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Polytope of Type {8,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,56}*1792a
if this polytope has a name.
Group : SmallGroup(1792,58267)
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 : {4,56}*896a, {8,56}*896a, {8,56}*896b, {8,28}*896a, {8,56}*896c, {8,56}*896d
   4-fold quotients : {4,56}*448a, {4,28}*448, {4,56}*448b, {8,28}*448a, {8,28}*448b
   7-fold quotients : {8,8}*256a
   8-fold quotients : {4,28}*224, {2,56}*224, {8,14}*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 : {2,28}*112, {4,14}*112
   28-fold quotients : {4,8}*64a, {8,4}*64a, {4,8}*64b, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,14}*56
   56-fold quotients : {4,4}*32, {2,8}*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)
( 57,519)( 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);;
s1 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 71, 78)
( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 92)( 86, 98)
( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)(101,111)
(102,110)(103,109)(104,108)(105,107)(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)(127,155)(128,161)(129,160)(130,159)(131,158)(132,157)
(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)
(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)(183,218)(184,224)
(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)
(193,215)(194,214)(195,213)(196,212)(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)(239,295)(240,301)(241,300)(242,299)(243,298)(244,297)
(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)(252,303)
(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)(267,323)(268,329)
(269,328)(270,327)(271,326)(272,325)(273,324)(274,330)(275,336)(276,335)
(277,334)(278,333)(279,332)(280,331)(337,421)(338,427)(339,426)(340,425)
(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)(347,432)(348,431)
(349,430)(350,429)(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)
(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)(371,394)(372,400)
(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)(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)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)
(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)
(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)(491,603)(492,609)
(493,608)(494,607)(495,606)(496,605)(497,604)(498,610)(499,616)(500,615)
(501,614)(502,613)(503,612)(504,611)(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)(519,638)(520,644)(521,643)(522,642)(523,641)(524,640)
(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)(532,632)
(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)(547,666)(548,672)
(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)
(557,663)(558,662)(559,661)(560,660)(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)(687,841)(688,847)(689,846)(690,845)(691,844)(692,843)
(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)(699,850)(700,849)
(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)(715,869)(716,875)
(717,874)(718,873)(719,872)(720,871)(721,870)(722,876)(723,882)(724,881)
(725,880)(726,879)(727,878)(728,877)(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)(743,785)(744,791)(745,790)(746,789)(747,788)(748,787)
(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)(755,794)(756,793)
(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)(771,813)(772,819)
(773,818)(774,817)(775,816)(776,815)(777,814)(778,820)(779,826)(780,825)
(781,824)(782,823)(783,822)(784,821);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
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, 
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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 57,519)( 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);
s1 := Sym(896)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 57, 64)( 58, 70)( 59, 69)( 60, 68)( 61, 67)( 62, 66)( 63, 65)
( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 85, 92)
( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)( 99,106)(100,112)
(101,111)(102,110)(103,109)(104,108)(105,107)(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)(127,155)(128,161)(129,160)(130,159)(131,158)
(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)(139,164)
(140,163)(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)(183,218)
(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)
(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,295)(240,301)(241,300)(242,299)(243,298)
(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)(251,304)
(252,303)(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)(267,323)
(268,329)(269,328)(270,327)(271,326)(272,325)(273,324)(274,330)(275,336)
(276,335)(277,334)(278,333)(279,332)(280,331)(337,421)(338,427)(339,426)
(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)(347,432)
(348,431)(349,430)(350,429)(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)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)(371,394)
(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)(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)(463,575)(464,581)(465,580)(466,579)(467,578)
(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)
(476,583)(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)(491,603)
(492,609)(493,608)(494,607)(495,606)(496,605)(497,604)(498,610)(499,616)
(500,615)(501,614)(502,613)(503,612)(504,611)(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)(519,638)(520,644)(521,643)(522,642)(523,641)
(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)
(532,632)(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)(547,666)
(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)
(556,664)(557,663)(558,662)(559,661)(560,660)(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)(687,841)(688,847)(689,846)(690,845)(691,844)
(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)(699,850)
(700,849)(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)(715,869)
(716,875)(717,874)(718,873)(719,872)(720,871)(721,870)(722,876)(723,882)
(724,881)(725,880)(726,879)(727,878)(728,877)(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)(743,785)(744,791)(745,790)(746,789)(747,788)
(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)(755,794)
(756,793)(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)(771,813)
(772,819)(773,818)(774,817)(775,816)(776,815)(777,814)(778,820)(779,826)
(780,825)(781,824)(782,823)(783,822)(784,821);
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
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, 
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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope