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Polytope of Type {16,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,28}*1792b
if this polytope has a name.
Group : SmallGroup(1792,81734)
Rank : 3
Schlafli Type : {16,28}
Number of vertices, edges, etc : 32, 448, 56
Order of s0s1s2 : 112
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-fold quotients : {4,28}*448, {8,28}*448a, {8,28}*448b
   7-fold quotients : {16,4}*256b
   8-fold quotients : {4,28}*224, {8,14}*224
   14-fold quotients : {8,4}*128a
   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)( 29,484)( 30,485)( 31,486)( 32,487)
( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)
( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)
( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)
( 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)( 85,547)( 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)
(169,666)(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)(253,708)(254,709)(255,710)(256,711)
(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)
(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)
(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)
(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)(309,771)(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)
(393,890)(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)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 44, 49)( 45, 48)( 46, 47)( 51, 56)
( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)
( 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)(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)
(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,204)
(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(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)(239,302)(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)
(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)(260,309)
(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(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)(337,428)(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)
(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)(483,597)(484,589)
(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)(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)(505,617)(506,623)(507,622)(508,621)
(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)(516,627)
(517,626)(518,625)(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)(547,659)(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)
(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)(707,891)(708,883)
(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)(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)(743,792)(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)
(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)(763,835)(764,827)
(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)(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)
( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)( 72,295)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)( 80,308)
( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)(112,332)
(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)
(169,408)(170,407)(171,413)(172,412)(173,411)(174,410)(175,409)(176,415)
(177,414)(178,420)(179,419)(180,418)(181,417)(182,416)(183,394)(184,393)
(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)(192,406)
(193,405)(194,404)(195,403)(196,402)(197,436)(198,435)(199,441)(200,440)
(201,439)(202,438)(203,437)(204,443)(205,442)(206,448)(207,447)(208,446)
(209,445)(210,444)(211,422)(212,421)(213,427)(214,426)(215,425)(216,424)
(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)(224,430)
(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)
(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)(512,737)
(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)(520,743)
(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)(528,756)
(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)(536,762)
(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)(544,768)
(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)(552,774)
(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)(560,780)
(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)
(617,856)(618,855)(619,861)(620,860)(621,859)(622,858)(623,857)(624,863)
(625,862)(626,868)(627,867)(628,866)(629,865)(630,864)(631,842)(632,841)
(633,847)(634,846)(635,845)(636,844)(637,843)(638,849)(639,848)(640,854)
(641,853)(642,852)(643,851)(644,850)(645,884)(646,883)(647,889)(648,888)
(649,887)(650,886)(651,885)(652,891)(653,890)(654,896)(655,895)(656,894)
(657,893)(658,892)(659,870)(660,869)(661,875)(662,874)(663,873)(664,872)
(665,871)(666,877)(667,876)(668,882)(669,881)(670,880)(671,879)(672,878);;
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*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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*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 ];;
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)( 29,484)( 30,485)( 31,486)
( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)
( 40,481)( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)
( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)
( 56,497)( 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)( 85,547)( 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)(169,666)(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)(253,708)(254,709)(255,710)
(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)
(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)
(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)
(280,721)(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)(309,771)(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)(393,890)(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)( 29, 36)( 30, 42)
( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 44, 49)( 45, 48)( 46, 47)
( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 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)(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)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)
(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(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)(239,302)(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)(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)
(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(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)(337,428)(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)(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)(483,597)
(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)(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)(505,617)(506,623)(507,622)
(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)
(516,627)(517,626)(518,625)(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)(547,659)
(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)(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)(707,891)
(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)(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)(743,792)(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)(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)(763,835)
(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)(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)( 57,282)( 58,281)( 59,287)( 60,286)( 61,285)( 62,284)( 63,283)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,296)
( 72,295)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,303)( 79,302)
( 80,308)( 81,307)( 82,306)( 83,305)( 84,304)( 85,310)( 86,309)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,317)( 93,316)( 94,322)( 95,321)
( 96,320)( 97,319)( 98,318)( 99,324)(100,323)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,331)(107,330)(108,336)(109,335)(110,334)(111,333)
(112,332)(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)(169,408)(170,407)(171,413)(172,412)(173,411)(174,410)(175,409)
(176,415)(177,414)(178,420)(179,419)(180,418)(181,417)(182,416)(183,394)
(184,393)(185,399)(186,398)(187,397)(188,396)(189,395)(190,401)(191,400)
(192,406)(193,405)(194,404)(195,403)(196,402)(197,436)(198,435)(199,441)
(200,440)(201,439)(202,438)(203,437)(204,443)(205,442)(206,448)(207,447)
(208,446)(209,445)(210,444)(211,422)(212,421)(213,427)(214,426)(215,425)
(216,424)(217,423)(218,429)(219,428)(220,434)(221,433)(222,432)(223,431)
(224,430)(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)(505,730)(506,729)(507,735)(508,734)(509,733)(510,732)(511,731)
(512,737)(513,736)(514,742)(515,741)(516,740)(517,739)(518,738)(519,744)
(520,743)(521,749)(522,748)(523,747)(524,746)(525,745)(526,751)(527,750)
(528,756)(529,755)(530,754)(531,753)(532,752)(533,758)(534,757)(535,763)
(536,762)(537,761)(538,760)(539,759)(540,765)(541,764)(542,770)(543,769)
(544,768)(545,767)(546,766)(547,772)(548,771)(549,777)(550,776)(551,775)
(552,774)(553,773)(554,779)(555,778)(556,784)(557,783)(558,782)(559,781)
(560,780)(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)(617,856)(618,855)(619,861)(620,860)(621,859)(622,858)(623,857)
(624,863)(625,862)(626,868)(627,867)(628,866)(629,865)(630,864)(631,842)
(632,841)(633,847)(634,846)(635,845)(636,844)(637,843)(638,849)(639,848)
(640,854)(641,853)(642,852)(643,851)(644,850)(645,884)(646,883)(647,889)
(648,888)(649,887)(650,886)(651,885)(652,891)(653,890)(654,896)(655,895)
(656,894)(657,893)(658,892)(659,870)(660,869)(661,875)(662,874)(663,873)
(664,872)(665,871)(666,877)(667,876)(668,882)(669,881)(670,880)(671,879)
(672,878);
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*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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*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 >; 
 
References : None.
to this polytope