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Polytope of Type {112,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {112,8}*1792e
if this polytope has a name.
Group : SmallGroup(1792,83050)
Rank : 3
Schlafli Type : {112,8}
Number of vertices, edges, etc : 112, 448, 8
Order of s0s1s2 : 112
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {56,8}*896a, {112,4}*896b
   4-fold quotients : {56,4}*448a, {28,8}*448b
   7-fold quotients : {16,8}*256e
   8-fold quotients : {28,4}*224, {56,2}*224
   14-fold quotients : {8,8}*128c, {16,4}*128b
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {8,4}*64a, {4,8}*64b
   32-fold quotients : {14,2}*56
   56-fold quotients : {4,4}*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 := (  1,449)(  2,455)(  3,454)(  4,453)(  5,452)(  6,451)(  7,450)(  8,456)
(  9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,463)( 16,469)
( 17,468)( 18,467)( 19,466)( 20,465)( 21,464)( 22,470)( 23,476)( 24,475)
( 25,474)( 26,473)( 27,472)( 28,471)( 29,484)( 30,490)( 31,489)( 32,488)
( 33,487)( 34,486)( 35,485)( 36,477)( 37,483)( 38,482)( 39,481)( 40,480)
( 41,479)( 42,478)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)( 48,500)
( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)( 56,492)
( 57,519)( 58,525)( 59,524)( 60,523)( 61,522)( 62,521)( 63,520)( 64,526)
( 65,532)( 66,531)( 67,530)( 68,529)( 69,528)( 70,527)( 71,505)( 72,511)
( 73,510)( 74,509)( 75,508)( 76,507)( 77,506)( 78,512)( 79,518)( 80,517)
( 81,516)( 82,515)( 83,514)( 84,513)( 85,554)( 86,560)( 87,559)( 88,558)
( 89,557)( 90,556)( 91,555)( 92,547)( 93,553)( 94,552)( 95,551)( 96,550)
( 97,549)( 98,548)( 99,540)(100,546)(101,545)(102,544)(103,543)(104,542)
(105,541)(106,533)(107,539)(108,538)(109,537)(110,536)(111,535)(112,534)
(113,589)(114,595)(115,594)(116,593)(117,592)(118,591)(119,590)(120,596)
(121,602)(122,601)(123,600)(124,599)(125,598)(126,597)(127,603)(128,609)
(129,608)(130,607)(131,606)(132,605)(133,604)(134,610)(135,616)(136,615)
(137,614)(138,613)(139,612)(140,611)(141,561)(142,567)(143,566)(144,565)
(145,564)(146,563)(147,562)(148,568)(149,574)(150,573)(151,572)(152,571)
(153,570)(154,569)(155,575)(156,581)(157,580)(158,579)(159,578)(160,577)
(161,576)(162,582)(163,588)(164,587)(165,586)(166,585)(167,584)(168,583)
(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)(176,666)
(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,645)(184,651)
(185,650)(186,649)(187,648)(188,647)(189,646)(190,652)(191,658)(192,657)
(193,656)(194,655)(195,654)(196,653)(197,631)(198,637)(199,636)(200,635)
(201,634)(202,633)(203,632)(204,638)(205,644)(206,643)(207,642)(208,641)
(209,640)(210,639)(211,617)(212,623)(213,622)(214,621)(215,620)(216,619)
(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)(224,625)
(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,680)
(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,687)(240,693)
(241,692)(242,691)(243,690)(244,689)(245,688)(246,694)(247,700)(248,699)
(249,698)(250,697)(251,696)(252,695)(253,708)(254,714)(255,713)(256,712)
(257,711)(258,710)(259,709)(260,701)(261,707)(262,706)(263,705)(264,704)
(265,703)(266,702)(267,722)(268,728)(269,727)(270,726)(271,725)(272,724)
(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)(280,716)
(281,743)(282,749)(283,748)(284,747)(285,746)(286,745)(287,744)(288,750)
(289,756)(290,755)(291,754)(292,753)(293,752)(294,751)(295,729)(296,735)
(297,734)(298,733)(299,732)(300,731)(301,730)(302,736)(303,742)(304,741)
(305,740)(306,739)(307,738)(308,737)(309,778)(310,784)(311,783)(312,782)
(313,781)(314,780)(315,779)(316,771)(317,777)(318,776)(319,775)(320,774)
(321,773)(322,772)(323,764)(324,770)(325,769)(326,768)(327,767)(328,766)
(329,765)(330,757)(331,763)(332,762)(333,761)(334,760)(335,759)(336,758)
(337,813)(338,819)(339,818)(340,817)(341,816)(342,815)(343,814)(344,820)
(345,826)(346,825)(347,824)(348,823)(349,822)(350,821)(351,827)(352,833)
(353,832)(354,831)(355,830)(356,829)(357,828)(358,834)(359,840)(360,839)
(361,838)(362,837)(363,836)(364,835)(365,785)(366,791)(367,790)(368,789)
(369,788)(370,787)(371,786)(372,792)(373,798)(374,797)(375,796)(376,795)
(377,794)(378,793)(379,799)(380,805)(381,804)(382,803)(383,802)(384,801)
(385,800)(386,806)(387,812)(388,811)(389,810)(390,809)(391,808)(392,807)
(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)(400,890)
(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,869)(408,875)
(409,874)(410,873)(411,872)(412,871)(413,870)(414,876)(415,882)(416,881)
(417,880)(418,879)(419,878)(420,877)(421,855)(422,861)(423,860)(424,859)
(425,858)(426,857)(427,856)(428,862)(429,868)(430,867)(431,866)(432,865)
(433,864)(434,863)(435,841)(436,847)(437,846)(438,845)(439,844)(440,843)
(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)(448,849);;
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, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)( 62, 81)
( 63, 80)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)
( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)
( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(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)(169,219)(170,218)(171,224)(172,223)(173,222)(174,221)
(175,220)(176,212)(177,211)(178,217)(179,216)(180,215)(181,214)(182,213)
(183,205)(184,204)(185,210)(186,209)(187,208)(188,207)(189,206)(190,198)
(191,197)(192,203)(193,202)(194,201)(195,200)(196,199)(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)(505,639)(506,638)
(507,644)(508,643)(509,642)(510,641)(511,640)(512,632)(513,631)(514,637)
(515,636)(516,635)(517,634)(518,633)(519,625)(520,624)(521,630)(522,629)
(523,628)(524,627)(525,626)(526,618)(527,617)(528,623)(529,622)(530,621)
(531,620)(532,619)(533,660)(534,659)(535,665)(536,664)(537,663)(538,662)
(539,661)(540,667)(541,666)(542,672)(543,671)(544,670)(545,669)(546,668)
(547,646)(548,645)(549,651)(550,650)(551,649)(552,648)(553,647)(554,653)
(555,652)(556,658)(557,657)(558,656)(559,655)(560,654)(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 := (  1,225)(  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);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(896)!(  1,449)(  2,455)(  3,454)(  4,453)(  5,452)(  6,451)(  7,450)
(  8,456)(  9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,463)
( 16,469)( 17,468)( 18,467)( 19,466)( 20,465)( 21,464)( 22,470)( 23,476)
( 24,475)( 25,474)( 26,473)( 27,472)( 28,471)( 29,484)( 30,490)( 31,489)
( 32,488)( 33,487)( 34,486)( 35,485)( 36,477)( 37,483)( 38,482)( 39,481)
( 40,480)( 41,479)( 42,478)( 43,498)( 44,504)( 45,503)( 46,502)( 47,501)
( 48,500)( 49,499)( 50,491)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)
( 56,492)( 57,519)( 58,525)( 59,524)( 60,523)( 61,522)( 62,521)( 63,520)
( 64,526)( 65,532)( 66,531)( 67,530)( 68,529)( 69,528)( 70,527)( 71,505)
( 72,511)( 73,510)( 74,509)( 75,508)( 76,507)( 77,506)( 78,512)( 79,518)
( 80,517)( 81,516)( 82,515)( 83,514)( 84,513)( 85,554)( 86,560)( 87,559)
( 88,558)( 89,557)( 90,556)( 91,555)( 92,547)( 93,553)( 94,552)( 95,551)
( 96,550)( 97,549)( 98,548)( 99,540)(100,546)(101,545)(102,544)(103,543)
(104,542)(105,541)(106,533)(107,539)(108,538)(109,537)(110,536)(111,535)
(112,534)(113,589)(114,595)(115,594)(116,593)(117,592)(118,591)(119,590)
(120,596)(121,602)(122,601)(123,600)(124,599)(125,598)(126,597)(127,603)
(128,609)(129,608)(130,607)(131,606)(132,605)(133,604)(134,610)(135,616)
(136,615)(137,614)(138,613)(139,612)(140,611)(141,561)(142,567)(143,566)
(144,565)(145,564)(146,563)(147,562)(148,568)(149,574)(150,573)(151,572)
(152,571)(153,570)(154,569)(155,575)(156,581)(157,580)(158,579)(159,578)
(160,577)(161,576)(162,582)(163,588)(164,587)(165,586)(166,585)(167,584)
(168,583)(169,659)(170,665)(171,664)(172,663)(173,662)(174,661)(175,660)
(176,666)(177,672)(178,671)(179,670)(180,669)(181,668)(182,667)(183,645)
(184,651)(185,650)(186,649)(187,648)(188,647)(189,646)(190,652)(191,658)
(192,657)(193,656)(194,655)(195,654)(196,653)(197,631)(198,637)(199,636)
(200,635)(201,634)(202,633)(203,632)(204,638)(205,644)(206,643)(207,642)
(208,641)(209,640)(210,639)(211,617)(212,623)(213,622)(214,621)(215,620)
(216,619)(217,618)(218,624)(219,630)(220,629)(221,628)(222,627)(223,626)
(224,625)(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,680)(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,687)
(240,693)(241,692)(242,691)(243,690)(244,689)(245,688)(246,694)(247,700)
(248,699)(249,698)(250,697)(251,696)(252,695)(253,708)(254,714)(255,713)
(256,712)(257,711)(258,710)(259,709)(260,701)(261,707)(262,706)(263,705)
(264,704)(265,703)(266,702)(267,722)(268,728)(269,727)(270,726)(271,725)
(272,724)(273,723)(274,715)(275,721)(276,720)(277,719)(278,718)(279,717)
(280,716)(281,743)(282,749)(283,748)(284,747)(285,746)(286,745)(287,744)
(288,750)(289,756)(290,755)(291,754)(292,753)(293,752)(294,751)(295,729)
(296,735)(297,734)(298,733)(299,732)(300,731)(301,730)(302,736)(303,742)
(304,741)(305,740)(306,739)(307,738)(308,737)(309,778)(310,784)(311,783)
(312,782)(313,781)(314,780)(315,779)(316,771)(317,777)(318,776)(319,775)
(320,774)(321,773)(322,772)(323,764)(324,770)(325,769)(326,768)(327,767)
(328,766)(329,765)(330,757)(331,763)(332,762)(333,761)(334,760)(335,759)
(336,758)(337,813)(338,819)(339,818)(340,817)(341,816)(342,815)(343,814)
(344,820)(345,826)(346,825)(347,824)(348,823)(349,822)(350,821)(351,827)
(352,833)(353,832)(354,831)(355,830)(356,829)(357,828)(358,834)(359,840)
(360,839)(361,838)(362,837)(363,836)(364,835)(365,785)(366,791)(367,790)
(368,789)(369,788)(370,787)(371,786)(372,792)(373,798)(374,797)(375,796)
(376,795)(377,794)(378,793)(379,799)(380,805)(381,804)(382,803)(383,802)
(384,801)(385,800)(386,806)(387,812)(388,811)(389,810)(390,809)(391,808)
(392,807)(393,883)(394,889)(395,888)(396,887)(397,886)(398,885)(399,884)
(400,890)(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,869)
(408,875)(409,874)(410,873)(411,872)(412,871)(413,870)(414,876)(415,882)
(416,881)(417,880)(418,879)(419,878)(420,877)(421,855)(422,861)(423,860)
(424,859)(425,858)(426,857)(427,856)(428,862)(429,868)(430,867)(431,866)
(432,865)(433,864)(434,863)(435,841)(436,847)(437,846)(438,845)(439,844)
(440,843)(441,842)(442,848)(443,854)(444,853)(445,852)(446,851)(447,850)
(448,849);
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, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)
( 62, 81)( 63, 80)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)
( 70, 73)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)
( 92,107)( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(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)(169,219)(170,218)(171,224)(172,223)(173,222)
(174,221)(175,220)(176,212)(177,211)(178,217)(179,216)(180,215)(181,214)
(182,213)(183,205)(184,204)(185,210)(186,209)(187,208)(188,207)(189,206)
(190,198)(191,197)(192,203)(193,202)(194,201)(195,200)(196,199)(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)(505,639)
(506,638)(507,644)(508,643)(509,642)(510,641)(511,640)(512,632)(513,631)
(514,637)(515,636)(516,635)(517,634)(518,633)(519,625)(520,624)(521,630)
(522,629)(523,628)(524,627)(525,626)(526,618)(527,617)(528,623)(529,622)
(530,621)(531,620)(532,619)(533,660)(534,659)(535,665)(536,664)(537,663)
(538,662)(539,661)(540,667)(541,666)(542,672)(543,671)(544,670)(545,669)
(546,668)(547,646)(548,645)(549,651)(550,650)(551,649)(552,648)(553,647)
(554,653)(555,652)(556,658)(557,657)(558,656)(559,655)(560,654)(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)!(  1,225)(  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);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*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 >; 
 
References : None.
to this polytope