Polytope of Type {4,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,56}*1792a
if this polytope has a name.
Group : SmallGroup(1792,81599)
Rank : 3
Schlafli Type : {4,56}
Number of vertices, edges, etc : 16, 448, 224
Order of s0s1s2 : 56
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,56}*896a, {4,28}*896, {4,56}*896b
4-fold quotients : {4,56}*448a, {4,28}*448, {4,56}*448b
7-fold quotients : {4,8}*256a
8-fold quotients : {4,28}*224, {2,56}*224
14-fold quotients : {4,8}*128a, {4,4}*128, {4,8}*128b
16-fold quotients : {2,28}*112, {4,14}*112
28-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
32-fold quotients : {2,14}*56
56-fold quotients : {4,4}*32, {2,8}*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)
( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)
( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)
( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)
( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)( 88,312)
( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)( 96,320)
( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(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)
(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)
(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)
(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)
(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)(200,438)
(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)
(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)(216,426)
(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)
(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)
(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)(512,736)
(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)(520,744)
(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)(528,752)
(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)(536,760)
(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)(544,768)
(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)(552,776)
(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)(560,784)
(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)
(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)(624,862)
(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)(632,842)
(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)(640,850)
(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)(648,886)
(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)(656,894)
(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)(664,874)
(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)(672,882);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)
( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)( 47, 53)
( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)
( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 86, 91)
( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)(101,111)
(102,110)(103,109)(104,108)(105,107)(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)(127,162)(128,168)(129,167)(130,166)(131,165)(132,164)
(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)(140,156)
(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,204)
(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)(184,224)
(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)(192,216)
(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)(244,304)
(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)
(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,316)
(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(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)(337,428)(338,434)(339,433)(340,432)
(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)(348,424)
(349,423)(350,422)(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)
(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)(372,393)
(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(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)(463,582)(464,588)(465,587)(466,586)(467,585)(468,584)
(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)(476,576)
(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)
(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(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)(505,617)(506,623)(507,622)(508,621)
(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)(516,627)
(517,626)(518,625)(519,638)(520,644)(521,643)(522,642)(523,641)(524,640)
(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)(532,632)
(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)
(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)(548,672)
(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)(556,664)
(557,663)(558,662)(559,661)(560,660)(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)(687,848)(688,854)(689,853)(690,852)(691,851)(692,850)
(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)(700,842)
(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)(708,890)
(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(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)(743,792)(744,798)(745,797)(746,796)(747,795)(748,794)
(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)(756,786)
(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)(764,834)
(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(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 := ( 1,450)( 2,449)( 3,455)( 4,454)( 5,453)( 6,452)( 7,451)( 8,457)
( 9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,464)( 16,463)
( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)( 24,476)
( 25,475)( 26,474)( 27,473)( 28,472)( 29,478)( 30,477)( 31,483)( 32,482)
( 33,481)( 34,480)( 35,479)( 36,485)( 37,484)( 38,490)( 39,489)( 40,488)
( 41,487)( 42,486)( 43,492)( 44,491)( 45,497)( 46,496)( 47,495)( 48,494)
( 49,493)( 50,499)( 51,498)( 52,504)( 53,503)( 54,502)( 55,501)( 56,500)
( 57,527)( 58,526)( 59,532)( 60,531)( 61,530)( 62,529)( 63,528)( 64,520)
( 65,519)( 66,525)( 67,524)( 68,523)( 69,522)( 70,521)( 71,513)( 72,512)
( 73,518)( 74,517)( 75,516)( 76,515)( 77,514)( 78,506)( 79,505)( 80,511)
( 81,510)( 82,509)( 83,508)( 84,507)( 85,555)( 86,554)( 87,560)( 88,559)
( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)( 96,551)
( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)(104,543)
(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)(112,535)
(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)(120,597)
(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)(128,603)
(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)(136,616)
(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)(144,566)
(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)(152,572)
(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)(160,578)
(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)(168,584)
(169,667)(170,666)(171,672)(172,671)(173,670)(174,669)(175,668)(176,660)
(177,659)(178,665)(179,664)(180,663)(181,662)(182,661)(183,653)(184,652)
(185,658)(186,657)(187,656)(188,655)(189,654)(190,646)(191,645)(192,651)
(193,650)(194,649)(195,648)(196,647)(197,639)(198,638)(199,644)(200,643)
(201,642)(202,641)(203,640)(204,632)(205,631)(206,637)(207,636)(208,635)
(209,634)(210,633)(211,625)(212,624)(213,630)(214,629)(215,628)(216,627)
(217,626)(218,618)(219,617)(220,623)(221,622)(222,621)(223,620)(224,619)
(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)(232,681)
(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,688)(240,687)
(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)(248,700)
(249,699)(250,698)(251,697)(252,696)(253,702)(254,701)(255,707)(256,706)
(257,705)(258,704)(259,703)(260,709)(261,708)(262,714)(263,713)(264,712)
(265,711)(266,710)(267,716)(268,715)(269,721)(270,720)(271,719)(272,718)
(273,717)(274,723)(275,722)(276,728)(277,727)(278,726)(279,725)(280,724)
(281,751)(282,750)(283,756)(284,755)(285,754)(286,753)(287,752)(288,744)
(289,743)(290,749)(291,748)(292,747)(293,746)(294,745)(295,737)(296,736)
(297,742)(298,741)(299,740)(300,739)(301,738)(302,730)(303,729)(304,735)
(305,734)(306,733)(307,732)(308,731)(309,779)(310,778)(311,784)(312,783)
(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)(320,775)
(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)(328,767)
(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)(336,759)
(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)(344,821)
(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)(352,827)
(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)(360,840)
(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)(368,790)
(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)(376,796)
(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)(384,802)
(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)(392,808)
(393,891)(394,890)(395,896)(396,895)(397,894)(398,893)(399,892)(400,884)
(401,883)(402,889)(403,888)(404,887)(405,886)(406,885)(407,877)(408,876)
(409,882)(410,881)(411,880)(412,879)(413,878)(414,870)(415,869)(416,875)
(417,874)(418,873)(419,872)(420,871)(421,863)(422,862)(423,868)(424,867)
(425,866)(426,865)(427,864)(428,856)(429,855)(430,861)(431,860)(432,859)
(433,858)(434,857)(435,849)(436,848)(437,854)(438,853)(439,852)(440,851)
(441,850)(442,842)(443,841)(444,847)(445,846)(446,845)(447,844)(448,843);;
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*s0*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*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)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)
( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)
( 72,296)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)
( 80,304)( 81,305)( 82,306)( 83,307)( 84,308)( 85,309)( 86,310)( 87,311)
( 88,312)( 89,313)( 90,314)( 91,315)( 92,316)( 93,317)( 94,318)( 95,319)
( 96,320)( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(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)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)
(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)
(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)
(192,402)(193,403)(194,404)(195,405)(196,406)(197,435)(198,436)(199,437)
(200,438)(201,439)(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)
(208,446)(209,447)(210,448)(211,421)(212,422)(213,423)(214,424)(215,425)
(216,426)(217,427)(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)
(224,434)(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)(505,729)(506,730)(507,731)(508,732)(509,733)(510,734)(511,735)
(512,736)(513,737)(514,738)(515,739)(516,740)(517,741)(518,742)(519,743)
(520,744)(521,745)(522,746)(523,747)(524,748)(525,749)(526,750)(527,751)
(528,752)(529,753)(530,754)(531,755)(532,756)(533,757)(534,758)(535,759)
(536,760)(537,761)(538,762)(539,763)(540,764)(541,765)(542,766)(543,767)
(544,768)(545,769)(546,770)(547,771)(548,772)(549,773)(550,774)(551,775)
(552,776)(553,777)(554,778)(555,779)(556,780)(557,781)(558,782)(559,783)
(560,784)(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)(617,855)(618,856)(619,857)(620,858)(621,859)(622,860)(623,861)
(624,862)(625,863)(626,864)(627,865)(628,866)(629,867)(630,868)(631,841)
(632,842)(633,843)(634,844)(635,845)(636,846)(637,847)(638,848)(639,849)
(640,850)(641,851)(642,852)(643,853)(644,854)(645,883)(646,884)(647,885)
(648,886)(649,887)(650,888)(651,889)(652,890)(653,891)(654,892)(655,893)
(656,894)(657,895)(658,896)(659,869)(660,870)(661,871)(662,872)(663,873)
(664,874)(665,875)(666,876)(667,877)(668,878)(669,879)(670,880)(671,881)
(672,882);
s1 := Sym(896)!( 2, 7)( 3, 6)( 4, 5)( 9, 14)( 10, 13)( 11, 12)( 15, 22)
( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 30, 35)( 31, 34)
( 32, 33)( 37, 42)( 38, 41)( 39, 40)( 43, 50)( 44, 56)( 45, 55)( 46, 54)
( 47, 53)( 48, 52)( 49, 51)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)
( 67, 68)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 91)( 87, 90)( 88, 89)( 93, 98)( 94, 97)( 95, 96)( 99,106)(100,112)
(101,111)(102,110)(103,109)(104,108)(105,107)(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)(127,162)(128,168)(129,167)(130,166)(131,165)
(132,164)(133,163)(134,155)(135,161)(136,160)(137,159)(138,158)(139,157)
(140,156)(169,197)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)
(176,204)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,218)
(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,211)(191,217)
(192,216)(193,215)(194,214)(195,213)(196,212)(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)(239,302)(240,308)(241,307)(242,306)(243,305)
(244,304)(245,303)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)
(252,296)(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)
(260,316)(261,322)(262,321)(263,320)(264,319)(265,318)(266,317)(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)(337,428)(338,434)(339,433)
(340,432)(341,431)(342,430)(343,429)(344,421)(345,427)(346,426)(347,425)
(348,424)(349,423)(350,422)(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)(365,400)(366,406)(367,405)(368,404)(369,403)(370,402)(371,401)
(372,393)(373,399)(374,398)(375,397)(376,396)(377,395)(378,394)(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)(463,582)(464,588)(465,587)(466,586)(467,585)
(468,584)(469,583)(470,575)(471,581)(472,580)(473,579)(474,578)(475,577)
(476,576)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)
(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(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)(505,617)(506,623)(507,622)
(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)
(516,627)(517,626)(518,625)(519,638)(520,644)(521,643)(522,642)(523,641)
(524,640)(525,639)(526,631)(527,637)(528,636)(529,635)(530,634)(531,633)
(532,632)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)
(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,666)
(548,672)(549,671)(550,670)(551,669)(552,668)(553,667)(554,659)(555,665)
(556,664)(557,663)(558,662)(559,661)(560,660)(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)(687,848)(688,854)(689,853)(690,852)(691,851)
(692,850)(693,849)(694,841)(695,847)(696,846)(697,845)(698,844)(699,843)
(700,842)(701,883)(702,889)(703,888)(704,887)(705,886)(706,885)(707,884)
(708,890)(709,896)(710,895)(711,894)(712,893)(713,892)(714,891)(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)(743,792)(744,798)(745,797)(746,796)(747,795)
(748,794)(749,793)(750,785)(751,791)(752,790)(753,789)(754,788)(755,787)
(756,786)(757,827)(758,833)(759,832)(760,831)(761,830)(762,829)(763,828)
(764,834)(765,840)(766,839)(767,838)(768,837)(769,836)(770,835)(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)!( 1,450)( 2,449)( 3,455)( 4,454)( 5,453)( 6,452)( 7,451)
( 8,457)( 9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,464)
( 16,463)( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,471)( 23,470)
( 24,476)( 25,475)( 26,474)( 27,473)( 28,472)( 29,478)( 30,477)( 31,483)
( 32,482)( 33,481)( 34,480)( 35,479)( 36,485)( 37,484)( 38,490)( 39,489)
( 40,488)( 41,487)( 42,486)( 43,492)( 44,491)( 45,497)( 46,496)( 47,495)
( 48,494)( 49,493)( 50,499)( 51,498)( 52,504)( 53,503)( 54,502)( 55,501)
( 56,500)( 57,527)( 58,526)( 59,532)( 60,531)( 61,530)( 62,529)( 63,528)
( 64,520)( 65,519)( 66,525)( 67,524)( 68,523)( 69,522)( 70,521)( 71,513)
( 72,512)( 73,518)( 74,517)( 75,516)( 76,515)( 77,514)( 78,506)( 79,505)
( 80,511)( 81,510)( 82,509)( 83,508)( 84,507)( 85,555)( 86,554)( 87,560)
( 88,559)( 89,558)( 90,557)( 91,556)( 92,548)( 93,547)( 94,553)( 95,552)
( 96,551)( 97,550)( 98,549)( 99,541)(100,540)(101,546)(102,545)(103,544)
(104,543)(105,542)(106,534)(107,533)(108,539)(109,538)(110,537)(111,536)
(112,535)(113,590)(114,589)(115,595)(116,594)(117,593)(118,592)(119,591)
(120,597)(121,596)(122,602)(123,601)(124,600)(125,599)(126,598)(127,604)
(128,603)(129,609)(130,608)(131,607)(132,606)(133,605)(134,611)(135,610)
(136,616)(137,615)(138,614)(139,613)(140,612)(141,562)(142,561)(143,567)
(144,566)(145,565)(146,564)(147,563)(148,569)(149,568)(150,574)(151,573)
(152,572)(153,571)(154,570)(155,576)(156,575)(157,581)(158,580)(159,579)
(160,578)(161,577)(162,583)(163,582)(164,588)(165,587)(166,586)(167,585)
(168,584)(169,667)(170,666)(171,672)(172,671)(173,670)(174,669)(175,668)
(176,660)(177,659)(178,665)(179,664)(180,663)(181,662)(182,661)(183,653)
(184,652)(185,658)(186,657)(187,656)(188,655)(189,654)(190,646)(191,645)
(192,651)(193,650)(194,649)(195,648)(196,647)(197,639)(198,638)(199,644)
(200,643)(201,642)(202,641)(203,640)(204,632)(205,631)(206,637)(207,636)
(208,635)(209,634)(210,633)(211,625)(212,624)(213,630)(214,629)(215,628)
(216,627)(217,626)(218,618)(219,617)(220,623)(221,622)(222,621)(223,620)
(224,619)(225,674)(226,673)(227,679)(228,678)(229,677)(230,676)(231,675)
(232,681)(233,680)(234,686)(235,685)(236,684)(237,683)(238,682)(239,688)
(240,687)(241,693)(242,692)(243,691)(244,690)(245,689)(246,695)(247,694)
(248,700)(249,699)(250,698)(251,697)(252,696)(253,702)(254,701)(255,707)
(256,706)(257,705)(258,704)(259,703)(260,709)(261,708)(262,714)(263,713)
(264,712)(265,711)(266,710)(267,716)(268,715)(269,721)(270,720)(271,719)
(272,718)(273,717)(274,723)(275,722)(276,728)(277,727)(278,726)(279,725)
(280,724)(281,751)(282,750)(283,756)(284,755)(285,754)(286,753)(287,752)
(288,744)(289,743)(290,749)(291,748)(292,747)(293,746)(294,745)(295,737)
(296,736)(297,742)(298,741)(299,740)(300,739)(301,738)(302,730)(303,729)
(304,735)(305,734)(306,733)(307,732)(308,731)(309,779)(310,778)(311,784)
(312,783)(313,782)(314,781)(315,780)(316,772)(317,771)(318,777)(319,776)
(320,775)(321,774)(322,773)(323,765)(324,764)(325,770)(326,769)(327,768)
(328,767)(329,766)(330,758)(331,757)(332,763)(333,762)(334,761)(335,760)
(336,759)(337,814)(338,813)(339,819)(340,818)(341,817)(342,816)(343,815)
(344,821)(345,820)(346,826)(347,825)(348,824)(349,823)(350,822)(351,828)
(352,827)(353,833)(354,832)(355,831)(356,830)(357,829)(358,835)(359,834)
(360,840)(361,839)(362,838)(363,837)(364,836)(365,786)(366,785)(367,791)
(368,790)(369,789)(370,788)(371,787)(372,793)(373,792)(374,798)(375,797)
(376,796)(377,795)(378,794)(379,800)(380,799)(381,805)(382,804)(383,803)
(384,802)(385,801)(386,807)(387,806)(388,812)(389,811)(390,810)(391,809)
(392,808)(393,891)(394,890)(395,896)(396,895)(397,894)(398,893)(399,892)
(400,884)(401,883)(402,889)(403,888)(404,887)(405,886)(406,885)(407,877)
(408,876)(409,882)(410,881)(411,880)(412,879)(413,878)(414,870)(415,869)
(416,875)(417,874)(418,873)(419,872)(420,871)(421,863)(422,862)(423,868)
(424,867)(425,866)(426,865)(427,864)(428,856)(429,855)(430,861)(431,860)
(432,859)(433,858)(434,857)(435,849)(436,848)(437,854)(438,853)(439,852)
(440,851)(441,850)(442,842)(443,841)(444,847)(445,846)(446,845)(447,844)
(448,843);
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*s0*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*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