Polytope of Type {112,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {112,8}*1792f
if this polytope has a name.
Group : SmallGroup(1792,83050)
Rank : 3
Schlafli Type : {112,8}
Number of vertices, edges, etc : 112, 448, 8
Order of s0s1s2 : 112
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {56,8}*896b, {112,4}*896b
4-fold quotients : {56,4}*448a, {28,8}*448a
7-fold quotients : {16,8}*256f
8-fold quotients : {28,4}*224, {56,2}*224, {14,8}*224
14-fold quotients : {8,8}*128b, {16,4}*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 := ( 1,673)( 2,679)( 3,678)( 4,677)( 5,676)( 6,675)( 7,674)( 8,680)
( 9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,687)( 16,693)
( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,694)( 23,700)( 24,699)
( 25,698)( 26,697)( 27,696)( 28,695)( 29,708)( 30,714)( 31,713)( 32,712)
( 33,711)( 34,710)( 35,709)( 36,701)( 37,707)( 38,706)( 39,705)( 40,704)
( 41,703)( 42,702)( 43,722)( 44,728)( 45,727)( 46,726)( 47,725)( 48,724)
( 49,723)( 50,715)( 51,721)( 52,720)( 53,719)( 54,718)( 55,717)( 56,716)
( 57,736)( 58,742)( 59,741)( 60,740)( 61,739)( 62,738)( 63,737)( 64,729)
( 65,735)( 66,734)( 67,733)( 68,732)( 69,731)( 70,730)( 71,750)( 72,756)
( 73,755)( 74,754)( 75,753)( 76,752)( 77,751)( 78,743)( 79,749)( 80,748)
( 81,747)( 82,746)( 83,745)( 84,744)( 85,757)( 86,763)( 87,762)( 88,761)
( 89,760)( 90,759)( 91,758)( 92,764)( 93,770)( 94,769)( 95,768)( 96,767)
( 97,766)( 98,765)( 99,771)(100,777)(101,776)(102,775)(103,774)(104,773)
(105,772)(106,778)(107,784)(108,783)(109,782)(110,781)(111,780)(112,779)
(113,827)(114,833)(115,832)(116,831)(117,830)(118,829)(119,828)(120,834)
(121,840)(122,839)(123,838)(124,837)(125,836)(126,835)(127,813)(128,819)
(129,818)(130,817)(131,816)(132,815)(133,814)(134,820)(135,826)(136,825)
(137,824)(138,823)(139,822)(140,821)(141,799)(142,805)(143,804)(144,803)
(145,802)(146,801)(147,800)(148,806)(149,812)(150,811)(151,810)(152,809)
(153,808)(154,807)(155,785)(156,791)(157,790)(158,789)(159,788)(160,787)
(161,786)(162,792)(163,798)(164,797)(165,796)(166,795)(167,794)(168,793)
(169,890)(170,896)(171,895)(172,894)(173,893)(174,892)(175,891)(176,883)
(177,889)(178,888)(179,887)(180,886)(181,885)(182,884)(183,876)(184,882)
(185,881)(186,880)(187,879)(188,878)(189,877)(190,869)(191,875)(192,874)
(193,873)(194,872)(195,871)(196,870)(197,862)(198,868)(199,867)(200,866)
(201,865)(202,864)(203,863)(204,855)(205,861)(206,860)(207,859)(208,858)
(209,857)(210,856)(211,848)(212,854)(213,853)(214,852)(215,851)(216,850)
(217,849)(218,841)(219,847)(220,846)(221,845)(222,844)(223,843)(224,842)
(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)(232,456)
(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,463)(240,469)
(241,468)(242,467)(243,466)(244,465)(245,464)(246,470)(247,476)(248,475)
(249,474)(250,473)(251,472)(252,471)(253,484)(254,490)(255,489)(256,488)
(257,487)(258,486)(259,485)(260,477)(261,483)(262,482)(263,481)(264,480)
(265,479)(266,478)(267,498)(268,504)(269,503)(270,502)(271,501)(272,500)
(273,499)(274,491)(275,497)(276,496)(277,495)(278,494)(279,493)(280,492)
(281,512)(282,518)(283,517)(284,516)(285,515)(286,514)(287,513)(288,505)
(289,511)(290,510)(291,509)(292,508)(293,507)(294,506)(295,526)(296,532)
(297,531)(298,530)(299,529)(300,528)(301,527)(302,519)(303,525)(304,524)
(305,523)(306,522)(307,521)(308,520)(309,533)(310,539)(311,538)(312,537)
(313,536)(314,535)(315,534)(316,540)(317,546)(318,545)(319,544)(320,543)
(321,542)(322,541)(323,547)(324,553)(325,552)(326,551)(327,550)(328,549)
(329,548)(330,554)(331,560)(332,559)(333,558)(334,557)(335,556)(336,555)
(337,603)(338,609)(339,608)(340,607)(341,606)(342,605)(343,604)(344,610)
(345,616)(346,615)(347,614)(348,613)(349,612)(350,611)(351,589)(352,595)
(353,594)(354,593)(355,592)(356,591)(357,590)(358,596)(359,602)(360,601)
(361,600)(362,599)(363,598)(364,597)(365,575)(366,581)(367,580)(368,579)
(369,578)(370,577)(371,576)(372,582)(373,588)(374,587)(375,586)(376,585)
(377,584)(378,583)(379,561)(380,567)(381,566)(382,565)(383,564)(384,563)
(385,562)(386,568)(387,574)(388,573)(389,572)(390,571)(391,570)(392,569)
(393,666)(394,672)(395,671)(396,670)(397,669)(398,668)(399,667)(400,659)
(401,665)(402,664)(403,663)(404,662)(405,661)(406,660)(407,652)(408,658)
(409,657)(410,656)(411,655)(412,654)(413,653)(414,645)(415,651)(416,650)
(417,649)(418,648)(419,647)(420,646)(421,638)(422,644)(423,643)(424,642)
(425,641)(426,640)(427,639)(428,631)(429,637)(430,636)(431,635)(432,634)
(433,633)(434,632)(435,624)(436,630)(437,629)(438,628)(439,627)(440,626)
(441,625)(442,617)(443,623)(444,622)(445,621)(446,620)(447,619)(448,618);;
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 := ( 1,225)( 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)
( 57,302)( 58,303)( 59,304)( 60,305)( 61,306)( 62,307)( 63,308)( 64,295)
( 65,296)( 66,297)( 67,298)( 68,299)( 69,300)( 70,301)( 71,288)( 72,289)
( 73,290)( 74,291)( 75,292)( 76,293)( 77,294)( 78,281)( 79,282)( 80,283)
( 81,284)( 82,285)( 83,286)( 84,287)( 85,330)( 86,331)( 87,332)( 88,333)
( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)( 96,327)
( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)(104,321)
(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)(112,315)
(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)
(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,393)
(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)(184,415)
(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)(192,409)
(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)(200,431)
(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)(208,425)
(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)
(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)
(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)
(505,750)(506,751)(507,752)(508,753)(509,754)(510,755)(511,756)(512,743)
(513,744)(514,745)(515,746)(516,747)(517,748)(518,749)(519,736)(520,737)
(521,738)(522,739)(523,740)(524,741)(525,742)(526,729)(527,730)(528,731)
(529,732)(530,733)(531,734)(532,735)(533,778)(534,779)(535,780)(536,781)
(537,782)(538,783)(539,784)(540,771)(541,772)(542,773)(543,774)(544,775)
(545,776)(546,777)(547,764)(548,765)(549,766)(550,767)(551,768)(552,769)
(553,770)(554,757)(555,758)(556,759)(557,760)(558,761)(559,762)(560,763)
(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)
(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)(624,841)
(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)(632,863)
(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)(640,857)
(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)(648,879)
(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)(656,873)
(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)(664,895)
(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889);;
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,
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*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*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)!( 1,673)( 2,679)( 3,678)( 4,677)( 5,676)( 6,675)( 7,674)
( 8,680)( 9,686)( 10,685)( 11,684)( 12,683)( 13,682)( 14,681)( 15,687)
( 16,693)( 17,692)( 18,691)( 19,690)( 20,689)( 21,688)( 22,694)( 23,700)
( 24,699)( 25,698)( 26,697)( 27,696)( 28,695)( 29,708)( 30,714)( 31,713)
( 32,712)( 33,711)( 34,710)( 35,709)( 36,701)( 37,707)( 38,706)( 39,705)
( 40,704)( 41,703)( 42,702)( 43,722)( 44,728)( 45,727)( 46,726)( 47,725)
( 48,724)( 49,723)( 50,715)( 51,721)( 52,720)( 53,719)( 54,718)( 55,717)
( 56,716)( 57,736)( 58,742)( 59,741)( 60,740)( 61,739)( 62,738)( 63,737)
( 64,729)( 65,735)( 66,734)( 67,733)( 68,732)( 69,731)( 70,730)( 71,750)
( 72,756)( 73,755)( 74,754)( 75,753)( 76,752)( 77,751)( 78,743)( 79,749)
( 80,748)( 81,747)( 82,746)( 83,745)( 84,744)( 85,757)( 86,763)( 87,762)
( 88,761)( 89,760)( 90,759)( 91,758)( 92,764)( 93,770)( 94,769)( 95,768)
( 96,767)( 97,766)( 98,765)( 99,771)(100,777)(101,776)(102,775)(103,774)
(104,773)(105,772)(106,778)(107,784)(108,783)(109,782)(110,781)(111,780)
(112,779)(113,827)(114,833)(115,832)(116,831)(117,830)(118,829)(119,828)
(120,834)(121,840)(122,839)(123,838)(124,837)(125,836)(126,835)(127,813)
(128,819)(129,818)(130,817)(131,816)(132,815)(133,814)(134,820)(135,826)
(136,825)(137,824)(138,823)(139,822)(140,821)(141,799)(142,805)(143,804)
(144,803)(145,802)(146,801)(147,800)(148,806)(149,812)(150,811)(151,810)
(152,809)(153,808)(154,807)(155,785)(156,791)(157,790)(158,789)(159,788)
(160,787)(161,786)(162,792)(163,798)(164,797)(165,796)(166,795)(167,794)
(168,793)(169,890)(170,896)(171,895)(172,894)(173,893)(174,892)(175,891)
(176,883)(177,889)(178,888)(179,887)(180,886)(181,885)(182,884)(183,876)
(184,882)(185,881)(186,880)(187,879)(188,878)(189,877)(190,869)(191,875)
(192,874)(193,873)(194,872)(195,871)(196,870)(197,862)(198,868)(199,867)
(200,866)(201,865)(202,864)(203,863)(204,855)(205,861)(206,860)(207,859)
(208,858)(209,857)(210,856)(211,848)(212,854)(213,853)(214,852)(215,851)
(216,850)(217,849)(218,841)(219,847)(220,846)(221,845)(222,844)(223,843)
(224,842)(225,449)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)
(232,456)(233,462)(234,461)(235,460)(236,459)(237,458)(238,457)(239,463)
(240,469)(241,468)(242,467)(243,466)(244,465)(245,464)(246,470)(247,476)
(248,475)(249,474)(250,473)(251,472)(252,471)(253,484)(254,490)(255,489)
(256,488)(257,487)(258,486)(259,485)(260,477)(261,483)(262,482)(263,481)
(264,480)(265,479)(266,478)(267,498)(268,504)(269,503)(270,502)(271,501)
(272,500)(273,499)(274,491)(275,497)(276,496)(277,495)(278,494)(279,493)
(280,492)(281,512)(282,518)(283,517)(284,516)(285,515)(286,514)(287,513)
(288,505)(289,511)(290,510)(291,509)(292,508)(293,507)(294,506)(295,526)
(296,532)(297,531)(298,530)(299,529)(300,528)(301,527)(302,519)(303,525)
(304,524)(305,523)(306,522)(307,521)(308,520)(309,533)(310,539)(311,538)
(312,537)(313,536)(314,535)(315,534)(316,540)(317,546)(318,545)(319,544)
(320,543)(321,542)(322,541)(323,547)(324,553)(325,552)(326,551)(327,550)
(328,549)(329,548)(330,554)(331,560)(332,559)(333,558)(334,557)(335,556)
(336,555)(337,603)(338,609)(339,608)(340,607)(341,606)(342,605)(343,604)
(344,610)(345,616)(346,615)(347,614)(348,613)(349,612)(350,611)(351,589)
(352,595)(353,594)(354,593)(355,592)(356,591)(357,590)(358,596)(359,602)
(360,601)(361,600)(362,599)(363,598)(364,597)(365,575)(366,581)(367,580)
(368,579)(369,578)(370,577)(371,576)(372,582)(373,588)(374,587)(375,586)
(376,585)(377,584)(378,583)(379,561)(380,567)(381,566)(382,565)(383,564)
(384,563)(385,562)(386,568)(387,574)(388,573)(389,572)(390,571)(391,570)
(392,569)(393,666)(394,672)(395,671)(396,670)(397,669)(398,668)(399,667)
(400,659)(401,665)(402,664)(403,663)(404,662)(405,661)(406,660)(407,652)
(408,658)(409,657)(410,656)(411,655)(412,654)(413,653)(414,645)(415,651)
(416,650)(417,649)(418,648)(419,647)(420,646)(421,638)(422,644)(423,643)
(424,642)(425,641)(426,640)(427,639)(428,631)(429,637)(430,636)(431,635)
(432,634)(433,633)(434,632)(435,624)(436,630)(437,629)(438,628)(439,627)
(440,626)(441,625)(442,617)(443,623)(444,622)(445,621)(446,620)(447,619)
(448,618);
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)!( 1,225)( 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)( 57,302)( 58,303)( 59,304)( 60,305)( 61,306)( 62,307)( 63,308)
( 64,295)( 65,296)( 66,297)( 67,298)( 68,299)( 69,300)( 70,301)( 71,288)
( 72,289)( 73,290)( 74,291)( 75,292)( 76,293)( 77,294)( 78,281)( 79,282)
( 80,283)( 81,284)( 82,285)( 83,286)( 84,287)( 85,330)( 86,331)( 87,332)
( 88,333)( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)
( 96,327)( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)
(104,321)(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)
(112,315)(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)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)
(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,414)
(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,407)(191,408)
(192,409)(193,410)(194,411)(195,412)(196,413)(197,428)(198,429)(199,430)
(200,431)(201,432)(202,433)(203,434)(204,421)(205,422)(206,423)(207,424)
(208,425)(209,426)(210,427)(211,442)(212,443)(213,444)(214,445)(215,446)
(216,447)(217,448)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)
(224,441)(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)(505,750)(506,751)(507,752)(508,753)(509,754)(510,755)(511,756)
(512,743)(513,744)(514,745)(515,746)(516,747)(517,748)(518,749)(519,736)
(520,737)(521,738)(522,739)(523,740)(524,741)(525,742)(526,729)(527,730)
(528,731)(529,732)(530,733)(531,734)(532,735)(533,778)(534,779)(535,780)
(536,781)(537,782)(538,783)(539,784)(540,771)(541,772)(542,773)(543,774)
(544,775)(545,776)(546,777)(547,764)(548,765)(549,766)(550,767)(551,768)
(552,769)(553,770)(554,757)(555,758)(556,759)(557,760)(558,761)(559,762)
(560,763)(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)(617,848)(618,849)(619,850)(620,851)(621,852)(622,853)(623,854)
(624,841)(625,842)(626,843)(627,844)(628,845)(629,846)(630,847)(631,862)
(632,863)(633,864)(634,865)(635,866)(636,867)(637,868)(638,855)(639,856)
(640,857)(641,858)(642,859)(643,860)(644,861)(645,876)(646,877)(647,878)
(648,879)(649,880)(650,881)(651,882)(652,869)(653,870)(654,871)(655,872)
(656,873)(657,874)(658,875)(659,890)(660,891)(661,892)(662,893)(663,894)
(664,895)(665,896)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)
(672,889);
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,
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*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*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