Polytope of Type {16,58}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,58}*1856
Also Known As : {16,58|2}. if this polytope has another name.
Group : SmallGroup(1856,968)
Rank : 3
Schlafli Type : {16,58}
Number of vertices, edges, etc : 16, 464, 58
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 : {8,58}*928
   4-fold quotients : {4,58}*464
   8-fold quotients : {2,58}*232
   16-fold quotients : {2,29}*116
   29-fold quotients : {16,2}*64
   58-fold quotients : {8,2}*32
   116-fold quotients : {4,2}*16
   232-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope