Polytope of Type {112,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {112,4}*1792b
if this polytope has a name.
Group : SmallGroup(1792,81735)
Rank : 3
Schlafli Type : {112,4}
Number of vertices, edges, etc : 224, 448, 8
Order of s₀s₁s₂ : 112
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {56,4}*896a
   4-fold quotients : {56,4}*448a, {28,4}*448, {56,4}*448b
   7-fold quotients : {16,4}*256b
   8-fold quotients : {28,4}*224, {56,2}*224
   14-fold quotients : {8,4}*128a
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*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)
( 57,526)( 58,532)( 59,531)( 60,530)( 61,529)( 62,528)( 63,527)( 64,519)
( 65,525)( 66,524)( 67,523)( 68,522)( 69,521)( 70,520)( 71,512)( 72,518)
( 73,517)( 74,516)( 75,515)( 76,514)( 77,513)( 78,505)( 79,511)( 80,510)
( 81,509)( 82,508)( 83,507)( 84,506)( 85,547)( 86,553)( 87,552)( 88,551)
( 89,550)( 90,549)( 91,548)( 92,554)( 93,560)( 94,559)( 95,558)( 96,557)
( 97,556)( 98,555)( 99,533)(100,539)(101,538)(102,537)(103,536)(104,535)
(105,534)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)(112,541)
(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)
(169,666)(170,672)(171,671)(172,670)(173,669)(174,668)(175,667)(176,659)
(177,665)(178,664)(179,663)(180,662)(181,661)(182,660)(183,652)(184,658)
(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)(192,650)
(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)(200,642)
(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)(208,634)
(209,633)(210,632)(211,624)(212,630)(213,629)(214,628)(215,627)(216,626)
(217,625)(218,617)(219,623)(220,622)(221,621)(222,620)(223,619)(224,618)
(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)
(281,750)(282,756)(283,755)(284,754)(285,753)(286,752)(287,751)(288,743)
(289,749)(290,748)(291,747)(292,746)(293,745)(294,744)(295,736)(296,742)
(297,741)(298,740)(299,739)(300,738)(301,737)(302,729)(303,735)(304,734)
(305,733)(306,732)(307,731)(308,730)(309,771)(310,777)(311,776)(312,775)
(313,774)(314,773)(315,772)(316,778)(317,784)(318,783)(319,782)(320,781)
(321,780)(322,779)(323,757)(324,763)(325,762)(326,761)(327,760)(328,759)
(329,758)(330,764)(331,770)(332,769)(333,768)(334,767)(335,766)(336,765)
(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)
(393,890)(394,896)(395,895)(396,894)(397,893)(398,892)(399,891)(400,883)
(401,889)(402,888)(403,887)(404,886)(405,885)(406,884)(407,876)(408,882)
(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)(416,874)
(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)(424,866)
(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)(432,858)
(433,857)(434,856)(435,848)(436,854)(437,853)(438,852)(439,851)(440,850)
(441,849)(442,841)(443,847)(444,846)(445,845)(446,844)(447,843)(448,842);;
s1 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 23)( 16, 22)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 37)( 30, 36)( 31, 42)
( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 44)( 45, 49)( 46, 48)( 50, 51)
( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)
( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85, 93)
( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)(101,105)
(102,104)(106,107)(108,112)(109,111)(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)(127,163)(128,162)(129,168)(130,167)(131,166)(132,165)
(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)(140,157)
(169,198)(170,197)(171,203)(172,202)(173,201)(174,200)(175,199)(176,205)
(177,204)(178,210)(179,209)(180,208)(181,207)(182,206)(183,219)(184,218)
(185,224)(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)(192,217)
(193,216)(194,215)(195,214)(196,213)(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)(239,303)(240,302)(241,308)(242,307)(243,306)(244,305)
(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)(252,297)
(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)(267,324)(268,323)
(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)(276,336)
(277,335)(278,334)(279,333)(280,332)(337,429)(338,428)(339,434)(340,433)
(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)(348,425)
(349,424)(350,423)(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)
(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)(372,394)
(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(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)(463,583)(464,582)(465,588)(466,587)(467,586)(468,585)
(469,584)(470,576)(471,575)(472,581)(473,580)(474,579)(475,578)(476,577)
(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)(491,604)(492,603)
(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)(500,616)
(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)(508,622)
(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)
(517,627)(518,626)(519,639)(520,638)(521,644)(522,643)(523,642)(524,641)
(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)(532,633)
(533,653)(534,652)(535,658)(536,657)(537,656)(538,655)(539,654)(540,646)
(541,645)(542,651)(543,650)(544,649)(545,648)(546,647)(547,660)(548,659)
(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)
(557,671)(558,670)(559,669)(560,668)(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)(687,849)(688,848)(689,854)(690,853)(691,852)(692,851)
(693,850)(694,842)(695,841)(696,847)(697,846)(698,845)(699,844)(700,843)
(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)(715,870)(716,869)
(717,875)(718,874)(719,873)(720,872)(721,871)(722,877)(723,876)(724,882)
(725,881)(726,880)(727,879)(728,878)(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)(743,793)(744,792)(745,798)(746,797)(747,796)(748,795)
(749,794)(750,786)(751,785)(752,791)(753,790)(754,789)(755,788)(756,787)
(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)(771,814)(772,813)
(773,819)(774,818)(775,817)(776,816)(777,815)(778,821)(779,820)(780,826)
(781,825)(782,824)(783,823)(784,822);;
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)
( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)
( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)
( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)
( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)( 88,312)
( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)( 96,320)
( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(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)
(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)
(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)
(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)
(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)(200,438)
(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)
(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)(216,426)
(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)
(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)
(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)(512,736)
(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)(520,744)
(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)(528,752)
(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)(536,760)
(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)(544,768)
(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)(552,776)
(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)(560,784)
(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)
(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)(624,862)
(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)(632,842)
(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)(640,850)
(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)(648,886)
(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)(656,894)
(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)(664,874)
(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)(672,882);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 ];;
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)( 57,526)( 58,532)( 59,531)( 60,530)( 61,529)( 62,528)( 63,527)
( 64,519)( 65,525)( 66,524)( 67,523)( 68,522)( 69,521)( 70,520)( 71,512)
( 72,518)( 73,517)( 74,516)( 75,515)( 76,514)( 77,513)( 78,505)( 79,511)
( 80,510)( 81,509)( 82,508)( 83,507)( 84,506)( 85,547)( 86,553)( 87,552)
( 88,551)( 89,550)( 90,549)( 91,548)( 92,554)( 93,560)( 94,559)( 95,558)
( 96,557)( 97,556)( 98,555)( 99,533)(100,539)(101,538)(102,537)(103,536)
(104,535)(105,534)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)
(112,541)(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)(169,666)(170,672)(171,671)(172,670)(173,669)(174,668)(175,667)
(176,659)(177,665)(178,664)(179,663)(180,662)(181,661)(182,660)(183,652)
(184,658)(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)
(192,650)(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)
(200,642)(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)
(208,634)(209,633)(210,632)(211,624)(212,630)(213,629)(214,628)(215,627)
(216,626)(217,625)(218,617)(219,623)(220,622)(221,621)(222,620)(223,619)
(224,618)(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)(281,750)(282,756)(283,755)(284,754)(285,753)(286,752)(287,751)
(288,743)(289,749)(290,748)(291,747)(292,746)(293,745)(294,744)(295,736)
(296,742)(297,741)(298,740)(299,739)(300,738)(301,737)(302,729)(303,735)
(304,734)(305,733)(306,732)(307,731)(308,730)(309,771)(310,777)(311,776)
(312,775)(313,774)(314,773)(315,772)(316,778)(317,784)(318,783)(319,782)
(320,781)(321,780)(322,779)(323,757)(324,763)(325,762)(326,761)(327,760)
(328,759)(329,758)(330,764)(331,770)(332,769)(333,768)(334,767)(335,766)
(336,765)(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)(393,890)(394,896)(395,895)(396,894)(397,893)(398,892)(399,891)
(400,883)(401,889)(402,888)(403,887)(404,886)(405,885)(406,884)(407,876)
(408,882)(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)
(416,874)(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)
(424,866)(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)
(432,858)(433,857)(434,856)(435,848)(436,854)(437,853)(438,852)(439,851)
(440,850)(441,849)(442,841)(443,847)(444,846)(445,845)(446,844)(447,843)
(448,842);
s1 := Sym(896)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 23)
( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 37)( 30, 36)
( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 44)( 45, 49)( 46, 48)
( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)
( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)
(101,105)(102,104)(106,107)(108,112)(109,111)(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)(127,163)(128,162)(129,168)(130,167)(131,166)
(132,165)(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)
(140,157)(169,198)(170,197)(171,203)(172,202)(173,201)(174,200)(175,199)
(176,205)(177,204)(178,210)(179,209)(180,208)(181,207)(182,206)(183,219)
(184,218)(185,224)(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)
(192,217)(193,216)(194,215)(195,214)(196,213)(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)(239,303)(240,302)(241,308)(242,307)(243,306)
(244,305)(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)
(252,297)(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)(267,324)
(268,323)(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)
(276,336)(277,335)(278,334)(279,333)(280,332)(337,429)(338,428)(339,434)
(340,433)(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)
(348,425)(349,424)(350,423)(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)(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)
(372,394)(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(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)(463,583)(464,582)(465,588)(466,587)(467,586)
(468,585)(469,584)(470,576)(471,575)(472,581)(473,580)(474,579)(475,578)
(476,577)(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)(491,604)
(492,603)(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)
(500,616)(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)
(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)
(516,628)(517,627)(518,626)(519,639)(520,638)(521,644)(522,643)(523,642)
(524,641)(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)
(532,633)(533,653)(534,652)(535,658)(536,657)(537,656)(538,655)(539,654)
(540,646)(541,645)(542,651)(543,650)(544,649)(545,648)(546,647)(547,660)
(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)
(556,672)(557,671)(558,670)(559,669)(560,668)(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)(687,849)(688,848)(689,854)(690,853)(691,852)
(692,851)(693,850)(694,842)(695,841)(696,847)(697,846)(698,845)(699,844)
(700,843)(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)(715,870)
(716,869)(717,875)(718,874)(719,873)(720,872)(721,871)(722,877)(723,876)
(724,882)(725,881)(726,880)(727,879)(728,878)(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)(743,793)(744,792)(745,798)(746,797)(747,796)
(748,795)(749,794)(750,786)(751,785)(752,791)(753,790)(754,789)(755,788)
(756,787)(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)(771,814)
(772,813)(773,819)(774,818)(775,817)(776,816)(777,815)(778,821)(779,820)
(780,826)(781,825)(782,824)(783,823)(784,822);
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)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)
( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)
( 72,296)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)
( 80,304)( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)
( 88,312)( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)
( 96,320)( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(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)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)
(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)
(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)
(192,402)(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)
(200,438)(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)
(208,446)(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)
(216,426)(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)
(224,434)(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)(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)
(512,736)(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)
(520,744)(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)
(528,752)(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)
(536,760)(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)
(544,768)(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)
(552,776)(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)
(560,784)(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)(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)
(624,862)(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)
(632,842)(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)
(640,850)(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)
(648,886)(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)
(656,894)(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)
(664,874)(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)
(672,882);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 >;

References : None.
to this polytope