,772)(682,771)(683,770)(684,769)(685,768)(686,767)(687,766)(688,765)(689,764)(690,763)(691,762)(692,761)(693,760)(694,759)(695,758)(696,757);; s2 := ( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)( 8,472)( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)( 16,480)( 17,481)( 18,482)( 19,483)( 20,484) ( 21,485)( 22,486)( 23,487)( 24,488)( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)( 32,496)( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)( 40,504)( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)( 48,512)( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)( 56,520)( 57,521)( 58,522)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)( 64,557)( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)( 72,565)( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)( 80,573)( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)( 88,523)( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)( 96,531)( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)(104,539)(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)(112,547)(113,548)(114,549)(115,550)(116,551)(117,639)(118,640)(119,641)(120,642)(121,643)(122,644)(123,645)(124,646)(125,647)(126,648)(127,649)(128,650)(129,651)(130,652)(131,653)(132,654)(133,655)(134,656)(135,657)(136,658)(137,659)(138,660)(139,661)(140,662)(141,663)(142,664)(143,665)(144,666)(145,667)(146,668)(147,669)(148,670)(149,671)(150,672)(151,673)(152,674)(153,675)(154,676)(155,677)(156,678)(157,679)(158,680)(159,681)(160,682)(161,683)(162,684)(163,685)(164,686)(165,687)(166,688)(167,689)(168,690)(169,691)(170,692)(171,693)(172,694)(173,695)(174,696)(175,581)(176,582)(177,583)(178,584)(179,585)(180,586)(181,587)(182,588)(183,589)(184,590)(185,591)(186,592)(187,593)(188,594)(189,595)(190,596)(191,597)(192,598)(193,599)(194,600)(195,601)(196,602)(197,603)(198,604)(199,605)(200,606)(201,607)(202,608)(203,609)(204,610)(205,611)(206,612)(207,613)(208,614)(209,615)(210,616)(211,617)(212,618)(213,619)(214,620)(215,621)(216,622)(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)(224,630)(225,631)(226,632)(227,633)(228,634)(229,635)(230,636)(231,637)(232,638)(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)(240,704)(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)(248,712)(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)(256,720)(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)(264,728)(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)(272,736)(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)(280,744)(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)(288,752)(289,753)(290,754)(291,784)(292,785)(293,786)(294,787)(295,788)(296,789)(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)(304,797)(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)(312,805)(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)(320,755)(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)(328,763)(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)(336,771)(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)(344,779)(345,780)(346,781)(347,782)(348,783)(349,871)(350,872)(351,873)(352,874)(353,875)(354,876)(355,877)(356,878)(357,879)(358,880)(359,881)(360,882)(361,883)(362,884)(363,885)(364,886)(365,887)(366,888)(367,889)(368,890)(369,891)(370,892)(371,893)(372,894)(373,895)(374,896)(375,897)(376,898)(377,899)(378,900)(379,901)(380,902)(381,903)(382,904)(383,905)(384,906)(385,907)(386,908)(387,909)(388,910)(389,911)(390,912)(391,913)(392,914)(393,915)(394,916)(395,917)(396,918)(397,919)(398,920)(399,921)(400,922)(401,923)(402,924)(403,925)(404,926)(405,927)(406,928)(407,813)(408,814)(409,815)(410,816)(411,817)(412,818)(413,819)(414,820)(415,821)(416,822)(417,823)(418,824)(419,825)(420,826)(421,827)(422,828)(423,829)(424,830)(425,831)(426,832)(427,833)(428,834)(429,835)(430,836)(431,837)(432,838)(433,839)(434,840)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854)(449,855)(450,856)(451,857)(452,858)(453,859)(454,860)(455,861)(456,862)(457,863)(458,864)(459,865)(460,866)(461,867)(462,868)(463,869)(464,870);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(928)!( 1,233)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)( 8,255)( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)( 16,247)( 17,246)( 18,245)( 19,244) ( 20,243)( 21,242)( 22,241)( 23,240)( 24,239)( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)( 32,289)( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)( 40,281)( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)( 48,273)( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)( 56,265)( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)( 64,315)( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)( 72,307)( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,320)( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)( 96,341)( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)(104,333)(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)(112,325)(113,324)(114,323)(115,322)(116,321)(117,349)(118,377)(119,376)(120,375)(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)(128,367)(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)(136,359)(137,358)(138,357)(139,356)(140,355)(141,354)(142,353)(143,352)(144,351)(145,350)(146,378)(147,406)(148,405)(149,404)(150,403)(151,402)(152,401)(153,400)(154,399)(155,398)(156,397)(157,396)(158,395)(159,394)(160,393)(161,392)(162,391)(163,390)(164,389)(165,388)(166,387)(167,386)(168,385)(169,384)(170,383)(171,382)(172,381)(173,380)(174,379)(175,407)(176,435)(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)(184,427)(185,426)(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)(192,419)(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)(200,411)(201,410)(202,409)(203,408)(204,436)(205,464)(206,463)(207,462)(208,461)(209,460)(210,459)(211,458)(212,457)(213,456)(214,455)(215,454)(216,453)(217,452)(218,451)(219,450)(220,449)(221,448)(222,447)(223,446)(224,445)(225,444)(226,443)(227,442)(228,441)(229,440)(230,439)(231,438)(232,437)(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)(472,719)(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)(480,711)(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)(488,703)(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)(496,753)(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)(504,745)(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)(512,737)(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)(520,729)(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)(528,779)(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)(536,771)(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)(544,763)(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)(552,784)(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)(560,805)(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)(568,797)(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)(576,789)(577,788)(578,787)(579,786)(580,785)(581,813)(582,841)(583,840)(584,839)(585,838)(586,837)(587,836)(588,835)(589,834)(590,833)(591,832)(592,831)(593,830)(594,829)(595,828)(596,827)(597,826)(598,825)(599,824)(600,823)(601,822)(602,821)(603,820)(604,819)(605,818)(606,817)(607,816)(608,815)(609,814)(610,842)(611,870)(612,869)(613,868)(614,867)(615,866)(616,865)(617,864)(618,863)(619,862)(620,861)(621,860)(622,859)(623,858)(624,857)(625,856)(626,855)(627,854)(628,853)(629,852)(630,851)(631,850)(632,849)(633,848)(634,847)(635,846)(636,845)(637,844)(638,843)(639,871)(640,899)(641,898)(642,897)(643,896)(644,895)(645,894)(646,893)(647,892)(648,891)(649,890)(650,889)(651,888)(652,887)(653,886)(654,885)(655,884)(656,883)(657,882)(658,881)(659,880)(660,879)(661,878)(662,877)(663,876)(664,875)(665,874)(666,873)(667,872)(668,900)(669,928)(670,927)(671,926)(672,925)(673,924)(674,923)(675,922)(676,921)(677,920)(678,919)(679,918)(680,917)(681,916)(682,915)(683,914)(684,913)(685,912)(686,911)(687,910)(688,909)(689,908)(690,907)(691,906)(692,905)(693,904)(694,903)(695,902)(696,901); s1 := Sym(928)!( 1,234)( 2,233)( 3,261)( 4,260)( 5,259)( 6,258)( 7,257)( 8,256)( 9,255)( 10,254)( 11,253)( 12,252)( 13,251)( 14,250)( 15,249)( 16,248)( 17,247)( 18,246)( 19,245) ( 20,244)( 21,243)( 22,242)( 23,241)( 24,240)( 25,239)( 26,238)( 27,237)( 28,236)( 29,235)( 30,263)( 31,262)( 32,290)( 33,289)( 34,288)( 35,287)( 36,286)( 37,285)( 38,284)( 39,283)( 40,282)( 41,281)( 42,280)( 43,279)( 44,278)( 45,277)( 46,276)( 47,275)( 48,274)( 49,273)( 50,272)( 51,271)( 52,270)( 53,269)( 54,268)( 55,267)( 56,266)( 57,265)( 58,264)( 59,321)( 60,320)( 61,348)( 62,347)( 63,346)( 64,345)( 65,344)( 66,343)( 67,342)( 68,341)( 69,340)( 70,339)( 71,338)( 72,337)( 73,336)( 74,335)( 75,334)( 76,333)( 77,332)( 78,331)( 79,330)( 80,329)( 81,328)( 82,327)( 83,326)( 84,325)( 85,324)( 86,323)( 87,322)( 88,292)( 89,291)( 90,319)( 91,318)( 92,317)( 93,316)( 94,315)( 95,314)( 96,313)( 97,312)( 98,311)( 99,310)(100,309)(101,308)(102,307)(103,306)(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)(112,297)(113,296)(114,295)(115,294)(116,293)(117,408)(118,407)(119,435)(120,434)(121,433)(122,432)(123,431)(124,430)(125,429)(126,428)(127,427)(128,426)(129,425)(130,424)(131,423)(132,422)(133,421)(134,420)(135,419)(136,418)(137,417)(138,416)(139,415)(140,414)(141,413)(142,412)(143,411)(144,410)(145,409)(146,437)(147,436)(148,464)(149,463)(150,462)(151,461)(152,460)(153,459)(154,458)(155,457)(156,456)(157,455)(158,454)(159,453)(160,452)(161,451)(162,450)(163,449)(164,448)(165,447)(166,446)(167,445)(168,444)(169,443)(170,442)(171,441)(172,440)(173,439)(174,438)(175,350)(176,349)(177,377)(178,376)(179,375)(180,374)(181,373)(182,372)(183,371)(184,370)(185,369)(186,368)(187,367)(188,366)(189,365)(190,364)(191,363)(192,362)(193,361)(194,360)(195,359)(196,358)(197,357)(198,356)(199,355)(200,354)(201,353)(202,352)(203,351)(204,379)(205,378)(206,406)(207,405)(208,404)(209,403)(210,402)(211,401)(212,400)(213,399)(214,398)(215,397)(216,396)(217,395)(218,394)(219,393)(220,392)(221,391)(222,390)(223,389)(224,388)(225,387)(226,386)(227,385)(228,384)(229,383)(230,382)(231,381)(232,380)(465,814)(466,813)(467,841)(468,840)(469,839)(470,838)(471,837)(472,836)(473,835)(474,834)(475,833)(476,832)(477,831)(478,830)(479,829)(480,828)(481,827)(482,826)(483,825)(484,824)(485,823)(486,822)(487,821)(488,820)(489,819)(490,818)(491,817)(492,816)(493,815)(494,843)(495,842)(496,870)(497,869)(498,868)(499,867)(500,866)(501,865)(502,864)(503,863)(504,862)(505,861)(506,860)(507,859)(508,858)(509,857)(510,856)(511,855)(512,854)(513,853)(514,852)(515,851)(516,850)(517,849)(518,848)(519,847)(520,846)(521,845)(522,844)(523,901)(524,900)(525,928)(526,927)(527,926)(528,925)(529,924)(530,923)(531,922)(532,921)(533,920)(534,919)(535,918)(536,917)(537,916)(538,915)(539,914)(540,913)(541,912)(542,911)(543,910)(544,909)(545,908)(546,907)(547,906)(548,905)(549,904)(550,903)(551,902)(552,872)(553,871)(554,899)(555,898)(556,897)(557,896)(558,895)(559,894)(560,893)(561,892)(562,891)(563,890)(564,889)(565,888)(566,887)(567,886)(568,885)(569,884)(570,883)(571,882)(572,881)(573,880)(574,879)(575,878)(576,877)(577,876)(578,875)(579,874)(580,873)(581,698)(582,697)(583,725)(584,724)(585,723)(586,722)(587,721)(588,720)(589,719)(590,718)(591,717)(592,716)(593,715)(594,714)(595,713)(596,712)(597,711)(598,710)(599,709)(600,708)(601,707)(602,706)(603,705)(604,704)(605,703)(606,702)(607,701)(608,700)(609,699)(610,727)(611,726)(612,754)(613,753)(614,752)(615,751)(616,750)(617,749)(618,748)(619,747)(620,746)(621,745)(622,744)(623,743)(624,742)(625,741)(626,740)(627,739)(628,738)(629,737)(630,736)(631,735)(632,734)(633,733)(634,732)(635,731)(636,730)(637,729)(638,728)(639,785)(640,784)(641,812)(642,811)(643,810)(644,809)(645,808)(646,807)(647,806)(648,805)(649,804)(650,803)(651,802)(652,801)(653,800)(654,799)(655,798)(656,797)(657,796)(658,795)(659,794)(660,793)(661,792)(662,791)(663,790)(664,789)(665,788)(666,787)(667,786)(668,756)(669,755)(670,783)(671,782)(672,781)(673,780)(674,779)(675,778)(676,777)(677,776)(678,775)(679,774)(680,773)(681,772)(682,771)(683,770)(684,769)(685,768)(686,767)(687,766)(688,765)(689,764)(690,763)(691,762)(692,761)(693,760)(694,759)(695,758)(696,757); s2 := Sym(928)!( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)( 8,472)( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)( 16,480)( 17,481)( 18,482)( 19,483) ( 20,484)( 21,485)( 22,486)( 23,487)( 24,488)( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)( 32,496)( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)( 40,504)( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)( 48,512)( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)( 56,520)( 57,521)( 58,522)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)( 64,557)( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)( 72,565)( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)( 80,573)( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)( 88,523)( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)( 96,531)( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)(104,539)(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)(112,547)(113,548)(114,549)(115,550)(116,551)(117,639)(118,640)(119,641)(120,642)(121,643)(122,644)(123,645)(124,646)(125,647)(126,648)(127,649)(128,650)(129,651)(130,652)(131,653)(132,654)(133,655)(134,656)(135,657)(136,658)(137,659)(138,660)(139,661)(140,662)(141,663)(142,664)(143,665)(144,666)(145,667)(146,668)(147,669)(148,670)(149,671)(150,672)(151,673)(152,674)(153,675)(154,676)(155,677)(156,678)(157,679)(158,680)(159,681)(160,682)(161,683)(162,684)(163,685)(164,686)(165,687)(166,688)(167,689)(168,690)(169,691)(170,692)(171,693)(172,694)(173,695)(174,696)(175,581)(176,582)(177,583)(178,584)(179,585)(180,586)(181,587)(182,588)(183,589)(184,590)(185,591)(186,592)(187,593)(188,594)(189,595)(190,596)(191,597)(192,598)(193,599)(194,600)(195,601)(196,602)(197,603)(198,604)(199,605)(200,606)(201,607)(202,608)(203,609)(204,610)(205,611)(206,612)(207,613)(208,614)(209,615)(210,616)(211,617)(212,618)(213,619)(214,620)(215,621)(216,622)(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)(224,630)(225,631)(226,632)(227,633)(228,634)(229,635)(230,636)(231,637)(232,638)(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)(240,704)(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)(248,712)(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)(256,720)(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)(264,728)(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)(272,736)(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)(280,744)(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)(288,752)(289,753)(290,754)(291,784)(292,785)(293,786)(294,787)(295,788)(296,789)(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)(304,797)(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)(312,805)(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)(320,755)(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)(328,763)(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)(336,771)(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)(344,779)(345,780)(346,781)(347,782)(348,783)(349,871)(350,872)(351,873)(352,874)(353,875)(354,876)(355,877)(356,878)(357,879)(358,880)(359,881)(360,882)(361,883)(362,884)(363,885)(364,886)(365,887)(366,888)(367,889)(368,890)(369,891)(370,892)(371,893)(372,894)(373,895)(374,896)(375,897)(376,898)(377,899)(378,900)(379,901)(380,902)(381,903)(382,904)(383,905)(384,906)(385,907)(386,908)(387,909)(388,910)(389,911)(390,912)(391,913)(392,914)(393,915)(394,916)(395,917)(396,918)(397,919)(398,920)(399,921)(400,922)(401,923)(402,924)(403,925)(404,926)(405,927)(406,928)(407,813)(408,814)(409,815)(410,816)(411,817)(412,818)(413,819)(414,820)(415,821)(416,822)(417,823)(418,824)(419,825)(420,826)(421,827)(422,828)(423,829)(424,830)(425,831)(426,832)(427,833)(428,834)(429,835)(430,836)(431,837)(432,838)(433,839)(434,840)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854)(449,855)(450,856)(451,857)(452,858)(453,859)(454,860)(455,861)(456,862)(457,863)(458,864)(459,865)(460,866)(461,867)(462,868)(463,869)(464,870); poly := sub<Sym(928)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.