Polytope of Type {56,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,8}*1792d
if this polytope has a name.
Group : SmallGroup(1792,81633)
Rank : 3
Schlafli Type : {56,8}
Number of vertices, edges, etc : 112, 448, 16
Order of s0s1s2 : 56
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {56,4}*896a, {28,8}*896b
4-fold quotients : {56,4}*448a, {28,4}*448, {56,4}*448b
7-fold quotients : {8,8}*256d
8-fold quotients : {28,4}*224, {56,2}*224
14-fold quotients : {8,4}*128a, {4,8}*128b
16-fold quotients : {28,2}*112, {14,4}*112
28-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
32-fold quotients : {14,2}*56
56-fold quotients : {4,4}*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 := ( 1,449)( 2,455)( 3,454)( 4,453)( 5,452)( 6,451)( 7,450)( 8,456)
( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,463)( 16,469)
( 17,468)( 18,467)( 19,466)( 20,465)( 21,464)( 22,470)( 23,476)( 24,475)
( 25,474)( 26,473)( 27,472)( 28,471)( 29,477)( 30,483)( 31,482)( 32,481)
( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)( 40,487)
( 41,486)( 42,485)( 43,491)( 44,497)( 45,496)( 46,495)( 47,494)( 48,493)
( 49,492)( 50,498)( 51,504)( 52,503)( 53,502)( 54,501)( 55,500)( 56,499)
( 57,526)( 58,532)( 59,531)( 60,530)( 61,529)( 62,528)( 63,527)( 64,519)
( 65,525)( 66,524)( 67,523)( 68,522)( 69,521)( 70,520)( 71,512)( 72,518)
( 73,517)( 74,516)( 75,515)( 76,514)( 77,513)( 78,505)( 79,511)( 80,510)
( 81,509)( 82,508)( 83,507)( 84,506)( 85,554)( 86,560)( 87,559)( 88,558)
( 89,557)( 90,556)( 91,555)( 92,547)( 93,553)( 94,552)( 95,551)( 96,550)
( 97,549)( 98,548)( 99,540)(100,546)(101,545)(102,544)(103,543)(104,542)
(105,541)(106,533)(107,539)(108,538)(109,537)(110,536)(111,535)(112,534)
(113,589)(114,595)(115,594)(116,593)(117,592)(118,591)(119,590)(120,596)
(121,602)(122,601)(123,600)(124,599)(125,598)(126,597)(127,603)(128,609)
(129,608)(130,607)(131,606)(132,605)(133,604)(134,610)(135,616)(136,615)
(137,614)(138,613)(139,612)(140,611)(141,561)(142,567)(143,566)(144,565)
(145,564)(146,563)(147,562)(148,568)(149,574)(150,573)(151,572)(152,571)
(153,570)(154,569)(155,575)(156,581)(157,580)(158,579)(159,578)(160,577)
(161,576)(162,582)(163,588)(164,587)(165,586)(166,585)(167,584)(168,583)
(169,666)(170,672)(171,671)(172,670)(173,669)(174,668)(175,667)(176,659)
(177,665)(178,664)(179,663)(180,662)(181,661)(182,660)(183,652)(184,658)
(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)(192,650)
(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)(200,642)
(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)(208,634)
(209,633)(210,632)(211,624)(212,630)(213,629)(214,628)(215,627)(216,626)
(217,625)(218,617)(219,623)(220,622)(221,621)(222,620)(223,619)(224,618)
(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,680)
(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,687)(240,693)
(241,692)(242,691)(243,690)(244,689)(245,688)(246,694)(247,700)(248,699)
(249,698)(250,697)(251,696)(252,695)(253,701)(254,707)(255,706)(256,705)
(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)(264,711)
(265,710)(266,709)(267,715)(268,721)(269,720)(270,719)(271,718)(272,717)
(273,716)(274,722)(275,728)(276,727)(277,726)(278,725)(279,724)(280,723)
(281,750)(282,756)(283,755)(284,754)(285,753)(286,752)(287,751)(288,743)
(289,749)(290,748)(291,747)(292,746)(293,745)(294,744)(295,736)(296,742)
(297,741)(298,740)(299,739)(300,738)(301,737)(302,729)(303,735)(304,734)
(305,733)(306,732)(307,731)(308,730)(309,778)(310,784)(311,783)(312,782)
(313,781)(314,780)(315,779)(316,771)(317,777)(318,776)(319,775)(320,774)
(321,773)(322,772)(323,764)(324,770)(325,769)(326,768)(327,767)(328,766)
(329,765)(330,757)(331,763)(332,762)(333,761)(334,760)(335,759)(336,758)
(337,813)(338,819)(339,818)(340,817)(341,816)(342,815)(343,814)(344,820)
(345,826)(346,825)(347,824)(348,823)(349,822)(350,821)(351,827)(352,833)
(353,832)(354,831)(355,830)(356,829)(357,828)(358,834)(359,840)(360,839)
(361,838)(362,837)(363,836)(364,835)(365,785)(366,791)(367,790)(368,789)
(369,788)(370,787)(371,786)(372,792)(373,798)(374,797)(375,796)(376,795)
(377,794)(378,793)(379,799)(380,805)(381,804)(382,803)(383,802)(384,801)
(385,800)(386,806)(387,812)(388,811)(389,810)(390,809)(391,808)(392,807)
(393,890)(394,896)(395,895)(396,894)(397,893)(398,892)(399,891)(400,883)
(401,889)(402,888)(403,887)(404,886)(405,885)(406,884)(407,876)(408,882)
(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)(416,874)
(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)(424,866)
(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)(432,858)
(433,857)(434,856)(435,848)(436,854)(437,853)(438,852)(439,851)(440,850)
(441,849)(442,841)(443,847)(444,846)(445,845)(446,844)(447,843)(448,842);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 23)( 16, 22)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 57, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)( 62, 67)
( 63, 66)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 93)
( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)(101,105)
(102,104)(106,107)(108,112)(109,111)(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)(127,163)(128,162)(129,168)(130,167)(131,166)(132,165)
(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)(140,157)
(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)(176,198)
(177,197)(178,203)(179,202)(180,201)(181,200)(182,199)(183,212)(184,211)
(185,217)(186,216)(187,215)(188,214)(189,213)(190,219)(191,218)(192,224)
(193,223)(194,222)(195,221)(196,220)(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)(239,303)(240,302)(241,308)(242,307)(243,306)(244,305)
(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)(252,297)
(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)
(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(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)(337,429)(338,428)(339,434)(340,433)
(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)(348,425)
(349,424)(350,423)(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)
(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)(372,394)
(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(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)(463,583)(464,582)(465,588)(466,587)(467,586)(468,585)
(469,584)(470,576)(471,575)(472,581)(473,580)(474,579)(475,578)(476,577)
(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)
(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(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)(505,625)(506,624)(507,630)(508,629)
(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)(516,621)
(517,620)(518,619)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)
(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)
(533,653)(534,652)(535,658)(536,657)(537,656)(538,655)(539,654)(540,646)
(541,645)(542,651)(543,650)(544,649)(545,648)(546,647)(547,660)(548,659)
(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)
(557,671)(558,670)(559,669)(560,668)(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)(687,849)(688,848)(689,854)(690,853)(691,852)(692,851)
(693,850)(694,842)(695,841)(696,847)(697,846)(698,845)(699,844)(700,843)
(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)(707,885)(708,891)
(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)(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)(743,793)(744,792)(745,798)(746,797)(747,796)(748,795)
(749,794)(750,786)(751,785)(752,791)(753,790)(754,789)(755,788)(756,787)
(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)(763,829)(764,835)
(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)(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 := ( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)
( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)
( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)
( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)
( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)
( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)( 48,272)
( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)
( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)( 64,281)
( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)( 72,303)
( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)( 80,297)
( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)( 88,319)
( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)( 96,313)
( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)(104,335)
(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)(112,329)
(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)(120,358)
(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,337)(128,338)
(129,339)(130,340)(131,341)(132,342)(133,343)(134,344)(135,345)(136,346)
(137,347)(138,348)(139,349)(140,350)(141,379)(142,380)(143,381)(144,382)
(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)
(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)(160,370)
(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)
(169,414)(170,415)(171,416)(172,417)(173,418)(174,419)(175,420)(176,407)
(177,408)(178,409)(179,410)(180,411)(181,412)(182,413)(183,400)(184,401)
(185,402)(186,403)(187,404)(188,405)(189,406)(190,393)(191,394)(192,395)
(193,396)(194,397)(195,398)(196,399)(197,442)(198,443)(199,444)(200,445)
(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)(208,439)
(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)(216,433)
(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)(224,427)
(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)(456,680)
(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)(464,688)
(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)(472,696)
(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)(480,704)
(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)(488,712)
(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)(496,720)
(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)(504,728)
(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)(512,729)
(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)(520,751)
(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)(528,745)
(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)(536,767)
(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)(544,761)
(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)(552,783)
(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)(560,777)
(561,799)(562,800)(563,801)(564,802)(565,803)(566,804)(567,805)(568,806)
(569,807)(570,808)(571,809)(572,810)(573,811)(574,812)(575,785)(576,786)
(577,787)(578,788)(579,789)(580,790)(581,791)(582,792)(583,793)(584,794)
(585,795)(586,796)(587,797)(588,798)(589,827)(590,828)(591,829)(592,830)
(593,831)(594,832)(595,833)(596,834)(597,835)(598,836)(599,837)(600,838)
(601,839)(602,840)(603,813)(604,814)(605,815)(606,816)(607,817)(608,818)
(609,819)(610,820)(611,821)(612,822)(613,823)(614,824)(615,825)(616,826)
(617,862)(618,863)(619,864)(620,865)(621,866)(622,867)(623,868)(624,855)
(625,856)(626,857)(627,858)(628,859)(629,860)(630,861)(631,848)(632,849)
(633,850)(634,851)(635,852)(636,853)(637,854)(638,841)(639,842)(640,843)
(641,844)(642,845)(643,846)(644,847)(645,890)(646,891)(647,892)(648,893)
(649,894)(650,895)(651,896)(652,883)(653,884)(654,885)(655,886)(656,887)
(657,888)(658,889)(659,876)(660,877)(661,878)(662,879)(663,880)(664,881)
(665,882)(666,869)(667,870)(668,871)(669,872)(670,873)(671,874)(672,875);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*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)!( 1,449)( 2,455)( 3,454)( 4,453)( 5,452)( 6,451)( 7,450)
( 8,456)( 9,462)( 10,461)( 11,460)( 12,459)( 13,458)( 14,457)( 15,463)
( 16,469)( 17,468)( 18,467)( 19,466)( 20,465)( 21,464)( 22,470)( 23,476)
( 24,475)( 25,474)( 26,473)( 27,472)( 28,471)( 29,477)( 30,483)( 31,482)
( 32,481)( 33,480)( 34,479)( 35,478)( 36,484)( 37,490)( 38,489)( 39,488)
( 40,487)( 41,486)( 42,485)( 43,491)( 44,497)( 45,496)( 46,495)( 47,494)
( 48,493)( 49,492)( 50,498)( 51,504)( 52,503)( 53,502)( 54,501)( 55,500)
( 56,499)( 57,526)( 58,532)( 59,531)( 60,530)( 61,529)( 62,528)( 63,527)
( 64,519)( 65,525)( 66,524)( 67,523)( 68,522)( 69,521)( 70,520)( 71,512)
( 72,518)( 73,517)( 74,516)( 75,515)( 76,514)( 77,513)( 78,505)( 79,511)
( 80,510)( 81,509)( 82,508)( 83,507)( 84,506)( 85,554)( 86,560)( 87,559)
( 88,558)( 89,557)( 90,556)( 91,555)( 92,547)( 93,553)( 94,552)( 95,551)
( 96,550)( 97,549)( 98,548)( 99,540)(100,546)(101,545)(102,544)(103,543)
(104,542)(105,541)(106,533)(107,539)(108,538)(109,537)(110,536)(111,535)
(112,534)(113,589)(114,595)(115,594)(116,593)(117,592)(118,591)(119,590)
(120,596)(121,602)(122,601)(123,600)(124,599)(125,598)(126,597)(127,603)
(128,609)(129,608)(130,607)(131,606)(132,605)(133,604)(134,610)(135,616)
(136,615)(137,614)(138,613)(139,612)(140,611)(141,561)(142,567)(143,566)
(144,565)(145,564)(146,563)(147,562)(148,568)(149,574)(150,573)(151,572)
(152,571)(153,570)(154,569)(155,575)(156,581)(157,580)(158,579)(159,578)
(160,577)(161,576)(162,582)(163,588)(164,587)(165,586)(166,585)(167,584)
(168,583)(169,666)(170,672)(171,671)(172,670)(173,669)(174,668)(175,667)
(176,659)(177,665)(178,664)(179,663)(180,662)(181,661)(182,660)(183,652)
(184,658)(185,657)(186,656)(187,655)(188,654)(189,653)(190,645)(191,651)
(192,650)(193,649)(194,648)(195,647)(196,646)(197,638)(198,644)(199,643)
(200,642)(201,641)(202,640)(203,639)(204,631)(205,637)(206,636)(207,635)
(208,634)(209,633)(210,632)(211,624)(212,630)(213,629)(214,628)(215,627)
(216,626)(217,625)(218,617)(219,623)(220,622)(221,621)(222,620)(223,619)
(224,618)(225,673)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,680)(233,686)(234,685)(235,684)(236,683)(237,682)(238,681)(239,687)
(240,693)(241,692)(242,691)(243,690)(244,689)(245,688)(246,694)(247,700)
(248,699)(249,698)(250,697)(251,696)(252,695)(253,701)(254,707)(255,706)
(256,705)(257,704)(258,703)(259,702)(260,708)(261,714)(262,713)(263,712)
(264,711)(265,710)(266,709)(267,715)(268,721)(269,720)(270,719)(271,718)
(272,717)(273,716)(274,722)(275,728)(276,727)(277,726)(278,725)(279,724)
(280,723)(281,750)(282,756)(283,755)(284,754)(285,753)(286,752)(287,751)
(288,743)(289,749)(290,748)(291,747)(292,746)(293,745)(294,744)(295,736)
(296,742)(297,741)(298,740)(299,739)(300,738)(301,737)(302,729)(303,735)
(304,734)(305,733)(306,732)(307,731)(308,730)(309,778)(310,784)(311,783)
(312,782)(313,781)(314,780)(315,779)(316,771)(317,777)(318,776)(319,775)
(320,774)(321,773)(322,772)(323,764)(324,770)(325,769)(326,768)(327,767)
(328,766)(329,765)(330,757)(331,763)(332,762)(333,761)(334,760)(335,759)
(336,758)(337,813)(338,819)(339,818)(340,817)(341,816)(342,815)(343,814)
(344,820)(345,826)(346,825)(347,824)(348,823)(349,822)(350,821)(351,827)
(352,833)(353,832)(354,831)(355,830)(356,829)(357,828)(358,834)(359,840)
(360,839)(361,838)(362,837)(363,836)(364,835)(365,785)(366,791)(367,790)
(368,789)(369,788)(370,787)(371,786)(372,792)(373,798)(374,797)(375,796)
(376,795)(377,794)(378,793)(379,799)(380,805)(381,804)(382,803)(383,802)
(384,801)(385,800)(386,806)(387,812)(388,811)(389,810)(390,809)(391,808)
(392,807)(393,890)(394,896)(395,895)(396,894)(397,893)(398,892)(399,891)
(400,883)(401,889)(402,888)(403,887)(404,886)(405,885)(406,884)(407,876)
(408,882)(409,881)(410,880)(411,879)(412,878)(413,877)(414,869)(415,875)
(416,874)(417,873)(418,872)(419,871)(420,870)(421,862)(422,868)(423,867)
(424,866)(425,865)(426,864)(427,863)(428,855)(429,861)(430,860)(431,859)
(432,858)(433,857)(434,856)(435,848)(436,854)(437,853)(438,852)(439,851)
(440,850)(441,849)(442,841)(443,847)(444,846)(445,845)(446,844)(447,843)
(448,842);
s1 := Sym(896)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 23)
( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 30)( 31, 35)
( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 52)( 57, 65)( 58, 64)( 59, 70)( 60, 69)( 61, 68)
( 62, 67)( 63, 66)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)
( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)
(101,105)(102,104)(106,107)(108,112)(109,111)(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)(127,163)(128,162)(129,168)(130,167)(131,166)
(132,165)(133,164)(134,156)(135,155)(136,161)(137,160)(138,159)(139,158)
(140,157)(169,205)(170,204)(171,210)(172,209)(173,208)(174,207)(175,206)
(176,198)(177,197)(178,203)(179,202)(180,201)(181,200)(182,199)(183,212)
(184,211)(185,217)(186,216)(187,215)(188,214)(189,213)(190,219)(191,218)
(192,224)(193,223)(194,222)(195,221)(196,220)(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)(239,303)(240,302)(241,308)(242,307)(243,306)
(244,305)(245,304)(246,296)(247,295)(248,301)(249,300)(250,299)(251,298)
(252,297)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)
(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(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)(337,429)(338,428)(339,434)
(340,433)(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)
(348,425)(349,424)(350,423)(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)(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)
(372,394)(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(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)(463,583)(464,582)(465,588)(466,587)(467,586)
(468,585)(469,584)(470,576)(471,575)(472,581)(473,580)(474,579)(475,578)
(476,577)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)
(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(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)(505,625)(506,624)(507,630)
(508,629)(509,628)(510,627)(511,626)(512,618)(513,617)(514,623)(515,622)
(516,621)(517,620)(518,619)(519,632)(520,631)(521,637)(522,636)(523,635)
(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)
(532,640)(533,653)(534,652)(535,658)(536,657)(537,656)(538,655)(539,654)
(540,646)(541,645)(542,651)(543,650)(544,649)(545,648)(546,647)(547,660)
(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)
(556,672)(557,671)(558,670)(559,669)(560,668)(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)(687,849)(688,848)(689,854)(690,853)(691,852)
(692,851)(693,850)(694,842)(695,841)(696,847)(697,846)(698,845)(699,844)
(700,843)(701,884)(702,883)(703,889)(704,888)(705,887)(706,886)(707,885)
(708,891)(709,890)(710,896)(711,895)(712,894)(713,893)(714,892)(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)(743,793)(744,792)(745,798)(746,797)(747,796)
(748,795)(749,794)(750,786)(751,785)(752,791)(753,790)(754,789)(755,788)
(756,787)(757,828)(758,827)(759,833)(760,832)(761,831)(762,830)(763,829)
(764,835)(765,834)(766,840)(767,839)(768,838)(769,837)(770,836)(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)!( 1,225)( 2,226)( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)
( 8,232)( 9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)
( 16,240)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)
( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)
( 32,256)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)
( 40,264)( 41,265)( 42,266)( 43,267)( 44,268)( 45,269)( 46,270)( 47,271)
( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)
( 56,280)( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)
( 64,281)( 65,282)( 66,283)( 67,284)( 68,285)( 69,286)( 70,287)( 71,302)
( 72,303)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,295)( 79,296)
( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,316)( 86,317)( 87,318)
( 88,319)( 89,320)( 90,321)( 91,322)( 92,309)( 93,310)( 94,311)( 95,312)
( 96,313)( 97,314)( 98,315)( 99,330)(100,331)(101,332)(102,333)(103,334)
(104,335)(105,336)(106,323)(107,324)(108,325)(109,326)(110,327)(111,328)
(112,329)(113,351)(114,352)(115,353)(116,354)(117,355)(118,356)(119,357)
(120,358)(121,359)(122,360)(123,361)(124,362)(125,363)(126,364)(127,337)
(128,338)(129,339)(130,340)(131,341)(132,342)(133,343)(134,344)(135,345)
(136,346)(137,347)(138,348)(139,349)(140,350)(141,379)(142,380)(143,381)
(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)
(152,390)(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)
(160,370)(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)
(168,378)(169,414)(170,415)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,407)(177,408)(178,409)(179,410)(180,411)(181,412)(182,413)(183,400)
(184,401)(185,402)(186,403)(187,404)(188,405)(189,406)(190,393)(191,394)
(192,395)(193,396)(194,397)(195,398)(196,399)(197,442)(198,443)(199,444)
(200,445)(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)
(208,439)(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)
(216,433)(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)
(224,427)(449,673)(450,674)(451,675)(452,676)(453,677)(454,678)(455,679)
(456,680)(457,681)(458,682)(459,683)(460,684)(461,685)(462,686)(463,687)
(464,688)(465,689)(466,690)(467,691)(468,692)(469,693)(470,694)(471,695)
(472,696)(473,697)(474,698)(475,699)(476,700)(477,701)(478,702)(479,703)
(480,704)(481,705)(482,706)(483,707)(484,708)(485,709)(486,710)(487,711)
(488,712)(489,713)(490,714)(491,715)(492,716)(493,717)(494,718)(495,719)
(496,720)(497,721)(498,722)(499,723)(500,724)(501,725)(502,726)(503,727)
(504,728)(505,736)(506,737)(507,738)(508,739)(509,740)(510,741)(511,742)
(512,729)(513,730)(514,731)(515,732)(516,733)(517,734)(518,735)(519,750)
(520,751)(521,752)(522,753)(523,754)(524,755)(525,756)(526,743)(527,744)
(528,745)(529,746)(530,747)(531,748)(532,749)(533,764)(534,765)(535,766)
(536,767)(537,768)(538,769)(539,770)(540,757)(541,758)(542,759)(543,760)
(544,761)(545,762)(546,763)(547,778)(548,779)(549,780)(550,781)(551,782)
(552,783)(553,784)(554,771)(555,772)(556,773)(557,774)(558,775)(559,776)
(560,777)(561,799)(562,800)(563,801)(564,802)(565,803)(566,804)(567,805)
(568,806)(569,807)(570,808)(571,809)(572,810)(573,811)(574,812)(575,785)
(576,786)(577,787)(578,788)(579,789)(580,790)(581,791)(582,792)(583,793)
(584,794)(585,795)(586,796)(587,797)(588,798)(589,827)(590,828)(591,829)
(592,830)(593,831)(594,832)(595,833)(596,834)(597,835)(598,836)(599,837)
(600,838)(601,839)(602,840)(603,813)(604,814)(605,815)(606,816)(607,817)
(608,818)(609,819)(610,820)(611,821)(612,822)(613,823)(614,824)(615,825)
(616,826)(617,862)(618,863)(619,864)(620,865)(621,866)(622,867)(623,868)
(624,855)(625,856)(626,857)(627,858)(628,859)(629,860)(630,861)(631,848)
(632,849)(633,850)(634,851)(635,852)(636,853)(637,854)(638,841)(639,842)
(640,843)(641,844)(642,845)(643,846)(644,847)(645,890)(646,891)(647,892)
(648,893)(649,894)(650,895)(651,896)(652,883)(653,884)(654,885)(655,886)
(656,887)(657,888)(658,889)(659,876)(660,877)(661,878)(662,879)(663,880)
(664,881)(665,882)(666,869)(667,870)(668,871)(669,872)(670,873)(671,874)
(672,875);
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*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