Polytope of Type {112,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {112,8}*1792c
if this polytope has a name.
Group : SmallGroup(1792,82994)
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}*896a
   4-fold quotients : {56,4}*448a, {28,8}*448b, {112,2}*448
   7-fold quotients : {16,8}*256c
   8-fold quotients : {28,4}*224, {56,2}*224
   14-fold quotients : {8,8}*128c, {16,4}*128a
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {8,4}*64a, {4,8}*64b, {16,2}*64
   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, 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 := (  1,225)(  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)
( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)
( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)( 72,282)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)
( 81,291)( 82,292)( 83,293)( 84,294)( 85,323)( 86,324)( 87,325)( 88,326)
( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)( 96,334)
( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)(104,314)
(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)
(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)
(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)
(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)
(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)
(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)
(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)
(505,743)(506,744)(507,745)(508,746)(509,747)(510,748)(511,749)(512,750)
(513,751)(514,752)(515,753)(516,754)(517,755)(518,756)(519,729)(520,730)
(521,731)(522,732)(523,733)(524,734)(525,735)(526,736)(527,737)(528,738)
(529,739)(530,740)(531,741)(532,742)(533,771)(534,772)(535,773)(536,774)
(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)(544,782)
(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)(552,762)
(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)(560,770)
(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)
(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)(624,848)
(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)(632,856)
(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)(640,864)
(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)(648,872)
(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)(656,880)
(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)(664,888)
(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)(672,896);;
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*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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)!(  1,449)(  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, 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)!(  1,225)(  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)( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)
( 64,302)( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)
( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)
( 80,290)( 81,291)( 82,292)( 83,293)( 84,294)( 85,323)( 86,324)( 87,325)
( 88,326)( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)
( 96,334)( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)
(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)
(112,322)(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)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)
(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)
(184,408)(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)
(192,416)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)
(208,432)(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448)(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)(505,743)(506,744)(507,745)(508,746)(509,747)(510,748)(511,749)
(512,750)(513,751)(514,752)(515,753)(516,754)(517,755)(518,756)(519,729)
(520,730)(521,731)(522,732)(523,733)(524,734)(525,735)(526,736)(527,737)
(528,738)(529,739)(530,740)(531,741)(532,742)(533,771)(534,772)(535,773)
(536,774)(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)
(544,782)(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)
(552,762)(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)
(560,770)(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)(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)
(624,848)(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)
(632,856)(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)
(640,864)(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)
(648,872)(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)
(656,880)(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)
(664,888)(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)
(672,896);
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*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*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