Polytope of Type {16,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,56}*1792f
if this polytope has a name.
Group : SmallGroup(1792,83051)
Rank : 3
Schlafli Type : {16,56}
Number of vertices, edges, etc : 16, 448, 56
Order of s0s1s2 : 112
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {8,56}*896b, {16,28}*896b
4-fold quotients : {4,56}*448a, {8,28}*448a
7-fold quotients : {16,8}*256f
8-fold quotients : {4,28}*224, {2,56}*224, {8,14}*224
14-fold quotients : {8,8}*128b, {16,4}*128b
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {4,8}*64a, {8,4}*64a
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 := ( 1,673)( 2,674)( 3,675)( 4,676)( 5,677)( 6,678)( 7,679)( 8,680)
( 9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)( 16,688)
( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)( 24,696)
( 25,697)( 26,698)( 27,699)( 28,700)( 29,708)( 30,709)( 31,710)( 32,711)
( 33,712)( 34,713)( 35,714)( 36,701)( 37,702)( 38,703)( 39,704)( 40,705)
( 41,706)( 42,707)( 43,722)( 44,723)( 45,724)( 46,725)( 47,726)( 48,727)
( 49,728)( 50,715)( 51,716)( 52,717)( 53,718)( 54,719)( 55,720)( 56,721)
( 57,736)( 58,737)( 59,738)( 60,739)( 61,740)( 62,741)( 63,742)( 64,729)
( 65,730)( 66,731)( 67,732)( 68,733)( 69,734)( 70,735)( 71,750)( 72,751)
( 73,752)( 74,753)( 75,754)( 76,755)( 77,756)( 78,743)( 79,744)( 80,745)
( 81,746)( 82,747)( 83,748)( 84,749)( 85,757)( 86,758)( 87,759)( 88,760)
( 89,761)( 90,762)( 91,763)( 92,764)( 93,765)( 94,766)( 95,767)( 96,768)
( 97,769)( 98,770)( 99,771)(100,772)(101,773)(102,774)(103,775)(104,776)
(105,777)(106,778)(107,779)(108,780)(109,781)(110,782)(111,783)(112,784)
(113,827)(114,828)(115,829)(116,830)(117,831)(118,832)(119,833)(120,834)
(121,835)(122,836)(123,837)(124,838)(125,839)(126,840)(127,813)(128,814)
(129,815)(130,816)(131,817)(132,818)(133,819)(134,820)(135,821)(136,822)
(137,823)(138,824)(139,825)(140,826)(141,799)(142,800)(143,801)(144,802)
(145,803)(146,804)(147,805)(148,806)(149,807)(150,808)(151,809)(152,810)
(153,811)(154,812)(155,785)(156,786)(157,787)(158,788)(159,789)(160,790)
(161,791)(162,792)(163,793)(164,794)(165,795)(166,796)(167,797)(168,798)
(169,890)(170,891)(171,892)(172,893)(173,894)(174,895)(175,896)(176,883)
(177,884)(178,885)(179,886)(180,887)(181,888)(182,889)(183,876)(184,877)
(185,878)(186,879)(187,880)(188,881)(189,882)(190,869)(191,870)(192,871)
(193,872)(194,873)(195,874)(196,875)(197,862)(198,863)(199,864)(200,865)
(201,866)(202,867)(203,868)(204,855)(205,856)(206,857)(207,858)(208,859)
(209,860)(210,861)(211,848)(212,849)(213,850)(214,851)(215,852)(216,853)
(217,854)(218,841)(219,842)(220,843)(221,844)(222,845)(223,846)(224,847)
(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)(232,456)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464)
(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)(248,472)
(249,473)(250,474)(251,475)(252,476)(253,484)(254,485)(255,486)(256,487)
(257,488)(258,489)(259,490)(260,477)(261,478)(262,479)(263,480)(264,481)
(265,482)(266,483)(267,498)(268,499)(269,500)(270,501)(271,502)(272,503)
(273,504)(274,491)(275,492)(276,493)(277,494)(278,495)(279,496)(280,497)
(281,512)(282,513)(283,514)(284,515)(285,516)(286,517)(287,518)(288,505)
(289,506)(290,507)(291,508)(292,509)(293,510)(294,511)(295,526)(296,527)
(297,528)(298,529)(299,530)(300,531)(301,532)(302,519)(303,520)(304,521)
(305,522)(306,523)(307,524)(308,525)(309,533)(310,534)(311,535)(312,536)
(313,537)(314,538)(315,539)(316,540)(317,541)(318,542)(319,543)(320,544)
(321,545)(322,546)(323,547)(324,548)(325,549)(326,550)(327,551)(328,552)
(329,553)(330,554)(331,555)(332,556)(333,557)(334,558)(335,559)(336,560)
(337,603)(338,604)(339,605)(340,606)(341,607)(342,608)(343,609)(344,610)
(345,611)(346,612)(347,613)(348,614)(349,615)(350,616)(351,589)(352,590)
(353,591)(354,592)(355,593)(356,594)(357,595)(358,596)(359,597)(360,598)
(361,599)(362,600)(363,601)(364,602)(365,575)(366,576)(367,577)(368,578)
(369,579)(370,580)(371,581)(372,582)(373,583)(374,584)(375,585)(376,586)
(377,587)(378,588)(379,561)(380,562)(381,563)(382,564)(383,565)(384,566)
(385,567)(386,568)(387,569)(388,570)(389,571)(390,572)(391,573)(392,574)
(393,666)(394,667)(395,668)(396,669)(397,670)(398,671)(399,672)(400,659)
(401,660)(402,661)(403,662)(404,663)(405,664)(406,665)(407,652)(408,653)
(409,654)(410,655)(411,656)(412,657)(413,658)(414,645)(415,646)(416,647)
(417,648)(418,649)(419,650)(420,651)(421,638)(422,639)(423,640)(424,641)
(425,642)(426,643)(427,644)(428,631)(429,632)(430,633)(431,634)(432,635)
(433,636)(434,637)(435,624)(436,625)(437,626)(438,627)(439,628)(440,629)
(441,630)(442,617)(443,618)(444,619)(445,620)(446,621)(447,622)(448,623);;
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)( 29, 36)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 57, 78)( 58, 84)( 59, 83)( 60, 82)( 61, 81)( 62, 80)
( 63, 79)( 64, 71)( 65, 77)( 66, 76)( 67, 75)( 68, 74)( 69, 73)( 70, 72)
( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)( 92,106)
( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(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)(169,218)(170,224)(171,223)(172,222)(173,221)(174,220)
(175,219)(176,211)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)
(183,204)(184,210)(185,209)(186,208)(187,207)(188,206)(189,205)(190,197)
(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(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)(253,316)(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)
(267,330)(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)(337,421)(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)(477,596)(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)
(491,610)(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)(505,638)(506,644)
(507,643)(508,642)(509,641)(510,640)(511,639)(512,631)(513,637)(514,636)
(515,635)(516,634)(517,633)(518,632)(519,624)(520,630)(521,629)(522,628)
(523,627)(524,626)(525,625)(526,617)(527,623)(528,622)(529,621)(530,620)
(531,619)(532,618)(533,659)(534,665)(535,664)(536,663)(537,662)(538,661)
(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)(546,667)
(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)(554,652)
(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(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)(701,890)(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)
(715,876)(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)(743,785)(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)(757,834)(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)
(771,820)(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)
( 57,303)( 58,302)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)( 64,296)
( 65,295)( 66,301)( 67,300)( 68,299)( 69,298)( 70,297)( 71,289)( 72,288)
( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)( 80,287)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,331)( 86,330)( 87,336)( 88,335)
( 89,334)( 90,333)( 91,332)( 92,324)( 93,323)( 94,329)( 95,328)( 96,327)
( 97,326)( 98,325)( 99,317)(100,316)(101,322)(102,321)(103,320)(104,319)
(105,318)(106,310)(107,309)(108,315)(109,314)(110,313)(111,312)(112,311)
(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)
(169,401)(170,400)(171,406)(172,405)(173,404)(174,403)(175,402)(176,394)
(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,415)(184,414)
(185,420)(186,419)(187,418)(188,417)(189,416)(190,408)(191,407)(192,413)
(193,412)(194,411)(195,410)(196,409)(197,429)(198,428)(199,434)(200,433)
(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)(208,425)
(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)(216,445)
(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)(224,437)
(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)
(505,751)(506,750)(507,756)(508,755)(509,754)(510,753)(511,752)(512,744)
(513,743)(514,749)(515,748)(516,747)(517,746)(518,745)(519,737)(520,736)
(521,742)(522,741)(523,740)(524,739)(525,738)(526,730)(527,729)(528,735)
(529,734)(530,733)(531,732)(532,731)(533,779)(534,778)(535,784)(536,783)
(537,782)(538,781)(539,780)(540,772)(541,771)(542,777)(543,776)(544,775)
(545,774)(546,773)(547,765)(548,764)(549,770)(550,769)(551,768)(552,767)
(553,766)(554,758)(555,757)(556,763)(557,762)(558,761)(559,760)(560,759)
(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)
(617,849)(618,848)(619,854)(620,853)(621,852)(622,851)(623,850)(624,842)
(625,841)(626,847)(627,846)(628,845)(629,844)(630,843)(631,863)(632,862)
(633,868)(634,867)(635,866)(636,865)(637,864)(638,856)(639,855)(640,861)
(641,860)(642,859)(643,858)(644,857)(645,877)(646,876)(647,882)(648,881)
(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)(656,873)
(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)(664,893)
(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)(672,885);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*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*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)!( 1,673)( 2,674)( 3,675)( 4,676)( 5,677)( 6,678)( 7,679)
( 8,680)( 9,681)( 10,682)( 11,683)( 12,684)( 13,685)( 14,686)( 15,687)
( 16,688)( 17,689)( 18,690)( 19,691)( 20,692)( 21,693)( 22,694)( 23,695)
( 24,696)( 25,697)( 26,698)( 27,699)( 28,700)( 29,708)( 30,709)( 31,710)
( 32,711)( 33,712)( 34,713)( 35,714)( 36,701)( 37,702)( 38,703)( 39,704)
( 40,705)( 41,706)( 42,707)( 43,722)( 44,723)( 45,724)( 46,725)( 47,726)
( 48,727)( 49,728)( 50,715)( 51,716)( 52,717)( 53,718)( 54,719)( 55,720)
( 56,721)( 57,736)( 58,737)( 59,738)( 60,739)( 61,740)( 62,741)( 63,742)
( 64,729)( 65,730)( 66,731)( 67,732)( 68,733)( 69,734)( 70,735)( 71,750)
( 72,751)( 73,752)( 74,753)( 75,754)( 76,755)( 77,756)( 78,743)( 79,744)
( 80,745)( 81,746)( 82,747)( 83,748)( 84,749)( 85,757)( 86,758)( 87,759)
( 88,760)( 89,761)( 90,762)( 91,763)( 92,764)( 93,765)( 94,766)( 95,767)
( 96,768)( 97,769)( 98,770)( 99,771)(100,772)(101,773)(102,774)(103,775)
(104,776)(105,777)(106,778)(107,779)(108,780)(109,781)(110,782)(111,783)
(112,784)(113,827)(114,828)(115,829)(116,830)(117,831)(118,832)(119,833)
(120,834)(121,835)(122,836)(123,837)(124,838)(125,839)(126,840)(127,813)
(128,814)(129,815)(130,816)(131,817)(132,818)(133,819)(134,820)(135,821)
(136,822)(137,823)(138,824)(139,825)(140,826)(141,799)(142,800)(143,801)
(144,802)(145,803)(146,804)(147,805)(148,806)(149,807)(150,808)(151,809)
(152,810)(153,811)(154,812)(155,785)(156,786)(157,787)(158,788)(159,789)
(160,790)(161,791)(162,792)(163,793)(164,794)(165,795)(166,796)(167,797)
(168,798)(169,890)(170,891)(171,892)(172,893)(173,894)(174,895)(175,896)
(176,883)(177,884)(178,885)(179,886)(180,887)(181,888)(182,889)(183,876)
(184,877)(185,878)(186,879)(187,880)(188,881)(189,882)(190,869)(191,870)
(192,871)(193,872)(194,873)(195,874)(196,875)(197,862)(198,863)(199,864)
(200,865)(201,866)(202,867)(203,868)(204,855)(205,856)(206,857)(207,858)
(208,859)(209,860)(210,861)(211,848)(212,849)(213,850)(214,851)(215,852)
(216,853)(217,854)(218,841)(219,842)(220,843)(221,844)(222,845)(223,846)
(224,847)(225,449)(226,450)(227,451)(228,452)(229,453)(230,454)(231,455)
(232,456)(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)
(240,464)(241,465)(242,466)(243,467)(244,468)(245,469)(246,470)(247,471)
(248,472)(249,473)(250,474)(251,475)(252,476)(253,484)(254,485)(255,486)
(256,487)(257,488)(258,489)(259,490)(260,477)(261,478)(262,479)(263,480)
(264,481)(265,482)(266,483)(267,498)(268,499)(269,500)(270,501)(271,502)
(272,503)(273,504)(274,491)(275,492)(276,493)(277,494)(278,495)(279,496)
(280,497)(281,512)(282,513)(283,514)(284,515)(285,516)(286,517)(287,518)
(288,505)(289,506)(290,507)(291,508)(292,509)(293,510)(294,511)(295,526)
(296,527)(297,528)(298,529)(299,530)(300,531)(301,532)(302,519)(303,520)
(304,521)(305,522)(306,523)(307,524)(308,525)(309,533)(310,534)(311,535)
(312,536)(313,537)(314,538)(315,539)(316,540)(317,541)(318,542)(319,543)
(320,544)(321,545)(322,546)(323,547)(324,548)(325,549)(326,550)(327,551)
(328,552)(329,553)(330,554)(331,555)(332,556)(333,557)(334,558)(335,559)
(336,560)(337,603)(338,604)(339,605)(340,606)(341,607)(342,608)(343,609)
(344,610)(345,611)(346,612)(347,613)(348,614)(349,615)(350,616)(351,589)
(352,590)(353,591)(354,592)(355,593)(356,594)(357,595)(358,596)(359,597)
(360,598)(361,599)(362,600)(363,601)(364,602)(365,575)(366,576)(367,577)
(368,578)(369,579)(370,580)(371,581)(372,582)(373,583)(374,584)(375,585)
(376,586)(377,587)(378,588)(379,561)(380,562)(381,563)(382,564)(383,565)
(384,566)(385,567)(386,568)(387,569)(388,570)(389,571)(390,572)(391,573)
(392,574)(393,666)(394,667)(395,668)(396,669)(397,670)(398,671)(399,672)
(400,659)(401,660)(402,661)(403,662)(404,663)(405,664)(406,665)(407,652)
(408,653)(409,654)(410,655)(411,656)(412,657)(413,658)(414,645)(415,646)
(416,647)(417,648)(418,649)(419,650)(420,651)(421,638)(422,639)(423,640)
(424,641)(425,642)(426,643)(427,644)(428,631)(429,632)(430,633)(431,634)
(432,635)(433,636)(434,637)(435,624)(436,625)(437,626)(438,627)(439,628)
(440,629)(441,630)(442,617)(443,618)(444,619)(445,620)(446,621)(447,622)
(448,623);
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)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 57, 78)( 58, 84)( 59, 83)( 60, 82)( 61, 81)
( 62, 80)( 63, 79)( 64, 71)( 65, 77)( 66, 76)( 67, 75)( 68, 74)( 69, 73)
( 70, 72)( 85, 99)( 86,105)( 87,104)( 88,103)( 89,102)( 90,101)( 91,100)
( 92,106)( 93,112)( 94,111)( 95,110)( 96,109)( 97,108)( 98,107)(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)(169,218)(170,224)(171,223)(172,222)(173,221)
(174,220)(175,219)(176,211)(177,217)(178,216)(179,215)(180,214)(181,213)
(182,212)(183,204)(184,210)(185,209)(186,208)(187,207)(188,206)(189,205)
(190,197)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(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)(253,316)(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)(267,330)(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)(337,421)
(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)(477,596)(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)(491,610)(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)(505,638)
(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,631)(513,637)
(514,636)(515,635)(516,634)(517,633)(518,632)(519,624)(520,630)(521,629)
(522,628)(523,627)(524,626)(525,625)(526,617)(527,623)(528,622)(529,621)
(530,620)(531,619)(532,618)(533,659)(534,665)(535,664)(536,663)(537,662)
(538,661)(539,660)(540,666)(541,672)(542,671)(543,670)(544,669)(545,668)
(546,667)(547,645)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)
(554,652)(555,658)(556,657)(557,656)(558,655)(559,654)(560,653)(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)(701,890)(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)(715,876)(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)(743,785)(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)(757,834)(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)(771,820)(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)( 57,303)( 58,302)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)
( 64,296)( 65,295)( 66,301)( 67,300)( 68,299)( 69,298)( 70,297)( 71,289)
( 72,288)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)
( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,331)( 86,330)( 87,336)
( 88,335)( 89,334)( 90,333)( 91,332)( 92,324)( 93,323)( 94,329)( 95,328)
( 96,327)( 97,326)( 98,325)( 99,317)(100,316)(101,322)(102,321)(103,320)
(104,319)(105,318)(106,310)(107,309)(108,315)(109,314)(110,313)(111,312)
(112,311)(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)(169,401)(170,400)(171,406)(172,405)(173,404)(174,403)(175,402)
(176,394)(177,393)(178,399)(179,398)(180,397)(181,396)(182,395)(183,415)
(184,414)(185,420)(186,419)(187,418)(188,417)(189,416)(190,408)(191,407)
(192,413)(193,412)(194,411)(195,410)(196,409)(197,429)(198,428)(199,434)
(200,433)(201,432)(202,431)(203,430)(204,422)(205,421)(206,427)(207,426)
(208,425)(209,424)(210,423)(211,443)(212,442)(213,448)(214,447)(215,446)
(216,445)(217,444)(218,436)(219,435)(220,441)(221,440)(222,439)(223,438)
(224,437)(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)(505,751)(506,750)(507,756)(508,755)(509,754)(510,753)(511,752)
(512,744)(513,743)(514,749)(515,748)(516,747)(517,746)(518,745)(519,737)
(520,736)(521,742)(522,741)(523,740)(524,739)(525,738)(526,730)(527,729)
(528,735)(529,734)(530,733)(531,732)(532,731)(533,779)(534,778)(535,784)
(536,783)(537,782)(538,781)(539,780)(540,772)(541,771)(542,777)(543,776)
(544,775)(545,774)(546,773)(547,765)(548,764)(549,770)(550,769)(551,768)
(552,767)(553,766)(554,758)(555,757)(556,763)(557,762)(558,761)(559,760)
(560,759)(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)(617,849)(618,848)(619,854)(620,853)(621,852)(622,851)(623,850)
(624,842)(625,841)(626,847)(627,846)(628,845)(629,844)(630,843)(631,863)
(632,862)(633,868)(634,867)(635,866)(636,865)(637,864)(638,856)(639,855)
(640,861)(641,860)(642,859)(643,858)(644,857)(645,877)(646,876)(647,882)
(648,881)(649,880)(650,879)(651,878)(652,870)(653,869)(654,875)(655,874)
(656,873)(657,872)(658,871)(659,891)(660,890)(661,896)(662,895)(663,894)
(664,893)(665,892)(666,884)(667,883)(668,889)(669,888)(670,887)(671,886)
(672,885);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*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*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