Polytope of Type {56,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,16}*1792c
if this polytope has a name.
Group : SmallGroup(1792,82993)
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}*896d, {28,16}*896a
4-fold quotients : {56,4}*448b, {28,8}*448a, {14,16}*448
7-fold quotients : {8,16}*256c
8-fold quotients : {28,4}*224, {14,8}*224
14-fold quotients : {8,8}*128a, {4,16}*128a
16-fold quotients : {28,2}*112, {14,4}*112
28-fold quotients : {4,8}*64a, {8,4}*64b, {2,16}*64
32-fold quotients : {14,2}*56
56-fold quotients : {4,4}*32, {2,8}*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)
( 57,295)( 58,301)( 59,300)( 60,299)( 61,298)( 62,297)( 63,296)( 64,302)
( 65,308)( 66,307)( 67,306)( 68,305)( 69,304)( 70,303)( 71,281)( 72,287)
( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,288)( 79,294)( 80,293)
( 81,292)( 82,291)( 83,290)( 84,289)( 85,323)( 86,329)( 87,328)( 88,327)
( 89,326)( 90,325)( 91,324)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,332)( 98,331)( 99,309)(100,315)(101,314)(102,313)(103,312)(104,311)
(105,310)(106,316)(107,322)(108,321)(109,320)(110,319)(111,318)(112,317)
(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)
(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,400)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)(184,413)
(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)(200,425)
(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)(208,431)
(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)(216,437)
(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)(224,443)
(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)
(505,743)(506,749)(507,748)(508,747)(509,746)(510,745)(511,744)(512,750)
(513,756)(514,755)(515,754)(516,753)(517,752)(518,751)(519,729)(520,735)
(521,734)(522,733)(523,732)(524,731)(525,730)(526,736)(527,742)(528,741)
(529,740)(530,739)(531,738)(532,737)(533,771)(534,777)(535,776)(536,775)
(537,774)(538,773)(539,772)(540,778)(541,784)(542,783)(543,782)(544,781)
(545,780)(546,779)(547,757)(548,763)(549,762)(550,761)(551,760)(552,759)
(553,758)(554,764)(555,770)(556,769)(557,768)(558,767)(559,766)(560,765)
(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)
(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)(624,848)
(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)(632,861)
(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)(640,867)
(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)(648,873)
(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)(656,879)
(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)(664,885)
(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)(672,891);;
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, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 73)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)
( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)( 92,100)
( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)
(175,213)(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)
(183,198)(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)
(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(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)(505,632)(506,631)
(507,637)(508,636)(509,635)(510,634)(511,633)(512,639)(513,638)(514,644)
(515,643)(516,642)(517,641)(518,640)(519,618)(520,617)(521,623)(522,622)
(523,621)(524,620)(525,619)(526,625)(527,624)(528,630)(529,629)(530,628)
(531,627)(532,626)(533,667)(534,666)(535,672)(536,671)(537,670)(538,669)
(539,668)(540,660)(541,659)(542,665)(543,664)(544,663)(545,662)(546,661)
(547,653)(548,652)(549,658)(550,657)(551,656)(552,655)(553,654)(554,646)
(555,645)(556,651)(557,650)(558,649)(559,648)(560,647)(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 := ( 1,449)( 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)
( 57,519)( 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)( 85,554)( 86,555)( 87,556)( 88,557)
( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)
( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)
(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)
(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)(253,708)(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)
(281,743)(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)(309,778)(310,779)(311,780)(312,781)
(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)
(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)
(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)
(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)(344,820)
(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,827)(352,828)
(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)(360,836)
(361,837)(362,838)(363,839)(364,840)(365,785)(366,786)(367,787)(368,788)
(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)(376,796)
(377,797)(378,798)(379,799)(380,800)(381,801)(382,802)(383,803)(384,804)
(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)(392,812)
(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)(400,890)
(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)(408,870)
(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)(416,878)
(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)(424,858)
(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)(432,866)
(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)(440,846)
(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)(448,854);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 ];;
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)( 57,295)( 58,301)( 59,300)( 60,299)( 61,298)( 62,297)( 63,296)
( 64,302)( 65,308)( 66,307)( 67,306)( 68,305)( 69,304)( 70,303)( 71,281)
( 72,287)( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,288)( 79,294)
( 80,293)( 81,292)( 82,291)( 83,290)( 84,289)( 85,323)( 86,329)( 87,328)
( 88,327)( 89,326)( 90,325)( 91,324)( 92,330)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,332)( 98,331)( 99,309)(100,315)(101,314)(102,313)(103,312)
(104,311)(105,310)(106,316)(107,322)(108,321)(109,320)(110,319)(111,318)
(112,317)(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)(169,393)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)
(176,400)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,407)
(184,413)(185,412)(186,411)(187,410)(188,409)(189,408)(190,414)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,421)(198,427)(199,426)
(200,425)(201,424)(202,423)(203,422)(204,428)(205,434)(206,433)(207,432)
(208,431)(209,430)(210,429)(211,435)(212,441)(213,440)(214,439)(215,438)
(216,437)(217,436)(218,442)(219,448)(220,447)(221,446)(222,445)(223,444)
(224,443)(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)(505,743)(506,749)(507,748)(508,747)(509,746)(510,745)(511,744)
(512,750)(513,756)(514,755)(515,754)(516,753)(517,752)(518,751)(519,729)
(520,735)(521,734)(522,733)(523,732)(524,731)(525,730)(526,736)(527,742)
(528,741)(529,740)(530,739)(531,738)(532,737)(533,771)(534,777)(535,776)
(536,775)(537,774)(538,773)(539,772)(540,778)(541,784)(542,783)(543,782)
(544,781)(545,780)(546,779)(547,757)(548,763)(549,762)(550,761)(551,760)
(552,759)(553,758)(554,764)(555,770)(556,769)(557,768)(558,767)(559,766)
(560,765)(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)(617,841)(618,847)(619,846)(620,845)(621,844)(622,843)(623,842)
(624,848)(625,854)(626,853)(627,852)(628,851)(629,850)(630,849)(631,855)
(632,861)(633,860)(634,859)(635,858)(636,857)(637,856)(638,862)(639,868)
(640,867)(641,866)(642,865)(643,864)(644,863)(645,869)(646,875)(647,874)
(648,873)(649,872)(650,871)(651,870)(652,876)(653,882)(654,881)(655,880)
(656,879)(657,878)(658,877)(659,883)(660,889)(661,888)(662,887)(663,886)
(664,885)(665,884)(666,890)(667,896)(668,895)(669,894)(670,893)(671,892)
(672,891);
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, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)
( 62, 74)( 63, 73)( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)
( 70, 80)( 85,107)( 86,106)( 87,112)( 88,111)( 89,110)( 90,109)( 91,108)
( 92,100)( 93, 99)( 94,105)( 95,104)( 96,103)( 97,102)( 98,101)(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)(169,212)(170,211)(171,217)(172,216)(173,215)
(174,214)(175,213)(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)
(182,220)(183,198)(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)
(190,205)(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(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)(505,632)
(506,631)(507,637)(508,636)(509,635)(510,634)(511,633)(512,639)(513,638)
(514,644)(515,643)(516,642)(517,641)(518,640)(519,618)(520,617)(521,623)
(522,622)(523,621)(524,620)(525,619)(526,625)(527,624)(528,630)(529,629)
(530,628)(531,627)(532,626)(533,667)(534,666)(535,672)(536,671)(537,670)
(538,669)(539,668)(540,660)(541,659)(542,665)(543,664)(544,663)(545,662)
(546,661)(547,653)(548,652)(549,658)(550,657)(551,656)(552,655)(553,654)
(554,646)(555,645)(556,651)(557,650)(558,649)(559,648)(560,647)(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)!( 1,449)( 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)( 57,519)( 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)( 85,554)( 86,555)( 87,556)
( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)
( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)
(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)
(112,539)(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)(253,708)(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)(281,743)(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)(309,778)(310,779)(311,780)
(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)
(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)
(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)
(336,763)(337,813)(338,814)(339,815)(340,816)(341,817)(342,818)(343,819)
(344,820)(345,821)(346,822)(347,823)(348,824)(349,825)(350,826)(351,827)
(352,828)(353,829)(354,830)(355,831)(356,832)(357,833)(358,834)(359,835)
(360,836)(361,837)(362,838)(363,839)(364,840)(365,785)(366,786)(367,787)
(368,788)(369,789)(370,790)(371,791)(372,792)(373,793)(374,794)(375,795)
(376,796)(377,797)(378,798)(379,799)(380,800)(381,801)(382,802)(383,803)
(384,804)(385,805)(386,806)(387,807)(388,808)(389,809)(390,810)(391,811)
(392,812)(393,883)(394,884)(395,885)(396,886)(397,887)(398,888)(399,889)
(400,890)(401,891)(402,892)(403,893)(404,894)(405,895)(406,896)(407,869)
(408,870)(409,871)(410,872)(411,873)(412,874)(413,875)(414,876)(415,877)
(416,878)(417,879)(418,880)(419,881)(420,882)(421,855)(422,856)(423,857)
(424,858)(425,859)(426,860)(427,861)(428,862)(429,863)(430,864)(431,865)
(432,866)(433,867)(434,868)(435,841)(436,842)(437,843)(438,844)(439,845)
(440,846)(441,847)(442,848)(443,849)(444,850)(445,851)(446,852)(447,853)
(448,854);
poly := sub<Sym(896)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*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 >;
References : None.
to this polytope