Polytope of Type {58,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {58,16}*1856
Also Known As : {58,16|2}. if this polytope has another name.
Group : SmallGroup(1856,968)
Rank : 3
Schlafli Type : {58,16}
Number of vertices, edges, etc : 58, 464, 16
Order of s0s1s2 : 464
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {58,8}*928
4-fold quotients : {58,4}*464
8-fold quotients : {58,2}*232
16-fold quotients : {29,2}*116
29-fold quotients : {2,16}*64
58-fold quotients : {2,8}*32
116-fold quotients : {2,4}*16
232-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
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