Polytope of Type {28,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,8}*1792a
if this polytope has a name.
Group : SmallGroup(1792,81598)
Rank : 3
Schlafli Type : {28,8}
Number of vertices, edges, etc : 112, 448, 32
Order of s0s1s2 : 56
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {28,8}*896a, {28,4}*896, {28,8}*896b
4-fold quotients : {28,4}*448, {28,8}*448a, {28,8}*448b
7-fold quotients : {4,8}*256a
8-fold quotients : {28,4}*224, {14,8}*224
14-fold quotients : {4,8}*128a, {4,4}*128, {4,8}*128b
16-fold quotients : {28,2}*112, {14,4}*112
28-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*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)
( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)( 64,288)
( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)( 72,301)
( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)( 80,307)
( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)( 96,319)
( 97,318)( 98,317)( 99,323)(100,329)(101,328)(102,327)(103,326)(104,325)
(105,324)(106,330)(107,336)(108,335)(109,334)(110,333)(111,332)(112,331)
(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)
(169,407)(170,413)(171,412)(172,411)(173,410)(174,409)(175,408)(176,414)
(177,420)(178,419)(179,418)(180,417)(181,416)(182,415)(183,393)(184,399)
(185,398)(186,397)(187,396)(188,395)(189,394)(190,400)(191,406)(192,405)
(193,404)(194,403)(195,402)(196,401)(197,435)(198,441)(199,440)(200,439)
(201,438)(202,437)(203,436)(204,442)(205,448)(206,447)(207,446)(208,445)
(209,444)(210,443)(211,421)(212,427)(213,426)(214,425)(215,424)(216,423)
(217,422)(218,428)(219,434)(220,433)(221,432)(222,431)(223,430)(224,429)
(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)
(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)(512,736)
(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)(520,749)
(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)(528,755)
(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)(536,761)
(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)(544,767)
(545,766)(546,765)(547,771)(548,777)(549,776)(550,775)(551,774)(552,773)
(553,772)(554,778)(555,784)(556,783)(557,782)(558,781)(559,780)(560,779)
(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)
(617,855)(618,861)(619,860)(620,859)(621,858)(622,857)(623,856)(624,862)
(625,868)(626,867)(627,866)(628,865)(629,864)(630,863)(631,841)(632,847)
(633,846)(634,845)(635,844)(636,843)(637,842)(638,848)(639,854)(640,853)
(641,852)(642,851)(643,850)(644,849)(645,883)(646,889)(647,888)(648,887)
(649,886)(650,885)(651,884)(652,890)(653,896)(654,895)(655,894)(656,893)
(657,892)(658,891)(659,869)(660,875)(661,874)(662,873)(663,872)(664,871)
(665,870)(666,876)(667,882)(668,881)(669,880)(670,879)(671,878)(672,877);;
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, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)
( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85, 86)
( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,107)(100,106)(101,112)
(102,111)(103,110)(104,109)(105,108)(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)(127,163)(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)
(169,198)(170,197)(171,203)(172,202)(173,201)(174,200)(175,199)(176,205)
(177,204)(178,210)(179,209)(180,208)(181,207)(182,206)(183,219)(184,218)
(185,224)(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)(192,217)
(193,216)(194,215)(195,214)(196,213)(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)(505,618)(506,617)(507,623)(508,622)
(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)
(517,627)(518,626)(519,639)(520,638)(521,644)(522,643)(523,642)(524,641)
(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)(532,633)
(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)(540,653)
(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,667)(548,666)
(549,672)(550,671)(551,670)(552,669)(553,668)(554,660)(555,659)(556,665)
(557,664)(558,663)(559,662)(560,661)(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 := ( 1,449)( 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)( 29,477)( 30,478)( 31,479)( 32,480)
( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)( 40,488)
( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)
( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,526)( 58,527)( 59,528)( 60,529)( 61,530)( 62,531)( 63,532)( 64,519)
( 65,520)( 66,521)( 67,522)( 68,523)( 69,524)( 70,525)( 71,512)( 72,513)
( 73,514)( 74,515)( 75,516)( 76,517)( 77,518)( 78,505)( 79,506)( 80,507)
( 81,508)( 82,509)( 83,510)( 84,511)( 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)
(169,666)(170,667)(171,668)(172,669)(173,670)(174,671)(175,672)(176,659)
(177,660)(178,661)(179,662)(180,663)(181,664)(182,665)(183,652)(184,653)
(185,654)(186,655)(187,656)(188,657)(189,658)(190,645)(191,646)(192,647)
(193,648)(194,649)(195,650)(196,651)(197,638)(198,639)(199,640)(200,641)
(201,642)(202,643)(203,644)(204,631)(205,632)(206,633)(207,634)(208,635)
(209,636)(210,637)(211,624)(212,625)(213,626)(214,627)(215,628)(216,629)
(217,630)(218,617)(219,618)(220,619)(221,620)(222,621)(223,622)(224,623)
(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)(253,701)(254,702)(255,703)(256,704)
(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)(264,712)
(265,713)(266,714)(267,715)(268,716)(269,717)(270,718)(271,719)(272,720)
(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)(280,728)
(281,750)(282,751)(283,752)(284,753)(285,754)(286,755)(287,756)(288,743)
(289,744)(290,745)(291,746)(292,747)(293,748)(294,749)(295,736)(296,737)
(297,738)(298,739)(299,740)(300,741)(301,742)(302,729)(303,730)(304,731)
(305,732)(306,733)(307,734)(308,735)(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)
(393,890)(394,891)(395,892)(396,893)(397,894)(398,895)(399,896)(400,883)
(401,884)(402,885)(403,886)(404,887)(405,888)(406,889)(407,876)(408,877)
(409,878)(410,879)(411,880)(412,881)(413,882)(414,869)(415,870)(416,871)
(417,872)(418,873)(419,874)(420,875)(421,862)(422,863)(423,864)(424,865)
(425,866)(426,867)(427,868)(428,855)(429,856)(430,857)(431,858)(432,859)
(433,860)(434,861)(435,848)(436,849)(437,850)(438,851)(439,852)(440,853)
(441,854)(442,841)(443,842)(444,843)(445,844)(446,845)(447,846)(448,847);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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*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)( 57,281)( 58,287)( 59,286)( 60,285)( 61,284)( 62,283)( 63,282)
( 64,288)( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,295)
( 72,301)( 73,300)( 74,299)( 75,298)( 76,297)( 77,296)( 78,302)( 79,308)
( 80,307)( 81,306)( 82,305)( 83,304)( 84,303)( 85,309)( 86,315)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,310)( 92,316)( 93,322)( 94,321)( 95,320)
( 96,319)( 97,318)( 98,317)( 99,323)(100,329)(101,328)(102,327)(103,326)
(104,325)(105,324)(106,330)(107,336)(108,335)(109,334)(110,333)(111,332)
(112,331)(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)(169,407)(170,413)(171,412)(172,411)(173,410)(174,409)(175,408)
(176,414)(177,420)(178,419)(179,418)(180,417)(181,416)(182,415)(183,393)
(184,399)(185,398)(186,397)(187,396)(188,395)(189,394)(190,400)(191,406)
(192,405)(193,404)(194,403)(195,402)(196,401)(197,435)(198,441)(199,440)
(200,439)(201,438)(202,437)(203,436)(204,442)(205,448)(206,447)(207,446)
(208,445)(209,444)(210,443)(211,421)(212,427)(213,426)(214,425)(215,424)
(216,423)(217,422)(218,428)(219,434)(220,433)(221,432)(222,431)(223,430)
(224,429)(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)(505,729)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)
(512,736)(513,742)(514,741)(515,740)(516,739)(517,738)(518,737)(519,743)
(520,749)(521,748)(522,747)(523,746)(524,745)(525,744)(526,750)(527,756)
(528,755)(529,754)(530,753)(531,752)(532,751)(533,757)(534,763)(535,762)
(536,761)(537,760)(538,759)(539,758)(540,764)(541,770)(542,769)(543,768)
(544,767)(545,766)(546,765)(547,771)(548,777)(549,776)(550,775)(551,774)
(552,773)(553,772)(554,778)(555,784)(556,783)(557,782)(558,781)(559,780)
