Polytope of Type {56,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,16}*1792f
if this polytope has a name.
Group : SmallGroup(1792,83051)
Rank : 3
Schlafli Type : {56,16}
Number of vertices, edges, etc : 56, 448, 16
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 : {56,8}*896b, {28,16}*896b
4-fold quotients : {56,4}*448a, {28,8}*448a
7-fold quotients : {8,16}*256f
8-fold quotients : {28,4}*224, {56,2}*224, {14,8}*224
14-fold quotients : {8,8}*128b, {4,16}*128b
16-fold quotients : {28,2}*112, {14,4}*112
28-fold quotients : {4,8}*64a, {8,4}*64a
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)
( 57,302)( 58,308)( 59,307)( 60,306)( 61,305)( 62,304)( 63,303)( 64,295)
( 65,301)( 66,300)( 67,299)( 68,298)( 69,297)( 70,296)( 71,288)( 72,294)
( 73,293)( 74,292)( 75,291)( 76,290)( 77,289)( 78,281)( 79,287)( 80,286)
( 81,285)( 82,284)( 83,283)( 84,282)( 85,330)( 86,336)( 87,335)( 88,334)
( 89,333)( 90,332)( 91,331)( 92,323)( 93,329)( 94,328)( 95,327)( 96,326)
( 97,325)( 98,324)( 99,316)(100,322)(101,321)(102,320)(103,319)(104,318)
(105,317)(106,309)(107,315)(108,314)(109,313)(110,312)(111,311)(112,310)
(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)
(169,400)(170,406)(171,405)(172,404)(173,403)(174,402)(175,401)(176,393)
(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,414)(184,420)
(185,419)(186,418)(187,417)(188,416)(189,415)(190,407)(191,413)(192,412)
(193,411)(194,410)(195,409)(196,408)(197,428)(198,434)(199,433)(200,432)
(201,431)(202,430)(203,429)(204,421)(205,427)(206,426)(207,425)(208,424)
(209,423)(210,422)(211,442)(212,448)(213,447)(214,446)(215,445)(216,444)
(217,443)(218,435)(219,441)(220,440)(221,439)(222,438)(223,437)(224,436)
(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)
(505,750)(506,756)(507,755)(508,754)(509,753)(510,752)(511,751)(512,743)
(513,749)(514,748)(515,747)(516,746)(517,745)(518,744)(519,736)(520,742)
(521,741)(522,740)(523,739)(524,738)(525,737)(526,729)(527,735)(528,734)
(529,733)(530,732)(531,731)(532,730)(533,778)(534,784)(535,783)(536,782)
(537,781)(538,780)(539,779)(540,771)(541,777)(542,776)(543,775)(544,774)
(545,773)(546,772)(547,764)(548,770)(549,769)(550,768)(551,767)(552,766)
(553,765)(554,757)(555,763)(556,762)(557,761)(558,760)(559,759)(560,758)
(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)
(617,848)(618,854)(619,853)(620,852)(621,851)(622,850)(623,849)(624,841)
(625,847)(626,846)(627,845)(628,844)(629,843)(630,842)(631,862)(632,868)
(633,867)(634,866)(635,865)(636,864)(637,863)(638,855)(639,861)(640,860)
(641,859)(642,858)(643,857)(644,856)(645,876)(646,882)(647,881)(648,880)
(649,879)(650,878)(651,877)(652,869)(653,875)(654,874)(655,873)(656,872)
(657,871)(658,870)(659,890)(660,896)(661,895)(662,894)(663,893)(664,892)
(665,891)(666,883)(667,889)(668,888)(669,887)(670,886)(671,885)(672,884);;
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, 37)( 30, 36)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 57, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)( 62, 81)
( 63, 80)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)
( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)
( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(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)(169,219)(170,218)(171,224)(172,223)(173,222)(174,221)
(175,220)(176,212)(177,211)(178,217)(179,216)(180,215)(181,214)(182,213)
(183,205)(184,204)(185,210)(186,209)(187,208)(188,207)(189,206)(190,198)
(191,197)(192,203)(193,202)(194,201)(195,200)(196,199)(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)(253,317)(254,316)(255,322)(256,321)(257,320)(258,319)
(259,318)(260,310)(261,309)(262,315)(263,314)(264,313)(265,312)(266,311)
(267,331)(268,330)(269,336)(270,335)(271,334)(272,333)(273,332)(274,324)
(275,323)(276,329)(277,328)(278,327)(279,326)(280,325)(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)(477,597)(478,596)(479,602)(480,601)(481,600)(482,599)
(483,598)(484,590)(485,589)(486,595)(487,594)(488,593)(489,592)(490,591)
(491,611)(492,610)(493,616)(494,615)(495,614)(496,613)(497,612)(498,604)
(499,603)(500,609)(501,608)(502,607)(503,606)(504,605)(505,639)(506,638)
(507,644)(508,643)(509,642)(510,641)(511,640)(512,632)(513,631)(514,637)
(515,636)(516,635)(517,634)(518,633)(519,625)(520,624)(521,630)(522,629)
(523,628)(524,627)(525,626)(526,618)(527,617)(528,623)(529,622)(530,621)
(531,620)(532,619)(533,660)(534,659)(535,665)(536,664)(537,663)(538,662)
(539,661)(540,667)(541,666)(542,672)(543,671)(544,670)(545,669)(546,668)
(547,646)(548,645)(549,651)(550,650)(551,649)(552,648)(553,647)(554,653)
(555,652)(556,658)(557,657)(558,656)(559,655)(560,654)(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)(701,891)(702,890)(703,896)(704,895)(705,894)(706,893)
(707,892)(708,884)(709,883)(710,889)(711,888)(712,887)(713,886)(714,885)
(715,877)(716,876)(717,882)(718,881)(719,880)(720,879)(721,878)(722,870)
(723,869)(724,875)(725,874)(726,873)(727,872)(728,871)(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)(757,835)(758,834)(759,840)(760,839)(761,838)(762,837)
(763,836)(764,828)(765,827)(766,833)(767,832)(768,831)(769,830)(770,829)
(771,821)(772,820)(773,826)(774,825)(775,824)(776,823)(777,822)(778,814)
(779,813)(780,819)(781,818)(782,817)(783,816)(784,815);;
s2 := ( 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);;
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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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)( 57,302)( 58,308)( 59,307)( 60,306)( 61,305)( 62,304)( 63,303)
( 64,295)( 65,301)( 66,300)( 67,299)( 68,298)( 69,297)( 70,296)( 71,288)
( 72,294)( 73,293)( 74,292)( 75,291)( 76,290)( 77,289)( 78,281)( 79,287)
( 80,286)( 81,285)( 82,284)( 83,283)( 84,282)( 85,330)( 86,336)( 87,335)
( 88,334)( 89,333)( 90,332)( 91,331)( 92,323)( 93,329)( 94,328)( 95,327)
( 96,326)( 97,325)( 98,324)( 99,316)(100,322)(101,321)(102,320)(103,319)
(104,318)(105,317)(106,309)(107,315)(108,314)(109,313)(110,312)(111,311)
(112,310)(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)(169,400)(170,406)(171,405)(172,404)(173,403)(174,402)(175,401)
(176,393)(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,414)
(184,420)(185,419)(186,418)(187,417)(188,416)(189,415)(190,407)(191,413)
(192,412)(193,411)(194,410)(195,409)(196,408)(197,428)(198,434)(199,433)
(200,432)(201,431)(202,430)(203,429)(204,421)(205,427)(206,426)(207,425)
(208,424)(209,423)(210,422)(211,442)(212,448)(213,447)(214,446)(215,445)
(216,444)(217,443)(218,435)(219,441)(220,440)(221,439)(222,438)(223,437)
(224,436)(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)(505,750)(506,756)(507,755)(508,754)(509,753)(510,752)(511,751)
(512,743)(513,749)(514,748)(515,747)(516,746)(517,745)(518,744)(519,736)
(520,742)(521,741)(522,740)(523,739)(524,738)(525,737)(526,729)(527,735)
(528,734)(529,733)(530,732)(531,731)(532,730)(533,778)(534,784)(535,783)
(536,782)(537,781)(538,780)(539,779)(540,771)(541,777)(542,776)(543,775)
(544,774)(545,773)(546,772)(547,764)(548,770)(549,769)(550,768)(551,767)
(552,766)(553,765)(554,757)(555,763)(556,762)(557,761)(558,760)(559,759)
(560,758)(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)(617,848)(618,854)(619,853)(620,852)(621,851)(622,850)(623,849)
(624,841)(625,847)(626,846)(627,845)(628,844)(629,843)(630,842)(631,862)
(632,868)(633,867)(634,866)(635,865)(636,864)(637,863)(638,855)(639,861)
(640,860)(641,859)(642,858)(643,857)(644,856)(645,876)(646,882)(647,881)
(648,880)(649,879)(650,878)(651,877)(652,869)(653,875)(654,874)(655,873)
(656,872)(657,871)(658,870)(659,890)(660,896)(661,895)(662,894)(663,893)
(664,892)(665,891)(666,883)(667,889)(668,888)(669,887)(670,886)(671,885)
(672,884);
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, 37)( 30, 36)( 31, 42)
( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 43, 51)( 44, 50)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 52)( 57, 79)( 58, 78)( 59, 84)( 60, 83)( 61, 82)
( 62, 81)( 63, 80)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)
( 70, 73)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)
( 92,107)( 93,106)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(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)(169,219)(170,218)(171,224)(172,223)(173,222)
(174,221)(175,220)(176,212)(177,211)(178,217)(179,216)(180,215)(181,214)
(182,213)(183,205)(184,204)(185,210)(186,209)(187,208)(188,207)(189,206)
(190,198)(191,197)(192,203)(193,202)(194,201)(195,200)(196,199)(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)(253,317)(254,316)(255,322)(256,321)(257,320)
(258,319)(259,318)(260,310)(261,309)(262,315)(263,314)(264,313)(265,312)
(266,311)(267,331)(268,330)(269,336)(270,335)(271,334)(272,333)(273,332)
(274,324)(275,323)(276,329)(277,328)(278,327)(279,326)(280,325)(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)(477,597)(478,596)(479,602)(480,601)(481,600)
(482,599)(483,598)(484,590)(485,589)(486,595)(487,594)(488,593)(489,592)
(490,591)(491,611)(492,610)(493,616)(494,615)(495,614)(496,613)(497,612)
(498,604)(499,603)(500,609)(501,608)(502,607)(503,606)(504,605)(505,639)
(506,638)(507,644)(508,643)(509,642)(510,641)(511,640)(512,632)(513,631)
(514,637)(515,636)(516,635)(517,634)(518,633)(519,625)(520,624)(521,630)
(522,629)(523,628)(524,627)(525,626)(526,618)(527,617)(528,623)(529,622)
(530,621)(531,620)(532,619)(533,660)(534,659)(535,665)(536,664)(537,663)
(538,662)(539,661)(540,667)(541,666)(542,672)(543,671)(544,670)(545,669)
(546,668)(547,646)(548,645)(549,651)(550,650)(551,649)(552,648)(553,647)
(554,653)(555,652)(556,658)(557,657)(558,656)(559,655)(560,654)(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)(701,891)(702,890)(703,896)(704,895)(705,894)
(706,893)(707,892)(708,884)(709,883)(710,889)(711,888)(712,887)(713,886)
(714,885)(715,877)(716,876)(717,882)(718,881)(719,880)(720,879)(721,878)
(722,870)(723,869)(724,875)(725,874)(726,873)(727,872)(728,871)(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)(757,835)(758,834)(759,840)(760,839)(761,838)
(762,837)(763,836)(764,828)(765,827)(766,833)(767,832)(768,831)(769,830)
(770,829)(771,821)(772,820)(773,826)(774,825)(775,824)(776,823)(777,822)
(778,814)(779,813)(780,819)(781,818)(782,817)(783,816)(784,815);
s2 := 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);
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,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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