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Polytope of Type {8,112}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,112}*1792e
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}*896a, {4,112}*896b
   4-fold quotients : {4,56}*448a, {8,28}*448b
   7-fold quotients : {8,16}*256e
   8-fold quotients : {4,28}*224, {2,56}*224
   14-fold quotients : {8,8}*128a, {4,16}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {4,8}*64a, {8,4}*64b
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {2,8}*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 := (  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)(  8,457)
(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,464)( 16,463)
( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)( 24,476)
( 25,475)( 26,474)( 27,473)( 28,472)( 29,485)( 30,484)( 31,490)( 32,489)
( 33,488)( 34,487)( 35,486)( 36,478)( 37,477)( 38,483)( 39,482)( 40,481)
( 41,480)( 42,479)( 43,499)( 44,498)( 45,504)( 46,503)( 47,502)( 48,501)
( 49,500)( 50,492)( 51,491)( 52,497)( 53,496)( 54,495)( 55,494)( 56,493)
( 57,520)( 58,519)( 59,525)( 60,524)( 61,523)( 62,522)( 63,521)( 64,527)
( 65,526)( 66,532)( 67,531)( 68,530)( 69,529)( 70,528)( 71,506)( 72,505)
( 73,511)( 74,510)( 75,509)( 76,508)( 77,507)( 78,513)( 79,512)( 80,518)
( 81,517)( 82,516)( 83,515)( 84,514)( 85,555)( 86,554)( 87,560)( 88,559)
( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)( 96,551)
( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)(104,543)
(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)(112,535)
(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)(120,597)
(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)(128,603)
(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)(136,616)
(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)(144,566)
(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)(152,572)
(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)(160,578)
(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)(168,584)
(169,660)(170,659)(171,665)(172,664)(173,663)(174,662)(175,661)(176,667)
(177,666)(178,672)(179,671)(180,670)(181,669)(182,668)(183,646)(184,645)
(185,651)(186,650)(187,649)(188,648)(189,647)(190,653)(191,652)(192,658)
(193,657)(194,656)(195,655)(196,654)(197,632)(198,631)(199,637)(200,636)
(201,635)(202,634)(203,633)(204,639)(205,638)(206,644)(207,643)(208,642)
(209,641)(210,640)(211,618)(212,617)(213,623)(214,622)(215,621)(216,620)
(217,619)(218,625)(219,624)(220,630)(221,629)(222,628)(223,627)(224,626)
(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)(232,681)
(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,688)(240,687)
(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)(248,700)
(249,699)(250,698)(251,697)(252,696)(253,709)(254,708)(255,714)(256,713)
(257,712)(258,711)(259,710)(260,702)(261,701)(262,707)(263,706)(264,705)
(265,704)(266,703)(267,723)(268,722)(269,728)(270,727)(271,726)(272,725)
(273,724)(274,716)(275,715)(276,721)(277,720)(278,719)(279,718)(280,717)
(281,744)(282,743)(283,749)(284,748)(285,747)(286,746)(287,745)(288,751)
(289,750)(290,756)(291,755)(292,754)(293,753)(294,752)(295,730)(296,729)
(297,735)(298,734)(299,733)(300,732)(301,731)(302,737)(303,736)(304,742)
(305,741)(306,740)(307,739)(308,738)(309,779)(310,778)(311,784)(312,783)
(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)(320,775)
(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)(328,767)
(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)(336,759)
(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)(344,821)
(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)(352,827)
(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)(360,840)
(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)(368,790)
(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)(376,796)
(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)(384,802)
(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)(392,808)
(393,884)(394,883)(395,889)(396,888)(397,887)(398,886)(399,885)(400,891)
(401,890)(402,896)(403,895)(404,894)(405,893)(406,892)(407,870)(408,869)
(409,875)(410,874)(411,873)(412,872)(413,871)(414,877)(415,876)(416,882)
(417,881)(418,880)(419,879)(420,878)(421,856)(422,855)(423,861)(424,860)
(425,859)(426,858)(427,857)(428,863)(429,862)(430,868)(431,867)(432,866)
(433,865)(434,864)(435,842)(436,841)(437,847)(438,846)(439,845)(440,844)
(441,843)(442,849)(443,848)(444,854)(445,853)(446,852)(447,851)(448,850);;
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, 
s1*s0*s2*s1*s0*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*s2*s1*s2*s0*s1*s2*s1*s2 ];;
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)!(  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)
(  8,457)(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,464)
( 16,463)( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)
( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 29,485)( 30,484)( 31,490)
( 32,489)( 33,488)( 34,487)( 35,486)( 36,478)( 37,477)( 38,483)( 39,482)
( 40,481)( 41,480)( 42,479)( 43,499)( 44,498)( 45,504)( 46,503)( 47,502)
( 48,501)( 49,500)( 50,492)( 51,491)( 52,497)( 53,496)( 54,495)( 55,494)
( 56,493)( 57,520)( 58,519)( 59,525)( 60,524)( 61,523)( 62,522)( 63,521)
( 64,527)( 65,526)( 66,532)( 67,531)( 68,530)( 69,529)( 70,528)( 71,506)
( 72,505)( 73,511)( 74,510)( 75,509)( 76,508)( 77,507)( 78,513)( 79,512)
( 80,518)( 81,517)( 82,516)( 83,515)( 84,514)( 85,555)( 86,554)( 87,560)
( 88,559)( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)
( 96,551)( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)
(104,543)(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)
(112,535)(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)
(120,597)(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)
(128,603)(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)
(136,616)(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)
(144,566)(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)
(152,572)(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)
(160,578)(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)
(168,584)(169,660)(170,659)(171,665)(172,664)(173,663)(174,662)(175,661)
(176,667)(177,666)(178,672)(179,671)(180,670)(181,669)(182,668)(183,646)
(184,645)(185,651)(186,650)(187,649)(188,648)(189,647)(190,653)(191,652)
(192,658)(193,657)(194,656)(195,655)(196,654)(197,632)(198,631)(199,637)
(200,636)(201,635)(202,634)(203,633)(204,639)(205,638)(206,644)(207,643)
(208,642)(209,641)(210,640)(211,618)(212,617)(213,623)(214,622)(215,621)
(216,620)(217,619)(218,625)(219,624)(220,630)(221,629)(222,628)(223,627)
(224,626)(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)
(232,681)(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,688)
(240,687)(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)
(248,700)(249,699)(250,698)(251,697)(252,696)(253,709)(254,708)(255,714)
(256,713)(257,712)(258,711)(259,710)(260,702)(261,701)(262,707)(263,706)
(264,705)(265,704)(266,703)(267,723)(268,722)(269,728)(270,727)(271,726)
(272,725)(273,724)(274,716)(275,715)(276,721)(277,720)(278,719)(279,718)
(280,717)(281,744)(282,743)(283,749)(284,748)(285,747)(286,746)(287,745)
(288,751)(289,750)(290,756)(291,755)(292,754)(293,753)(294,752)(295,730)
(296,729)(297,735)(298,734)(299,733)(300,732)(301,731)(302,737)(303,736)
(304,742)(305,741)(306,740)(307,739)(308,738)(309,779)(310,778)(311,784)
(312,783)(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)
(320,775)(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)
(328,767)(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)
(336,759)(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)
(344,821)(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)
(352,827)(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)
(360,840)(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)
(368,790)(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)
(376,796)(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)
(384,802)(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)
(392,808)(393,884)(394,883)(395,889)(396,888)(397,887)(398,886)(399,885)
(400,891)(401,890)(402,896)(403,895)(404,894)(405,893)(406,892)(407,870)
(408,869)(409,875)(410,874)(411,873)(412,872)(413,871)(414,877)(415,876)
(416,882)(417,881)(418,880)(419,879)(420,878)(421,856)(422,855)(423,861)
(424,860)(425,859)(426,858)(427,857)(428,863)(429,862)(430,868)(431,867)
(432,866)(433,865)(434,864)(435,842)(436,841)(437,847)(438,846)(439,845)
(440,844)(441,843)(442,849)(443,848)(444,854)(445,853)(446,852)(447,851)
(448,850);
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, 
s1*s0*s2*s1*s0*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*s2*s1*s2*s0*s1*s2*s1*s2 >; 
 
References : None.
to this polytope