(560,779)(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)(617,855)(618,861)(619,860)(620,859)(621,858)(622,857)(623,856)
(624,862)(625,868)(626,867)(627,866)(628,865)(629,864)(630,863)(631,841)
(632,847)(633,846)(634,845)(635,844)(636,843)(637,842)(638,848)(639,854)
(640,853)(641,852)(642,851)(643,850)(644,849)(645,883)(646,889)(647,888)
(648,887)(649,886)(650,885)(651,884)(652,890)(653,896)(654,895)(655,894)
(656,893)(657,892)(658,891)(659,869)(660,875)(661,874)(662,873)(663,872)
(664,871)(665,870)(666,876)(667,882)(668,881)(669,880)(670,879)(671,878)
(672,877);
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, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)
( 67, 69)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,107)(100,106)
(101,112)(102,111)(103,110)(104,109)(105,108)(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)(127,163)(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)(169,198)(170,197)(171,203)(172,202)(173,201)(174,200)(175,199)
(176,205)(177,204)(178,210)(179,209)(180,208)(181,207)(182,206)(183,219)
(184,218)(185,224)(186,223)(187,222)(188,221)(189,220)(190,212)(191,211)
(192,217)(193,216)(194,215)(195,214)(196,213)(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)(505,618)(506,617)(507,623)
(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)
(516,628)(517,627)(518,626)(519,639)(520,638)(521,644)(522,643)(523,642)
(524,641)(525,640)(526,632)(527,631)(528,637)(529,636)(530,635)(531,634)
(532,633)(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)
(540,653)(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,667)
(548,666)(549,672)(550,671)(551,670)(552,669)(553,668)(554,660)(555,659)
(556,665)(557,664)(558,663)(559,662)(560,661)(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)!( 1,449)( 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)( 29,477)( 30,478)( 31,479)
( 32,480)( 33,481)( 34,482)( 35,483)( 36,484)( 37,485)( 38,486)( 39,487)
( 40,488)( 41,489)( 42,490)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)
( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)
( 56,504)( 57,526)( 58,527)( 59,528)( 60,529)( 61,530)( 62,531)( 63,532)
( 64,519)( 65,520)( 66,521)( 67,522)( 68,523)( 69,524)( 70,525)( 71,512)
( 72,513)( 73,514)( 74,515)( 75,516)( 76,517)( 77,518)( 78,505)( 79,506)
( 80,507)( 81,508)( 82,509)( 83,510)( 84,511)( 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)(169,666)(170,667)(171,668)(172,669)(173,670)(174,671)(175,672)
(176,659)(177,660)(178,661)(179,662)(180,663)(181,664)(182,665)(183,652)
(184,653)(185,654)(186,655)(187,656)(188,657)(189,658)(190,645)(191,646)
(192,647)(193,648)(194,649)(195,650)(196,651)(197,638)(198,639)(199,640)
(200,641)(201,642)(202,643)(203,644)(204,631)(205,632)(206,633)(207,634)
(208,635)(209,636)(210,637)(211,624)(212,625)(213,626)(214,627)(215,628)
(216,629)(217,630)(218,617)(219,618)(220,619)(221,620)(222,621)(223,622)
(224,623)(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)(253,701)(254,702)(255,703)
(256,704)(257,705)(258,706)(259,707)(260,708)(261,709)(262,710)(263,711)
(264,712)(265,713)(266,714)(267,715)(268,716)(269,717)(270,718)(271,719)
(272,720)(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)
(280,728)(281,750)(282,751)(283,752)(284,753)(285,754)(286,755)(287,756)
(288,743)(289,744)(290,745)(291,746)(292,747)(293,748)(294,749)(295,736)
(296,737)(297,738)(298,739)(299,740)(300,741)(301,742)(302,729)(303,730)
(304,731)(305,732)(306,733)(307,734)(308,735)(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)(393,890)(394,891)(395,892)(396,893)(397,894)(398,895)(399,896)
(400,883)(401,884)(402,885)(403,886)(404,887)(405,888)(406,889)(407,876)
(408,877)(409,878)(410,879)(411,880)(412,881)(413,882)(414,869)(415,870)
(416,871)(417,872)(418,873)(419,874)(420,875)(421,862)(422,863)(423,864)
(424,865)(425,866)(426,867)(427,868)(428,855)(429,856)(430,857)(431,858)
(432,859)(433,860)(434,861)(435,848)(436,849)(437,850)(438,851)(439,852)
(440,853)(441,854)(442,841)(443,842)(444,843)(445,844)(446,845)(447,846)
(448,847);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope