Polytope of Type {8,112}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,112}*1792f
if this polytope has a name.
Group : SmallGroup(1792,83050)
Rank : 3
Schlafli Type : {8,112}
Number of vertices, edges, etc : 8, 448, 112
Order of s₀s₁s₂ : 112
Order of s₀s₁s₂s₁ : 4
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 : {8,56}*896b, {4,112}*896b
   4-fold quotients : {4,56}*448a, {8,28}*448a
   7-fold quotients : {8,16}*256f
   8-fold quotients : {4,28}*224, {2,56}*224, {8,14}*224
   14-fold quotients : {8,8}*128b, {4,16}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,8}*64a, {8,4}*64a
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   64-fold quotients : {2,7}*28
   112-fold quotients : {2,4}*16, {4,2}*16
   224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope