Polytope of Type {8,112}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,112}*1792d
Also Known As : {8,112|2}. if this polytope has another name.
Group : SmallGroup(1792,82994)
Rank : 3
Schlafli Type : {8,112}
Number of vertices, edges, etc : 8, 448, 112
Order of s0s1s2 : 112
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,56}*896b, {4,112}*896a
4-fold quotients : {4,56}*448a, {8,28}*448a, {2,112}*448
7-fold quotients : {8,16}*256d
8-fold quotients : {4,28}*224, {2,56}*224, {8,14}*224
14-fold quotients : {8,8}*128b, {4,16}*128a
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {4,8}*64a, {8,4}*64a, {2,16}*64
32-fold quotients : {2,14}*56
56-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
64-fold quotients : {2,7}*28
112-fold quotients : {2,4}*16, {4,2}*16
224-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,225)( 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)
( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)
( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)( 72,282)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)
( 81,291)( 82,292)( 83,293)( 84,294)( 85,323)( 86,324)( 87,325)( 88,326)
( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)( 96,334)
( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)(104,314)
(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)
(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)
(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)
(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)
(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)(208,432)
(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)(216,440)
(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)
(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)
(505,743)(506,744)(507,745)(508,746)(509,747)(510,748)(511,749)(512,750)
(513,751)(514,752)(515,753)(516,754)(517,755)(518,756)(519,729)(520,730)
(521,731)(522,732)(523,733)(524,734)(525,735)(526,736)(527,737)(528,738)
(529,739)(530,740)(531,741)(532,742)(533,771)(534,772)(535,773)(536,774)
(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)(544,782)
(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)(552,762)
(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)(560,770)
(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)
(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)(624,848)
(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)(632,856)
(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)(640,864)
(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)(648,872)
(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)(656,880)
(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)(664,888)
(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)(672,896);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 57, 71)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)( 70, 79)
( 85,106)( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)( 92, 99)
( 93,105)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(113,141)(114,147)
(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)(122,153)
(123,152)(124,151)(125,150)(126,149)(127,155)(128,161)(129,160)(130,159)
(131,158)(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)(138,165)
(139,164)(140,163)(169,211)(170,217)(171,216)(172,215)(173,214)(174,213)
(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)
(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,204)
(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(225,281)(226,287)
(227,286)(228,285)(229,284)(230,283)(231,282)(232,288)(233,294)(234,293)
(235,292)(236,291)(237,290)(238,289)(239,295)(240,301)(241,300)(242,299)
(243,298)(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)(250,305)
(251,304)(252,303)(253,316)(254,322)(255,321)(256,320)(257,319)(258,318)
(259,317)(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)
(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)
(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(337,421)(338,427)
(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)(346,433)
(347,432)(348,431)(349,430)(350,429)(351,435)(352,441)(353,440)(354,439)
(355,438)(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)(362,445)
(363,444)(364,443)(365,393)(366,399)(367,398)(368,397)(369,396)(370,395)
(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)(378,401)
(379,407)(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)(386,414)
(387,420)(388,419)(389,418)(390,417)(391,416)(392,415)(449,561)(450,567)
(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)
(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)(465,580)(466,579)
(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)
(475,584)(476,583)(477,596)(478,602)(479,601)(480,600)(481,599)(482,598)
(483,597)(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)(490,590)
(491,610)(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)(498,603)
(499,609)(500,608)(501,607)(502,606)(503,605)(504,604)(505,631)(506,637)
(507,636)(508,635)(509,634)(510,633)(511,632)(512,638)(513,644)(514,643)
(515,642)(516,641)(517,640)(518,639)(519,617)(520,623)(521,622)(522,621)
(523,620)(524,619)(525,618)(526,624)(527,630)(528,629)(529,628)(530,627)
(531,626)(532,625)(533,666)(534,672)(535,671)(536,670)(537,669)(538,668)
(539,667)(540,659)(541,665)(542,664)(543,663)(544,662)(545,661)(546,660)
(547,652)(548,658)(549,657)(550,656)(551,655)(552,654)(553,653)(554,645)
(555,651)(556,650)(557,649)(558,648)(559,647)(560,646)(673,855)(674,861)
(675,860)(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)(682,867)
(683,866)(684,865)(685,864)(686,863)(687,841)(688,847)(689,846)(690,845)
(691,844)(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)(698,851)
(699,850)(700,849)(701,890)(702,896)(703,895)(704,894)(705,893)(706,892)
(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)(714,884)
(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)(722,869)
(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,799)(730,805)
(731,804)(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)(738,811)
(739,810)(740,809)(741,808)(742,807)(743,785)(744,791)(745,790)(746,789)
(747,788)(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)(754,795)
(755,794)(756,793)(757,834)(758,840)(759,839)(760,838)(761,837)(762,836)
(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)(770,828)
(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)(778,813)
(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);;
s2 := ( 1,674)( 2,673)( 3,679)( 4,678)( 5,677)( 6,676)( 7,675)( 8,681)
( 9,680)( 10,686)( 11,685)( 12,684)( 13,683)( 14,682)( 15,688)( 16,687)
( 17,693)( 18,692)( 19,691)( 20,690)( 21,689)( 22,695)( 23,694)( 24,700)
( 25,699)( 26,698)( 27,697)( 28,696)( 29,709)( 30,708)( 31,714)( 32,713)
( 33,712)( 34,711)( 35,710)( 36,702)( 37,701)( 38,707)( 39,706)( 40,705)
( 41,704)( 42,703)( 43,723)( 44,722)( 45,728)( 46,727)( 47,726)( 48,725)
( 49,724)( 50,716)( 51,715)( 52,721)( 53,720)( 54,719)( 55,718)( 56,717)
( 57,730)( 58,729)( 59,735)( 60,734)( 61,733)( 62,732)( 63,731)( 64,737)
( 65,736)( 66,742)( 67,741)( 68,740)( 69,739)( 70,738)( 71,744)( 72,743)
( 73,749)( 74,748)( 75,747)( 76,746)( 77,745)( 78,751)( 79,750)( 80,756)
( 81,755)( 82,754)( 83,753)( 84,752)( 85,765)( 86,764)( 87,770)( 88,769)
( 89,768)( 90,767)( 91,766)( 92,758)( 93,757)( 94,763)( 95,762)( 96,761)
( 97,760)( 98,759)( 99,779)(100,778)(101,784)(102,783)(103,782)(104,781)
(105,780)(106,772)(107,771)(108,777)(109,776)(110,775)(111,774)(112,773)
(113,828)(114,827)(115,833)(116,832)(117,831)(118,830)(119,829)(120,835)
(121,834)(122,840)(123,839)(124,838)(125,837)(126,836)(127,814)(128,813)
(129,819)(130,818)(131,817)(132,816)(133,815)(134,821)(135,820)(136,826)
(137,825)(138,824)(139,823)(140,822)(141,800)(142,799)(143,805)(144,804)
(145,803)(146,802)(147,801)(148,807)(149,806)(150,812)(151,811)(152,810)
(153,809)(154,808)(155,786)(156,785)(157,791)(158,790)(159,789)(160,788)
(161,787)(162,793)(163,792)(164,798)(165,797)(166,796)(167,795)(168,794)
(169,884)(170,883)(171,889)(172,888)(173,887)(174,886)(175,885)(176,891)
(177,890)(178,896)(179,895)(180,894)(181,893)(182,892)(183,870)(184,869)
(185,875)(186,874)(187,873)(188,872)(189,871)(190,877)(191,876)(192,882)
(193,881)(194,880)(195,879)(196,878)(197,856)(198,855)(199,861)(200,860)
(201,859)(202,858)(203,857)(204,863)(205,862)(206,868)(207,867)(208,866)
(209,865)(210,864)(211,842)(212,841)(213,847)(214,846)(215,845)(216,844)
(217,843)(218,849)(219,848)(220,854)(221,853)(222,852)(223,851)(224,850)
(225,450)(226,449)(227,455)(228,454)(229,453)(230,452)(231,451)(232,457)
(233,456)(234,462)(235,461)(236,460)(237,459)(238,458)(239,464)(240,463)
(241,469)(242,468)(243,467)(244,466)(245,465)(246,471)(247,470)(248,476)
(249,475)(250,474)(251,473)(252,472)(253,485)(254,484)(255,490)(256,489)
(257,488)(258,487)(259,486)(260,478)(261,477)(262,483)(263,482)(264,481)
(265,480)(266,479)(267,499)(268,498)(269,504)(270,503)(271,502)(272,501)
(273,500)(274,492)(275,491)(276,497)(277,496)(278,495)(279,494)(280,493)
(281,506)(282,505)(283,511)(284,510)(285,509)(286,508)(287,507)(288,513)
(289,512)(290,518)(291,517)(292,516)(293,515)(294,514)(295,520)(296,519)
(297,525)(298,524)(299,523)(300,522)(301,521)(302,527)(303,526)(304,532)
(305,531)(306,530)(307,529)(308,528)(309,541)(310,540)(311,546)(312,545)
(313,544)(314,543)(315,542)(316,534)(317,533)(318,539)(319,538)(320,537)
(321,536)(322,535)(323,555)(324,554)(325,560)(326,559)(327,558)(328,557)
(329,556)(330,548)(331,547)(332,553)(333,552)(334,551)(335,550)(336,549)
(337,604)(338,603)(339,609)(340,608)(341,607)(342,606)(343,605)(344,611)
(345,610)(346,616)(347,615)(348,614)(349,613)(350,612)(351,590)(352,589)
(353,595)(354,594)(355,593)(356,592)(357,591)(358,597)(359,596)(360,602)
(361,601)(362,600)(363,599)(364,598)(365,576)(366,575)(367,581)(368,580)
(369,579)(370,578)(371,577)(372,583)(373,582)(374,588)(375,587)(376,586)
(377,585)(378,584)(379,562)(380,561)(381,567)(382,566)(383,565)(384,564)
(385,563)(386,569)(387,568)(388,574)(389,573)(390,572)(391,571)(392,570)
(393,660)(394,659)(395,665)(396,664)(397,663)(398,662)(399,661)(400,667)
(401,666)(402,672)(403,671)(404,670)(405,669)(406,668)(407,646)(408,645)
(409,651)(410,650)(411,649)(412,648)(413,647)(414,653)(415,652)(416,658)
(417,657)(418,656)(419,655)(420,654)(421,632)(422,631)(423,637)(424,636)
(425,635)(426,634)(427,633)(428,639)(429,638)(430,644)(431,643)(432,642)
(433,641)(434,640)(435,618)(436,617)(437,623)(438,622)(439,621)(440,620)
(441,619)(442,625)(443,624)(444,630)(445,629)(446,628)(447,627)(448,626);;
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,225)( 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)( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)
( 64,302)( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)
( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)
( 80,290)( 81,291)( 82,292)( 83,293)( 84,294)( 85,323)( 86,324)( 87,325)
( 88,326)( 89,327)( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)
( 96,334)( 97,335)( 98,336)( 99,309)(100,310)(101,311)(102,312)(103,313)
(104,314)(105,315)(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)
(112,322)(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)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)
(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)
(184,408)(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)
(192,416)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,425)(202,426)(203,427)(204,428)(205,429)(206,430)(207,431)
(208,432)(209,433)(210,434)(211,435)(212,436)(213,437)(214,438)(215,439)
(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)
(224,448)(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)(505,743)(506,744)(507,745)(508,746)(509,747)(510,748)(511,749)
(512,750)(513,751)(514,752)(515,753)(516,754)(517,755)(518,756)(519,729)
(520,730)(521,731)(522,732)(523,733)(524,734)(525,735)(526,736)(527,737)
(528,738)(529,739)(530,740)(531,741)(532,742)(533,771)(534,772)(535,773)
(536,774)(537,775)(538,776)(539,777)(540,778)(541,779)(542,780)(543,781)
(544,782)(545,783)(546,784)(547,757)(548,758)(549,759)(550,760)(551,761)
(552,762)(553,763)(554,764)(555,765)(556,766)(557,767)(558,768)(559,769)
(560,770)(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)(617,841)(618,842)(619,843)(620,844)(621,845)(622,846)(623,847)
(624,848)(625,849)(626,850)(627,851)(628,852)(629,853)(630,854)(631,855)
(632,856)(633,857)(634,858)(635,859)(636,860)(637,861)(638,862)(639,863)
(640,864)(641,865)(642,866)(643,867)(644,868)(645,869)(646,870)(647,871)
(648,872)(649,873)(650,874)(651,875)(652,876)(653,877)(654,878)(655,879)
(656,880)(657,881)(658,882)(659,883)(660,884)(661,885)(662,886)(663,887)
(664,888)(665,889)(666,890)(667,891)(668,892)(669,893)(670,894)(671,895)
(672,896);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 29, 36)( 30, 42)( 31, 41)
( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 57, 71)( 58, 77)( 59, 76)( 60, 75)( 61, 74)
( 62, 73)( 63, 72)( 64, 78)( 65, 84)( 66, 83)( 67, 82)( 68, 81)( 69, 80)
( 70, 79)( 85,106)( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)
( 92, 99)( 93,105)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,148)(121,154)
(122,153)(123,152)(124,151)(125,150)(126,149)(127,155)(128,161)(129,160)
(130,159)(131,158)(132,157)(133,156)(134,162)(135,168)(136,167)(137,166)
(138,165)(139,164)(140,163)(169,211)(170,217)(171,216)(172,215)(173,214)
(174,213)(175,212)(176,218)(177,224)(178,223)(179,222)(180,221)(181,220)
(182,219)(183,197)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)
(190,204)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(225,281)
(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)(232,288)(233,294)
(234,293)(235,292)(236,291)(237,290)(238,289)(239,295)(240,301)(241,300)
(242,299)(243,298)(244,297)(245,296)(246,302)(247,308)(248,307)(249,306)
(250,305)(251,304)(252,303)(253,316)(254,322)(255,321)(256,320)(257,319)
(258,318)(259,317)(260,309)(261,315)(262,314)(263,313)(264,312)(265,311)
(266,310)(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)
(274,323)(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(337,421)
(338,427)(339,426)(340,425)(341,424)(342,423)(343,422)(344,428)(345,434)
(346,433)(347,432)(348,431)(349,430)(350,429)(351,435)(352,441)(353,440)
(354,439)(355,438)(356,437)(357,436)(358,442)(359,448)(360,447)(361,446)
(362,445)(363,444)(364,443)(365,393)(366,399)(367,398)(368,397)(369,396)
(370,395)(371,394)(372,400)(373,406)(374,405)(375,404)(376,403)(377,402)
(378,401)(379,407)(380,413)(381,412)(382,411)(383,410)(384,409)(385,408)
(386,414)(387,420)(388,419)(389,418)(390,417)(391,416)(392,415)(449,561)
(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)
(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)(465,580)
(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)
(474,585)(475,584)(476,583)(477,596)(478,602)(479,601)(480,600)(481,599)
(482,598)(483,597)(484,589)(485,595)(486,594)(487,593)(488,592)(489,591)
(490,590)(491,610)(492,616)(493,615)(494,614)(495,613)(496,612)(497,611)
(498,603)(499,609)(500,608)(501,607)(502,606)(503,605)(504,604)(505,631)
(506,637)(507,636)(508,635)(509,634)(510,633)(511,632)(512,638)(513,644)
(514,643)(515,642)(516,641)(517,640)(518,639)(519,617)(520,623)(521,622)
(522,621)(523,620)(524,619)(525,618)(526,624)(527,630)(528,629)(529,628)
(530,627)(531,626)(532,625)(533,666)(534,672)(535,671)(536,670)(537,669)
(538,668)(539,667)(540,659)(541,665)(542,664)(543,663)(544,662)(545,661)
(546,660)(547,652)(548,658)(549,657)(550,656)(551,655)(552,654)(553,653)
(554,645)(555,651)(556,650)(557,649)(558,648)(559,647)(560,646)(673,855)
(674,861)(675,860)(676,859)(677,858)(678,857)(679,856)(680,862)(681,868)
(682,867)(683,866)(684,865)(685,864)(686,863)(687,841)(688,847)(689,846)
(690,845)(691,844)(692,843)(693,842)(694,848)(695,854)(696,853)(697,852)
(698,851)(699,850)(700,849)(701,890)(702,896)(703,895)(704,894)(705,893)
(706,892)(707,891)(708,883)(709,889)(710,888)(711,887)(712,886)(713,885)
(714,884)(715,876)(716,882)(717,881)(718,880)(719,879)(720,878)(721,877)
(722,869)(723,875)(724,874)(725,873)(726,872)(727,871)(728,870)(729,799)
(730,805)(731,804)(732,803)(733,802)(734,801)(735,800)(736,806)(737,812)
(738,811)(739,810)(740,809)(741,808)(742,807)(743,785)(744,791)(745,790)
(746,789)(747,788)(748,787)(749,786)(750,792)(751,798)(752,797)(753,796)
(754,795)(755,794)(756,793)(757,834)(758,840)(759,839)(760,838)(761,837)
(762,836)(763,835)(764,827)(765,833)(766,832)(767,831)(768,830)(769,829)
(770,828)(771,820)(772,826)(773,825)(774,824)(775,823)(776,822)(777,821)
(778,813)(779,819)(780,818)(781,817)(782,816)(783,815)(784,814);
s2 := Sym(896)!( 1,674)( 2,673)( 3,679)( 4,678)( 5,677)( 6,676)( 7,675)
( 8,681)( 9,680)( 10,686)( 11,685)( 12,684)( 13,683)( 14,682)( 15,688)
( 16,687)( 17,693)( 18,692)( 19,691)( 20,690)( 21,689)( 22,695)( 23,694)
( 24,700)( 25,699)( 26,698)( 27,697)( 28,696)( 29,709)( 30,708)( 31,714)
( 32,713)( 33,712)( 34,711)( 35,710)( 36,702)( 37,701)( 38,707)( 39,706)
( 40,705)( 41,704)( 42,703)( 43,723)( 44,722)( 45,728)( 46,727)( 47,726)
( 48,725)( 49,724)( 50,716)( 51,715)( 52,721)( 53,720)( 54,719)( 55,718)
( 56,717)( 57,730)( 58,729)( 59,735)( 60,734)( 61,733)( 62,732)( 63,731)
( 64,737)( 65,736)( 66,742)( 67,741)( 68,740)( 69,739)( 70,738)( 71,744)
( 72,743)( 73,749)( 74,748)( 75,747)( 76,746)( 77,745)( 78,751)( 79,750)
( 80,756)( 81,755)( 82,754)( 83,753)( 84,752)( 85,765)( 86,764)( 87,770)
( 88,769)( 89,768)( 90,767)( 91,766)( 92,758)( 93,757)( 94,763)( 95,762)
( 96,761)( 97,760)( 98,759)( 99,779)(100,778)(101,784)(102,783)(103,782)
(104,781)(105,780)(106,772)(107,771)(108,777)(109,776)(110,775)(111,774)
(112,773)(113,828)(114,827)(115,833)(116,832)(117,831)(118,830)(119,829)
(120,835)(121,834)(122,840)(123,839)(124,838)(125,837)(126,836)(127,814)
(128,813)(129,819)(130,818)(131,817)(132,816)(133,815)(134,821)(135,820)
(136,826)(137,825)(138,824)(139,823)(140,822)(141,800)(142,799)(143,805)
(144,804)(145,803)(146,802)(147,801)(148,807)(149,806)(150,812)(151,811)
(152,810)(153,809)(154,808)(155,786)(156,785)(157,791)(158,790)(159,789)
(160,788)(161,787)(162,793)(163,792)(164,798)(165,797)(166,796)(167,795)
(168,794)(169,884)(170,883)(171,889)(172,888)(173,887)(174,886)(175,885)
(176,891)(177,890)(178,896)(179,895)(180,894)(181,893)(182,892)(183,870)
(184,869)(185,875)(186,874)(187,873)(188,872)(189,871)(190,877)(191,876)
(192,882)(193,881)(194,880)(195,879)(196,878)(197,856)(198,855)(199,861)
(200,860)(201,859)(202,858)(203,857)(204,863)(205,862)(206,868)(207,867)
(208,866)(209,865)(210,864)(211,842)(212,841)(213,847)(214,846)(215,845)
(216,844)(217,843)(218,849)(219,848)(220,854)(221,853)(222,852)(223,851)
(224,850)(225,450)(226,449)(227,455)(228,454)(229,453)(230,452)(231,451)
(232,457)(233,456)(234,462)(235,461)(236,460)(237,459)(238,458)(239,464)
(240,463)(241,469)(242,468)(243,467)(244,466)(245,465)(246,471)(247,470)
(248,476)(249,475)(250,474)(251,473)(252,472)(253,485)(254,484)(255,490)
(256,489)(257,488)(258,487)(259,486)(260,478)(261,477)(262,483)(263,482)
(264,481)(265,480)(266,479)(267,499)(268,498)(269,504)(270,503)(271,502)
(272,501)(273,500)(274,492)(275,491)(276,497)(277,496)(278,495)(279,494)
(280,493)(281,506)(282,505)(283,511)(284,510)(285,509)(286,508)(287,507)
(288,513)(289,512)(290,518)(291,517)(292,516)(293,515)(294,514)(295,520)
(296,519)(297,525)(298,524)(299,523)(300,522)(301,521)(302,527)(303,526)
(304,532)(305,531)(306,530)(307,529)(308,528)(309,541)(310,540)(311,546)
(312,545)(313,544)(314,543)(315,542)(316,534)(317,533)(318,539)(319,538)
(320,537)(321,536)(322,535)(323,555)(324,554)(325,560)(326,559)(327,558)
(328,557)(329,556)(330,548)(331,547)(332,553)(333,552)(334,551)(335,550)
(336,549)(337,604)(338,603)(339,609)(340,608)(341,607)(342,606)(343,605)
(344,611)(345,610)(346,616)(347,615)(348,614)(349,613)(350,612)(351,590)
(352,589)(353,595)(354,594)(355,593)(356,592)(357,591)(358,597)(359,596)
(360,602)(361,601)(362,600)(363,599)(364,598)(365,576)(366,575)(367,581)
(368,580)(369,579)(370,578)(371,577)(372,583)(373,582)(374,588)(375,587)
(376,586)(377,585)(378,584)(379,562)(380,561)(381,567)(382,566)(383,565)
(384,564)(385,563)(386,569)(387,568)(388,574)(389,573)(390,572)(391,571)
(392,570)(393,660)(394,659)(395,665)(396,664)(397,663)(398,662)(399,661)
(400,667)(401,666)(402,672)(403,671)(404,670)(405,669)(406,668)(407,646)
(408,645)(409,651)(410,650)(411,649)(412,648)(413,647)(414,653)(415,652)
(416,658)(417,657)(418,656)(419,655)(420,654)(421,632)(422,631)(423,637)
(424,636)(425,635)(426,634)(427,633)(428,639)(429,638)(430,644)(431,643)
(432,642)(433,641)(434,640)(435,618)(436,617)(437,623)(438,622)(439,621)
(440,620)(441,619)(442,625)(443,624)(444,630)(445,629)(446,628)(447,627)
(448,626);
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*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope