Polytope of Type {56,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,8}*1792a
if this polytope has a name.
Group : SmallGroup(1792,58267)
Rank : 3
Schlafli Type : {56,8}
Number of vertices, edges, etc : 112, 448, 16
Order of s₀s₁s₂ : 56
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {56,4}*896a, {56,8}*896a, {56,8}*896b, {28,8}*896a, {56,8}*896c, {56,8}*896d
   4-fold quotients : {56,4}*448a, {28,4}*448, {56,4}*448b, {28,8}*448a, {28,8}*448b
   7-fold quotients : {8,8}*256a
   8-fold quotients : {28,4}*224, {56,2}*224, {14,8}*224
   14-fold quotients : {4,8}*128a, {8,4}*128a, {8,8}*128a, {8,8}*128b, {8,8}*128c, {8,8}*128d
   16-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
   32-fold quotients : {14,2}*56
   56-fold quotients : {4,4}*32, {2,8}*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 := (  1,225)(  2,231)(  3,230)(  4,229)(  5,228)(  6,227)(  7,226)(  8,232)
(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)( 24,251)
( 25,250)( 26,249)( 27,248)( 28,247)( 29,253)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,255)( 35,254)( 36,260)( 37,266)( 38,265)( 39,264)( 40,263)
( 41,262)( 42,261)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)( 48,269)
( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)( 56,275)
( 57,288)( 58,294)( 59,293)( 60,292)( 61,291)( 62,290)( 63,289)( 64,281)
( 65,287)( 66,286)( 67,285)( 68,284)( 69,283)( 70,282)( 71,302)( 72,308)
( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,295)( 79,301)( 80,300)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,316)( 86,322)( 87,321)( 88,320)
( 89,319)( 90,318)( 91,317)( 92,309)( 93,315)( 94,314)( 95,313)( 96,312)
( 97,311)( 98,310)( 99,330)(100,336)(101,335)(102,334)(103,333)(104,332)
(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)(112,324)
(113,351)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)(120,358)
(121,364)(122,363)(123,362)(124,361)(125,360)(126,359)(127,337)(128,343)
(129,342)(130,341)(131,340)(132,339)(133,338)(134,344)(135,350)(136,349)
(137,348)(138,347)(139,346)(140,345)(141,379)(142,385)(143,384)(144,383)
(145,382)(146,381)(147,380)(148,386)(149,392)(150,391)(151,390)(152,389)
(153,388)(154,387)(155,365)(156,371)(157,370)(158,369)(159,368)(160,367)
(161,366)(162,372)(163,378)(164,377)(165,376)(166,375)(167,374)(168,373)
(169,414)(170,420)(171,419)(172,418)(173,417)(174,416)(175,415)(176,407)
(177,413)(178,412)(179,411)(180,410)(181,409)(182,408)(183,400)(184,406)
(185,405)(186,404)(187,403)(188,402)(189,401)(190,393)(191,399)(192,398)
(193,397)(194,396)(195,395)(196,394)(197,442)(198,448)(199,447)(200,446)
(201,445)(202,444)(203,443)(204,435)(205,441)(206,440)(207,439)(208,438)
(209,437)(210,436)(211,428)(212,434)(213,433)(214,432)(215,431)(216,430)
(217,429)(218,421)(219,427)(220,426)(221,425)(222,424)(223,423)(224,422)
(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)
(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)(464,693)
(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)(472,699)
(473,698)(474,697)(475,696)(476,695)(477,701)(478,707)(479,706)(480,705)
(481,704)(482,703)(483,702)(484,708)(485,714)(486,713)(487,712)(488,711)
(489,710)(490,709)(491,715)(492,721)(493,720)(494,719)(495,718)(496,717)
(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)(504,723)
(505,736)(506,742)(507,741)(508,740)(509,739)(510,738)(511,737)(512,729)
(513,735)(514,734)(515,733)(516,732)(517,731)(518,730)(519,750)(520,756)
(521,755)(522,754)(523,753)(524,752)(525,751)(526,743)(527,749)(528,748)
(529,747)(530,746)(531,745)(532,744)(533,764)(534,770)(535,769)(536,768)
(537,767)(538,766)(539,765)(540,757)(541,763)(542,762)(543,761)(544,760)
(545,759)(546,758)(547,778)(548,784)(549,783)(550,782)(551,781)(552,780)
(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)(560,772)
(561,799)(562,805)(563,804)(564,803)(565,802)(566,801)(567,800)(568,806)
(569,812)(570,811)(571,810)(572,809)(573,808)(574,807)(575,785)(576,791)
(577,790)(578,789)(579,788)(580,787)(581,786)(582,792)(583,798)(584,797)
(585,796)(586,795)(587,794)(588,793)(589,827)(590,833)(591,832)(592,831)
(593,830)(594,829)(595,828)(596,834)(597,840)(598,839)(599,838)(600,837)
(601,836)(602,835)(603,813)(604,819)(605,818)(606,817)(607,816)(608,815)
(609,814)(610,820)(611,826)(612,825)(613,824)(614,823)(615,822)(616,821)
(617,862)(618,868)(619,867)(620,866)(621,865)(622,864)(623,863)(624,855)
(625,861)(626,860)(627,859)(628,858)(629,857)(630,856)(631,848)(632,854)
(633,853)(634,852)(635,851)(636,850)(637,849)(638,841)(639,847)(640,846)
(641,845)(642,844)(643,843)(644,842)(645,890)(646,896)(647,895)(648,894)
(649,893)(650,892)(651,891)(652,883)(653,889)(654,888)(655,887)(656,886)
(657,885)(658,884)(659,876)(660,882)(661,881)(662,880)(663,879)(664,878)
(665,877)(666,869)(667,875)(668,874)(669,873)(670,872)(671,871)(672,870);;
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, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)( 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)( 99,107)(100,106)(101,112)
(102,111)(103,110)(104,109)(105,108)(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)
(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)(176,198)
(177,197)(178,203)(179,202)(180,201)(181,200)(182,199)(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)(239,296)(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)
(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)
(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(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)(337,422)(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)
(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)
(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(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)(505,625)(506,624)(507,630)(508,629)
(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)(516,621)
(517,620)(518,619)(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)(547,667)(548,666)
(549,672)(550,671)(551,670)(552,669)(553,668)(554,660)(555,659)(556,665)
(557,664)(558,663)(559,662)(560,661)(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)
(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)(707,885)(708,891)
(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)(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)(743,786)(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)
(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)(763,829)(764,835)
(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)(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 := (  1,449)(  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)
( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)
( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)
( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)
( 81,515)( 82,516)( 83,517)( 84,518)( 85,547)( 86,548)( 87,549)( 88,550)
( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)( 96,558)
( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)(104,538)
(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)(112,546)
(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)
(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)(176,666)
(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,645)(184,646)
(185,647)(186,648)(187,649)(188,650)(189,651)(190,652)(191,653)(192,654)
(193,655)(194,656)(195,657)(196,658)(197,631)(198,632)(199,633)(200,634)
(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)(208,642)
(209,643)(210,644)(211,617)(212,618)(213,619)(214,620)(215,621)(216,622)
(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)(224,630)
(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)
(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)
(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)
(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)
(305,739)(306,740)(307,741)(308,742)(309,771)(310,772)(311,773)(312,774)
(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)(320,782)
(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)(328,762)
(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)(336,770)
(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)
(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)(400,890)
(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)(408,870)
(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)(416,878)
(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)(424,858)
(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)(432,866)
(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)
(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854);;
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  1,225)(  2,231)(  3,230)(  4,229)(  5,228)(  6,227)(  7,226)
(  8,232)(  9,238)( 10,237)( 11,236)( 12,235)( 13,234)( 14,233)( 15,239)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,246)( 23,252)
( 24,251)( 25,250)( 26,249)( 27,248)( 28,247)( 29,253)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,255)( 35,254)( 36,260)( 37,266)( 38,265)( 39,264)
( 40,263)( 41,262)( 42,261)( 43,267)( 44,273)( 45,272)( 46,271)( 47,270)
( 48,269)( 49,268)( 50,274)( 51,280)( 52,279)( 53,278)( 54,277)( 55,276)
( 56,275)( 57,288)( 58,294)( 59,293)( 60,292)( 61,291)( 62,290)( 63,289)
( 64,281)( 65,287)( 66,286)( 67,285)( 68,284)( 69,283)( 70,282)( 71,302)
( 72,308)( 73,307)( 74,306)( 75,305)( 76,304)( 77,303)( 78,295)( 79,301)
( 80,300)( 81,299)( 82,298)( 83,297)( 84,296)( 85,316)( 86,322)( 87,321)
( 88,320)( 89,319)( 90,318)( 91,317)( 92,309)( 93,315)( 94,314)( 95,313)
( 96,312)( 97,311)( 98,310)( 99,330)(100,336)(101,335)(102,334)(103,333)
(104,332)(105,331)(106,323)(107,329)(108,328)(109,327)(110,326)(111,325)
(112,324)(113,351)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)
(120,358)(121,364)(122,363)(123,362)(124,361)(125,360)(126,359)(127,337)
(128,343)(129,342)(130,341)(131,340)(132,339)(133,338)(134,344)(135,350)
(136,349)(137,348)(138,347)(139,346)(140,345)(141,379)(142,385)(143,384)
(144,383)(145,382)(146,381)(147,380)(148,386)(149,392)(150,391)(151,390)
(152,389)(153,388)(154,387)(155,365)(156,371)(157,370)(158,369)(159,368)
(160,367)(161,366)(162,372)(163,378)(164,377)(165,376)(166,375)(167,374)
(168,373)(169,414)(170,420)(171,419)(172,418)(173,417)(174,416)(175,415)
(176,407)(177,413)(178,412)(179,411)(180,410)(181,409)(182,408)(183,400)
(184,406)(185,405)(186,404)(187,403)(188,402)(189,401)(190,393)(191,399)
(192,398)(193,397)(194,396)(195,395)(196,394)(197,442)(198,448)(199,447)
(200,446)(201,445)(202,444)(203,443)(204,435)(205,441)(206,440)(207,439)
(208,438)(209,437)(210,436)(211,428)(212,434)(213,433)(214,432)(215,431)
(216,430)(217,429)(218,421)(219,427)(220,426)(221,425)(222,424)(223,423)
(224,422)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)
(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,687)
(464,693)(465,692)(466,691)(467,690)(468,689)(469,688)(470,694)(471,700)
(472,699)(473,698)(474,697)(475,696)(476,695)(477,701)(478,707)(479,706)
(480,705)(481,704)(482,703)(483,702)(484,708)(485,714)(486,713)(487,712)
(488,711)(489,710)(490,709)(491,715)(492,721)(493,720)(494,719)(495,718)
(496,717)(497,716)(498,722)(499,728)(500,727)(501,726)(502,725)(503,724)
(504,723)(505,736)(506,742)(507,741)(508,740)(509,739)(510,738)(511,737)
(512,729)(513,735)(514,734)(515,733)(516,732)(517,731)(518,730)(519,750)
(520,756)(521,755)(522,754)(523,753)(524,752)(525,751)(526,743)(527,749)
(528,748)(529,747)(530,746)(531,745)(532,744)(533,764)(534,770)(535,769)
(536,768)(537,767)(538,766)(539,765)(540,757)(541,763)(542,762)(543,761)
(544,760)(545,759)(546,758)(547,778)(548,784)(549,783)(550,782)(551,781)
(552,780)(553,779)(554,771)(555,777)(556,776)(557,775)(558,774)(559,773)
(560,772)(561,799)(562,805)(563,804)(564,803)(565,802)(566,801)(567,800)
(568,806)(569,812)(570,811)(571,810)(572,809)(573,808)(574,807)(575,785)
(576,791)(577,790)(578,789)(579,788)(580,787)(581,786)(582,792)(583,798)
(584,797)(585,796)(586,795)(587,794)(588,793)(589,827)(590,833)(591,832)
(592,831)(593,830)(594,829)(595,828)(596,834)(597,840)(598,839)(599,838)
(600,837)(601,836)(602,835)(603,813)(604,819)(605,818)(606,817)(607,816)
(608,815)(609,814)(610,820)(611,826)(612,825)(613,824)(614,823)(615,822)
(616,821)(617,862)(618,868)(619,867)(620,866)(621,865)(622,864)(623,863)
(624,855)(625,861)(626,860)(627,859)(628,858)(629,857)(630,856)(631,848)
(632,854)(633,853)(634,852)(635,851)(636,850)(637,849)(638,841)(639,847)
(640,846)(641,845)(642,844)(643,843)(644,842)(645,890)(646,896)(647,895)
(648,894)(649,893)(650,892)(651,891)(652,883)(653,889)(654,888)(655,887)
(656,886)(657,885)(658,884)(659,876)(660,882)(661,881)(662,880)(663,879)
(664,878)(665,877)(666,869)(667,875)(668,874)(669,873)(670,872)(671,871)
(672,870);
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, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)
( 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)( 99,107)(100,106)
(101,112)(102,111)(103,110)(104,109)(105,108)(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)(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)
(176,198)(177,197)(178,203)(179,202)(180,201)(181,200)(182,199)(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)(239,296)(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)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)
(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(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)(337,422)(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)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)
(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(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)(505,625)(506,624)(507,630)
(508,629)(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)
(516,621)(517,620)(518,619)(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)(547,667)
(548,666)(549,672)(550,671)(551,670)(552,669)(553,668)(554,660)(555,659)
(556,665)(557,664)(558,663)(559,662)(560,661)(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)(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)(707,885)
(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)(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)(743,786)(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)(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)(763,829)
(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)(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)!(  1,449)(  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)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)
( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)
( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)
( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,547)( 86,548)( 87,549)
( 88,550)( 89,551)( 90,552)( 91,553)( 92,554)( 93,555)( 94,556)( 95,557)
( 96,558)( 97,559)( 98,560)( 99,533)(100,534)(101,535)(102,536)(103,537)
(104,538)(105,539)(106,540)(107,541)(108,542)(109,543)(110,544)(111,545)
(112,546)(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)(169,659)(170,660)(171,661)(172,662)(173,663)(174,664)(175,665)
(176,666)(177,667)(178,668)(179,669)(180,670)(181,671)(182,672)(183,645)
(184,646)(185,647)(186,648)(187,649)(188,650)(189,651)(190,652)(191,653)
(192,654)(193,655)(194,656)(195,657)(196,658)(197,631)(198,632)(199,633)
(200,634)(201,635)(202,636)(203,637)(204,638)(205,639)(206,640)(207,641)
(208,642)(209,643)(210,644)(211,617)(212,618)(213,619)(214,620)(215,621)
(216,622)(217,623)(218,624)(219,625)(220,626)(221,627)(222,628)(223,629)
(224,630)(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)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)
(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)
(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)
(304,738)(305,739)(306,740)(307,741)(308,742)(309,771)(310,772)(311,773)
(312,774)(313,775)(314,776)(315,777)(316,778)(317,779)(318,780)(319,781)
(320,782)(321,783)(322,784)(323,757)(324,758)(325,759)(326,760)(327,761)
(328,762)(329,763)(330,764)(331,765)(332,766)(333,767)(334,768)(335,769)
(336,770)(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)(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)
(400,890)(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)
(408,870)(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)
(416,878)(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)
(424,858)(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)
(432,866)(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)
(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)
(448,854);
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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