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# Polytope of Type {56,16}

Atlas Canonical Name : {56,16}*1792d
Also Known As : {56,16|2}. if this polytope has another name.
Group : SmallGroup(1792,82995)
Rank : 3
Schlafli Type : {56,16}
Number of vertices, edges, etc : 56, 448, 16
Order of s0s1s2 : 112
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 : {56,8}*896b, {28,16}*896a
4-fold quotients : {56,4}*448a, {28,8}*448a, {14,16}*448
7-fold quotients : {8,16}*256d
8-fold quotients : {28,4}*224, {56,2}*224, {14,8}*224
14-fold quotients : {8,8}*128b, {4,16}*128a
16-fold quotients : {28,2}*112, {14,4}*112
28-fold quotients : {4,8}*64a, {8,4}*64a, {2,16}*64
32-fold quotients : {14,2}*56
56-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
64-fold quotients : {7,2}*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)(  2,231)(  3,230)(  4,229)(  5,228)(  6,227)(  7,226)(  8,232)
(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,253)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,255)( 35,254)( 36,260)( 37,266)( 38,265)( 39,264)( 40,263)
( 41,262)( 42,261)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)( 48,269)
( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)( 56,275)
( 57,295)( 58,301)( 59,300)( 60,299)( 61,298)( 62,297)( 63,296)( 64,302)
( 65,308)( 66,307)( 67,306)( 68,305)( 69,304)( 70,303)( 71,281)( 72,287)
( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,288)( 79,294)( 80,293)
( 81,292)( 82,291)( 83,290)( 84,289)( 85,323)( 86,329)( 87,328)( 88,327)
( 89,326)( 90,325)( 91,324)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,332)( 98,331)( 99,309)(100,315)(101,314)(102,313)(103,312)(104,311)
(105,310)(106,316)(107,322)(108,321)(109,320)(110,319)(111,318)(112,317)
(113,351)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)(120,358)
(121,364)(122,363)(123,362)(124,361)(125,360)(126,359)(127,337)(128,343)
(129,342)(130,341)(131,340)(132,339)(133,338)(134,344)(135,350)(136,349)
(137,348)(138,347)(139,346)(140,345)(141,379)(142,385)(143,384)(144,383)
(145,382)(146,381)(147,380)(148,386)(149,392)(150,391)(151,390)(152,389)
(153,388)(154,387)(155,365)(156,371)(157,370)(158,369)(159,368)(160,367)
(161,366)(162,372)(163,378)(164,377)(165,376)(166,375)(167,374)(168,373)
(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,400)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)(184,413)
(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)(200,425)
(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)(208,431)
(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)(216,437)
(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)(224,443)
(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)
(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)(464,693)
(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)(472,699)
(473,698)(474,697)(475,696)(476,695)(477,701)(478,707)(479,706)(480,705)
(481,704)(482,703)(483,702)(484,708)(485,714)(486,713)(487,712)(488,711)
(489,710)(490,709)(491,715)(492,721)(493,720)(494,719)(495,718)(496,717)
(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)(504,723)
(505,743)(506,749)(507,748)(508,747)(509,746)(510,745)(511,744)(512,750)
(513,756)(514,755)(515,754)(516,753)(517,752)(518,751)(519,729)(520,735)
(521,734)(522,733)(523,732)(524,731)(525,730)(526,736)(527,742)(528,741)
(529,740)(530,739)(531,738)(532,737)(533,771)(534,777)(535,776)(536,775)
(537,774)(538,773)(539,772)(540,778)(541,784)(542,783)(543,782)(544,781)
(545,780)(546,779)(547,757)(548,763)(549,762)(550,761)(551,760)(552,759)
(553,758)(554,764)(555,770)(556,769)(557,768)(558,767)(559,766)(560,765)
(561,799)(562,805)(563,804)(564,803)(565,802)(566,801)(567,800)(568,806)
(569,812)(570,811)(571,810)(572,809)(573,808)(574,807)(575,785)(576,791)
(577,790)(578,789)(579,788)(580,787)(581,786)(582,792)(583,798)(584,797)
(585,796)(586,795)(587,794)(588,793)(589,827)(590,833)(591,832)(592,831)
(593,830)(594,829)(595,828)(596,834)(597,840)(598,839)(599,838)(600,837)
(601,836)(602,835)(603,813)(604,819)(605,818)(606,817)(607,816)(608,815)
(609,814)(610,820)(611,826)(612,825)(613,824)(614,823)(615,822)(616,821)
(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)(624,848)
(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)(632,861)
(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)(640,867)
(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)(648,873)
(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)(656,879)
(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)(664,885)
(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)(672,891);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)
( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)( 92,100)
( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(113,142)(114,141)
(115,147)(116,146)(117,145)(118,144)(119,143)(120,149)(121,148)(122,154)
(123,153)(124,152)(125,151)(126,150)(127,156)(128,155)(129,161)(130,160)
(131,159)(132,158)(133,157)(134,163)(135,162)(136,168)(137,167)(138,166)
(139,165)(140,164)(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)
(175,213)(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)
(183,198)(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)
(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(225,282)(226,281)
(227,287)(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)
(235,293)(236,292)(237,291)(238,290)(239,296)(240,295)(241,301)(242,300)
(243,299)(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)
(251,305)(252,304)(253,317)(254,316)(255,322)(256,321)(257,320)(258,319)
(259,318)(260,310)(261,309)(262,315)(263,314)(264,313)(265,312)(266,311)
(267,331)(268,330)(269,336)(270,335)(271,334)(272,333)(273,332)(274,324)
(275,323)(276,329)(277,328)(278,327)(279,326)(280,325)(337,422)(338,421)
(339,427)(340,426)(341,425)(342,424)(343,423)(344,429)(345,428)(346,434)
(347,433)(348,432)(349,431)(350,430)(351,436)(352,435)(353,441)(354,440)
(355,439)(356,438)(357,437)(358,443)(359,442)(360,448)(361,447)(362,446)
(363,445)(364,444)(365,394)(366,393)(367,399)(368,398)(369,397)(370,396)
(371,395)(372,401)(373,400)(374,406)(375,405)(376,404)(377,403)(378,402)
(379,408)(380,407)(381,413)(382,412)(383,411)(384,410)(385,409)(386,415)
(387,414)(388,420)(389,419)(390,418)(391,417)(392,416)(449,562)(450,561)
(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)
(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)
(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)
(475,585)(476,584)(477,597)(478,596)(479,602)(480,601)(481,600)(482,599)
(483,598)(484,590)(485,589)(486,595)(487,594)(488,593)(489,592)(490,591)
(491,611)(492,610)(493,616)(494,615)(495,614)(496,613)(497,612)(498,604)
(499,603)(500,609)(501,608)(502,607)(503,606)(504,605)(505,632)(506,631)
(507,637)(508,636)(509,635)(510,634)(511,633)(512,639)(513,638)(514,644)
(515,643)(516,642)(517,641)(518,640)(519,618)(520,617)(521,623)(522,622)
(523,621)(524,620)(525,619)(526,625)(527,624)(528,630)(529,629)(530,628)
(531,627)(532,626)(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)
(539,668)(540,660)(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)
(547,653)(548,652)(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)
(555,645)(556,651)(557,650)(558,649)(559,648)(560,647)(673,856)(674,855)
(675,861)(676,860)(677,859)(678,858)(679,857)(680,863)(681,862)(682,868)
(683,867)(684,866)(685,865)(686,864)(687,842)(688,841)(689,847)(690,846)
(691,845)(692,844)(693,843)(694,849)(695,848)(696,854)(697,853)(698,852)
(699,851)(700,850)(701,891)(702,890)(703,896)(704,895)(705,894)(706,893)
(707,892)(708,884)(709,883)(710,889)(711,888)(712,887)(713,886)(714,885)
(715,877)(716,876)(717,882)(718,881)(719,880)(720,879)(721,878)(722,870)
(723,869)(724,875)(725,874)(726,873)(727,872)(728,871)(729,800)(730,799)
(731,805)(732,804)(733,803)(734,802)(735,801)(736,807)(737,806)(738,812)
(739,811)(740,810)(741,809)(742,808)(743,786)(744,785)(745,791)(746,790)
(747,789)(748,788)(749,787)(750,793)(751,792)(752,798)(753,797)(754,796)
(755,795)(756,794)(757,835)(758,834)(759,840)(760,839)(761,838)(762,837)
(763,836)(764,828)(765,827)(766,833)(767,832)(768,831)(769,830)(770,829)
(771,821)(772,820)(773,826)(774,825)(775,824)(776,823)(777,822)(778,814)
(779,813)(780,819)(781,818)(782,817)(783,816)(784,815);;
s2 := (  1,673)(  2,674)(  3,675)(  4,676)(  5,677)(  6,678)(  7,679)(  8,680)
(  9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)( 16,688)
( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)( 24,696)
( 25,697)( 26,698)( 27,699)( 28,700)( 29,708)( 30,709)( 31,710)( 32,711)
( 33,712)( 34,713)( 35,714)( 36,701)( 37,702)( 38,703)( 39,704)( 40,705)
( 41,706)( 42,707)( 43,722)( 44,723)( 45,724)( 46,725)( 47,726)( 48,727)
( 49,728)( 50,715)( 51,716)( 52,717)( 53,718)( 54,719)( 55,720)( 56,721)
( 57,729)( 58,730)( 59,731)( 60,732)( 61,733)( 62,734)( 63,735)( 64,736)
( 65,737)( 66,738)( 67,739)( 68,740)( 69,741)( 70,742)( 71,743)( 72,744)
( 73,745)( 74,746)( 75,747)( 76,748)( 77,749)( 78,750)( 79,751)( 80,752)
( 81,753)( 82,754)( 83,755)( 84,756)( 85,764)( 86,765)( 87,766)( 88,767)
( 89,768)( 90,769)( 91,770)( 92,757)( 93,758)( 94,759)( 95,760)( 96,761)
( 97,762)( 98,763)( 99,778)(100,779)(101,780)(102,781)(103,782)(104,783)
(105,784)(106,771)(107,772)(108,773)(109,774)(110,775)(111,776)(112,777)
(113,827)(114,828)(115,829)(116,830)(117,831)(118,832)(119,833)(120,834)
(121,835)(122,836)(123,837)(124,838)(125,839)(126,840)(127,813)(128,814)
(129,815)(130,816)(131,817)(132,818)(133,819)(134,820)(135,821)(136,822)
(137,823)(138,824)(139,825)(140,826)(141,799)(142,800)(143,801)(144,802)
(145,803)(146,804)(147,805)(148,806)(149,807)(150,808)(151,809)(152,810)
(153,811)(154,812)(155,785)(156,786)(157,787)(158,788)(159,789)(160,790)
(161,791)(162,792)(163,793)(164,794)(165,795)(166,796)(167,797)(168,798)
(169,883)(170,884)(171,885)(172,886)(173,887)(174,888)(175,889)(176,890)
(177,891)(178,892)(179,893)(180,894)(181,895)(182,896)(183,869)(184,870)
(185,871)(186,872)(187,873)(188,874)(189,875)(190,876)(191,877)(192,878)
(193,879)(194,880)(195,881)(196,882)(197,855)(198,856)(199,857)(200,858)
(201,859)(202,860)(203,861)(204,862)(205,863)(206,864)(207,865)(208,866)
(209,867)(210,868)(211,841)(212,842)(213,843)(214,844)(215,845)(216,846)
(217,847)(218,848)(219,849)(220,850)(221,851)(222,852)(223,853)(224,854)
(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)(232,456)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464)
(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)(248,472)
(249,473)(250,474)(251,475)(252,476)(253,484)(254,485)(255,486)(256,487)
(257,488)(258,489)(259,490)(260,477)(261,478)(262,479)(263,480)(264,481)
(265,482)(266,483)(267,498)(268,499)(269,500)(270,501)(271,502)(272,503)
(273,504)(274,491)(275,492)(276,493)(277,494)(278,495)(279,496)(280,497)
(281,505)(282,506)(283,507)(284,508)(285,509)(286,510)(287,511)(288,512)
(289,513)(290,514)(291,515)(292,516)(293,517)(294,518)(295,519)(296,520)
(297,521)(298,522)(299,523)(300,524)(301,525)(302,526)(303,527)(304,528)
(305,529)(306,530)(307,531)(308,532)(309,540)(310,541)(311,542)(312,543)
(313,544)(314,545)(315,546)(316,533)(317,534)(318,535)(319,536)(320,537)
(321,538)(322,539)(323,554)(324,555)(325,556)(326,557)(327,558)(328,559)
(329,560)(330,547)(331,548)(332,549)(333,550)(334,551)(335,552)(336,553)
(337,603)(338,604)(339,605)(340,606)(341,607)(342,608)(343,609)(344,610)
(345,611)(346,612)(347,613)(348,614)(349,615)(350,616)(351,589)(352,590)
(353,591)(354,592)(355,593)(356,594)(357,595)(358,596)(359,597)(360,598)
(361,599)(362,600)(363,601)(364,602)(365,575)(366,576)(367,577)(368,578)
(369,579)(370,580)(371,581)(372,582)(373,583)(374,584)(375,585)(376,586)
(377,587)(378,588)(379,561)(380,562)(381,563)(382,564)(383,565)(384,566)
(385,567)(386,568)(387,569)(388,570)(389,571)(390,572)(391,573)(392,574)
(393,659)(394,660)(395,661)(396,662)(397,663)(398,664)(399,665)(400,666)
(401,667)(402,668)(403,669)(404,670)(405,671)(406,672)(407,645)(408,646)
(409,647)(410,648)(411,649)(412,650)(413,651)(414,652)(415,653)(416,654)
(417,655)(418,656)(419,657)(420,658)(421,631)(422,632)(423,633)(424,634)
(425,635)(426,636)(427,637)(428,638)(429,639)(430,640)(431,641)(432,642)
(433,643)(434,644)(435,617)(436,618)(437,619)(438,620)(439,621)(440,622)
(441,623)(442,624)(443,625)(444,626)(445,627)(446,628)(447,629)(448,630);;
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 ];;
poly := F / rels;;

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

References : None.
to this polytope