Polytope of Type {8,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792c
if this polytope has a name.
Group : SmallGroup(1792,81632)
Rank : 3
Schlafli Type : {8,56}
Number of vertices, edges, etc : 16, 448, 112
Order of s₀s₁s₂ : 56
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {8,28}*896a, {4,56}*896b
   4-fold quotients : {4,28}*448, {8,28}*448a, {8,28}*448b
   7-fold quotients : {8,8}*256d
   8-fold quotients : {4,28}*224, {8,14}*224
   14-fold quotients : {8,4}*128a, {4,8}*128b
   16-fold quotients : {2,28}*112, {4,14}*112
   28-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {8,2}*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 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)
(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)
( 25,473)( 26,474)( 27,475)( 28,476)( 29,477)( 30,478)( 31,479)( 32,480)
( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)
( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)
( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,526)( 58,527)( 59,528)( 60,529)( 61,530)( 62,531)( 63,532)( 64,519)
( 65,520)( 66,521)( 67,522)( 68,523)( 69,524)( 70,525)( 71,512)( 72,513)
( 73,514)( 74,515)( 75,516)( 76,517)( 77,518)( 78,505)( 79,506)( 80,507)
( 81,508)( 82,509)( 83,510)( 84,511)( 85,554)( 86,555)( 87,556)( 88,557)
( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)
( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)
(113,589)(114,590)(115,591)(116,592)(117,593)(118,594)(119,595)(120,596)
(121,597)(122,598)(123,599)(124,600)(125,601)(126,602)(127,603)(128,604)
(129,605)(130,606)(131,607)(132,608)(133,609)(134,610)(135,611)(136,612)
(137,613)(138,614)(139,615)(140,616)(141,561)(142,562)(143,563)(144,564)
(145,565)(146,566)(147,567)(148,568)(149,569)(150,570)(151,571)(152,572)
(153,573)(154,574)(155,575)(156,576)(157,577)(158,578)(159,579)(160,580)
(161,581)(162,582)(163,583)(164,584)(165,585)(166,586)(167,587)(168,588)
(169,666)(170,667)(171,668)(172,669)(173,670)(174,671)(175,672)(176,659)
(177,660)(178,661)(179,662)(180,663)(181,664)(182,665)(183,652)(184,653)
(185,654)(186,655)(187,656)(188,657)(189,658)(190,645)(191,646)(192,647)
(193,648)(194,649)(195,650)(196,651)(197,638)(198,639)(199,640)(200,641)
(201,642)(202,643)(203,644)(204,631)(205,632)(206,633)(207,634)(208,635)
(209,636)(210,637)(211,624)(212,625)(213,626)(214,627)(215,628)(216,629)
(217,630)(218,617)(219,618)(220,619)(221,620)(222,621)(223,622)(224,623)
(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)
(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,687)(240,688)
(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)
(249,697)(250,698)(251,699)(252,700)(253,701)(254,702)(255,703)(256,704)
(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)(264,712)
(265,713)(266,714)(267,715)(268,716)(269,717)(270,718)(271,719)(272,720)
(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)(280,728)
(281,750)(282,751)(283,752)(284,753)(285,754)(286,755)(287,756)(288,743)
(289,744)(290,745)(291,746)(292,747)(293,748)(294,749)(295,736)(296,737)
(297,738)(298,739)(299,740)(300,741)(301,742)(302,729)(303,730)(304,731)
(305,732)(306,733)(307,734)(308,735)(309,778)(310,779)(311,780)(312,781)
(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)
(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)
(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)
(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)(344,820)
(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,827)(352,828)
(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)(360,836)
(361,837)(362,838)(363,839)(364,840)(365,785)(366,786)(367,787)(368,788)
(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)(376,796)
(377,797)(378,798)(379,799)(380,800)(381,801)(382,802)(383,803)(384,804)
(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)(392,812)
(393,890)(394,891)(395,892)(396,893)(397,894)(398,895)(399,896)(400,883)
(401,884)(402,885)(403,886)(404,887)(405,888)(406,889)(407,876)(408,877)
(409,878)(410,879)(411,880)(412,881)(413,882)(414,869)(415,870)(416,871)
(417,872)(418,873)(419,874)(420,875)(421,862)(422,863)(423,864)(424,865)
(425,866)(426,867)(427,868)(428,855)(429,856)(430,857)(431,858)(432,859)
(433,860)(434,861)(435,848)(436,849)(437,850)(438,851)(439,852)(440,853)
(441,854)(442,841)(443,842)(444,843)(445,844)(446,845)(447,846)(448,847);;
s1 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)
( 63, 65)( 72, 77)( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 85, 92)
( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)(100,105)(101,104)
(102,103)(107,112)(108,111)(109,110)(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)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)
(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(169,204)(170,210)(171,209)(172,208)(173,207)(174,206)(175,205)(176,197)
(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(183,211)(184,217)
(185,216)(186,215)(187,214)(188,213)(189,212)(190,218)(191,224)(192,223)
(193,222)(194,221)(195,220)(196,219)(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)(239,302)(240,308)(241,307)(242,306)(243,305)(244,304)
(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)
(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,316)
(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(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)(337,428)(338,434)(339,433)(340,432)
(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)(348,424)
(349,423)(350,422)(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)
(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)(372,393)
(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(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)(463,582)(464,588)(465,587)(466,586)(467,585)(468,584)
(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)(476,576)
(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)
(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(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)(505,624)(506,630)(507,629)(508,628)
(509,627)(510,626)(511,625)(512,617)(513,623)(514,622)(515,621)(516,620)
(517,619)(518,618)(519,631)(520,637)(521,636)(522,635)(523,634)(524,633)
(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)
(533,652)(534,658)(535,657)(536,656)(537,655)(538,654)(539,653)(540,645)
(541,651)(542,650)(543,649)(544,648)(545,647)(546,646)(547,659)(548,665)
(549,664)(550,663)(551,662)(552,661)(553,660)(554,666)(555,672)(556,671)
(557,670)(558,669)(559,668)(560,667)(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)(687,848)(688,854)(689,853)(690,852)(691,851)(692,850)
(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)(700,842)
(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)(708,890)
(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(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)(743,792)(744,798)(745,797)(746,796)(747,795)(748,794)
(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)(756,786)
(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)(764,834)
(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(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 := (  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)(  8,233)
(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,254)( 30,253)( 31,259)( 32,258)
( 33,257)( 34,256)( 35,255)( 36,261)( 37,260)( 38,266)( 39,265)( 40,264)
( 41,263)( 42,262)( 43,268)( 44,267)( 45,273)( 46,272)( 47,271)( 48,270)
( 49,269)( 50,275)( 51,274)( 52,280)( 53,279)( 54,278)( 55,277)( 56,276)
( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)( 64,282)
( 65,281)( 66,287)( 67,286)( 68,285)( 69,284)( 70,283)( 71,303)( 72,302)
( 73,308)( 74,307)( 75,306)( 76,305)( 77,304)( 78,296)( 79,295)( 80,301)
( 81,300)( 82,299)( 83,298)( 84,297)( 85,317)( 86,316)( 87,322)( 88,321)
( 89,320)( 90,319)( 91,318)( 92,310)( 93,309)( 94,315)( 95,314)( 96,313)
( 97,312)( 98,311)( 99,331)(100,330)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,324)(107,323)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,352)(114,351)(115,357)(116,356)(117,355)(118,354)(119,353)(120,359)
(121,358)(122,364)(123,363)(124,362)(125,361)(126,360)(127,338)(128,337)
(129,343)(130,342)(131,341)(132,340)(133,339)(134,345)(135,344)(136,350)
(137,349)(138,348)(139,347)(140,346)(141,380)(142,379)(143,385)(144,384)
(145,383)(146,382)(147,381)(148,387)(149,386)(150,392)(151,391)(152,390)
(153,389)(154,388)(155,366)(156,365)(157,371)(158,370)(159,369)(160,368)
(161,367)(162,373)(163,372)(164,378)(165,377)(166,376)(167,375)(168,374)
(169,415)(170,414)(171,420)(172,419)(173,418)(174,417)(175,416)(176,408)
(177,407)(178,413)(179,412)(180,411)(181,410)(182,409)(183,401)(184,400)
(185,406)(186,405)(187,404)(188,403)(189,402)(190,394)(191,393)(192,399)
(193,398)(194,397)(195,396)(196,395)(197,443)(198,442)(199,448)(200,447)
(201,446)(202,445)(203,444)(204,436)(205,435)(206,441)(207,440)(208,439)
(209,438)(210,437)(211,429)(212,428)(213,434)(214,433)(215,432)(216,431)
(217,430)(218,422)(219,421)(220,427)(221,426)(222,425)(223,424)(224,423)
(449,674)(450,673)(451,679)(452,678)(453,677)(454,676)(455,675)(456,681)
(457,680)(458,686)(459,685)(460,684)(461,683)(462,682)(463,688)(464,687)
(465,693)(466,692)(467,691)(468,690)(469,689)(470,695)(471,694)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,702)(478,701)(479,707)(480,706)
(481,705)(482,704)(483,703)(484,709)(485,708)(486,714)(487,713)(488,712)
(489,711)(490,710)(491,716)(492,715)(493,721)(494,720)(495,719)(496,718)
(497,717)(498,723)(499,722)(500,728)(501,727)(502,726)(503,725)(504,724)
(505,737)(506,736)(507,742)(508,741)(509,740)(510,739)(511,738)(512,730)
(513,729)(514,735)(515,734)(516,733)(517,732)(518,731)(519,751)(520,750)
(521,756)(522,755)(523,754)(524,753)(525,752)(526,744)(527,743)(528,749)
(529,748)(530,747)(531,746)(532,745)(533,765)(534,764)(535,770)(536,769)
(537,768)(538,767)(539,766)(540,758)(541,757)(542,763)(543,762)(544,761)
(545,760)(546,759)(547,779)(548,778)(549,784)(550,783)(551,782)(552,781)
(553,780)(554,772)(555,771)(556,777)(557,776)(558,775)(559,774)(560,773)
(561,800)(562,799)(563,805)(564,804)(565,803)(566,802)(567,801)(568,807)
(569,806)(570,812)(571,811)(572,810)(573,809)(574,808)(575,786)(576,785)
(577,791)(578,790)(579,789)(580,788)(581,787)(582,793)(583,792)(584,798)
(585,797)(586,796)(587,795)(588,794)(589,828)(590,827)(591,833)(592,832)
(593,831)(594,830)(595,829)(596,835)(597,834)(598,840)(599,839)(600,838)
(601,837)(602,836)(603,814)(604,813)(605,819)(606,818)(607,817)(608,816)
(609,815)(610,821)(611,820)(612,826)(613,825)(614,824)(615,823)(616,822)
(617,863)(618,862)(619,868)(620,867)(621,866)(622,865)(623,864)(624,856)
(625,855)(626,861)(627,860)(628,859)(629,858)(630,857)(631,849)(632,848)
(633,854)(634,853)(635,852)(636,851)(637,850)(638,842)(639,841)(640,847)
(641,846)(642,845)(643,844)(644,843)(645,891)(646,890)(647,896)(648,895)
(649,894)(650,893)(651,892)(652,884)(653,883)(654,889)(655,888)(656,887)
(657,886)(658,885)(659,877)(660,876)(661,882)(662,881)(663,880)(664,879)
(665,878)(666,870)(667,869)(668,875)(669,874)(670,873)(671,872)(672,871);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s0*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*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*s0*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;

References : None.
to this polytope