Polytope of Type {6,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*1728h
if this polytope has a name.
Group : SmallGroup(1728,33416)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 18, 432, 144
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
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 : {6,24}*864h
3-fold quotients : {6,16}*576
4-fold quotients : {6,12}*432i
6-fold quotients : {6,8}*288
8-fold quotients : {6,12}*216c
9-fold quotients : {2,48}*192
12-fold quotients : {6,4}*144
18-fold quotients : {2,24}*96
24-fold quotients : {6,4}*72
27-fold quotients : {2,16}*64
36-fold quotients : {2,12}*48
54-fold quotients : {2,8}*32
72-fold quotients : {2,6}*24
108-fold quotients : {2,4}*16
144-fold quotients : {2,3}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)( 16,337)
( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)( 24,350)
( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,361)( 38,363)( 39,362)( 40,367)
( 41,369)( 42,368)( 43,364)( 44,366)( 45,365)( 46,370)( 47,372)( 48,371)
( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,379)( 56,381)
( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,388)
( 65,390)( 66,389)( 67,394)( 68,396)( 69,395)( 70,391)( 71,393)( 72,392)
( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)( 80,402)
( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)( 96,422)
( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)(104,432)
(105,431)(106,427)(107,429)(108,428)(109,298)(110,300)(111,299)(112,304)
(113,306)(114,305)(115,301)(116,303)(117,302)(118,307)(119,309)(120,308)
(121,313)(122,315)(123,314)(124,310)(125,312)(126,311)(127,316)(128,318)
(129,317)(130,322)(131,324)(132,323)(133,319)(134,321)(135,320)(136,271)
(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)(144,275)
(145,280)(146,282)(147,281)(148,286)(149,288)(150,287)(151,283)(152,285)
(153,284)(154,289)(155,291)(156,290)(157,295)(158,297)(159,296)(160,292)
(161,294)(162,293)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)
(169,220)(170,222)(171,221)(172,226)(173,228)(174,227)(175,232)(176,234)
(177,233)(178,229)(179,231)(180,230)(181,235)(182,237)(183,236)(184,241)
(185,243)(186,242)(187,238)(188,240)(189,239)(190,244)(191,246)(192,245)
(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,253)(200,255)
(201,254)(202,259)(203,261)(204,260)(205,256)(206,258)(207,257)(208,262)
(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)(216,266)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,766)(443,768)(444,767)(445,772)(446,774)(447,773)(448,769)
(449,771)(450,770)(451,775)(452,777)(453,776)(454,781)(455,783)(456,782)
(457,778)(458,780)(459,779)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,793)(470,795)(471,794)(472,799)
(473,801)(474,800)(475,796)(476,798)(477,797)(478,802)(479,804)(480,803)
(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,811)(488,813)
(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,820)
(497,822)(498,821)(499,826)(500,828)(501,827)(502,823)(503,825)(504,824)
(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)(512,834)
(513,833)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)
(521,843)(522,842)(523,847)(524,849)(525,848)(526,853)(527,855)(528,854)
(529,850)(530,852)(531,851)(532,856)(533,858)(534,857)(535,862)(536,864)
(537,863)(538,859)(539,861)(540,860)(541,730)(542,732)(543,731)(544,736)
(545,738)(546,737)(547,733)(548,735)(549,734)(550,739)(551,741)(552,740)
(553,745)(554,747)(555,746)(556,742)(557,744)(558,743)(559,748)(560,750)
(561,749)(562,754)(563,756)(564,755)(565,751)(566,753)(567,752)(568,703)
(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)(576,707)
(577,712)(578,714)(579,713)(580,718)(581,720)(582,719)(583,715)(584,717)
(585,716)(586,721)(587,723)(588,722)(589,727)(590,729)(591,728)(592,724)
(593,726)(594,725)(595,649)(596,651)(597,650)(598,655)(599,657)(600,656)
(601,652)(602,654)(603,653)(604,658)(605,660)(606,659)(607,664)(608,666)
(609,665)(610,661)(611,663)(612,662)(613,667)(614,669)(615,668)(616,673)
(617,675)(618,674)(619,670)(620,672)(621,671)(622,676)(623,678)(624,677)
(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,685)(632,687)
(633,686)(634,691)(635,693)(636,692)(637,688)(638,690)(639,689)(640,694)
(641,696)(642,695)(643,700)(644,702)(645,701)(646,697)(647,699)(648,698);;
s1 := ( 1, 4)( 3, 9)( 5, 8)( 10, 22)( 11, 20)( 12, 27)( 13, 19)( 14, 26)
( 15, 24)( 16, 25)( 17, 23)( 18, 21)( 28, 31)( 30, 36)( 32, 35)( 37, 49)
( 38, 47)( 39, 54)( 40, 46)( 41, 53)( 42, 51)( 43, 52)( 44, 50)( 45, 48)
( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)( 60, 87)( 61, 88)( 62, 86)
( 63, 84)( 64,103)( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)( 70,106)
( 71,104)( 72,102)( 73, 94)( 74, 92)( 75, 99)( 76, 91)( 77, 98)( 78, 96)
( 79, 97)( 80, 95)( 81, 93)(109,166)(110,164)(111,171)(112,163)(113,170)
(114,168)(115,169)(116,167)(117,165)(118,184)(119,182)(120,189)(121,181)
(122,188)(123,186)(124,187)(125,185)(126,183)(127,175)(128,173)(129,180)
(130,172)(131,179)(132,177)(133,178)(134,176)(135,174)(136,193)(137,191)
(138,198)(139,190)(140,197)(141,195)(142,196)(143,194)(144,192)(145,211)
(146,209)(147,216)(148,208)(149,215)(150,213)(151,214)(152,212)(153,210)
(154,202)(155,200)(156,207)(157,199)(158,206)(159,204)(160,205)(161,203)
(162,201)(217,301)(218,299)(219,306)(220,298)(221,305)(222,303)(223,304)
(224,302)(225,300)(226,319)(227,317)(228,324)(229,316)(230,323)(231,321)
(232,322)(233,320)(234,318)(235,310)(236,308)(237,315)(238,307)(239,314)
(240,312)(241,313)(242,311)(243,309)(244,274)(245,272)(246,279)(247,271)
(248,278)(249,276)(250,277)(251,275)(252,273)(253,292)(254,290)(255,297)
(256,289)(257,296)(258,294)(259,295)(260,293)(261,291)(262,283)(263,281)
(264,288)(265,280)(266,287)(267,285)(268,286)(269,284)(270,282)(325,328)
(327,333)(329,332)(334,346)(335,344)(336,351)(337,343)(338,350)(339,348)
(340,349)(341,347)(342,345)(352,355)(354,360)(356,359)(361,373)(362,371)
(363,378)(364,370)(365,377)(366,375)(367,376)(368,374)(369,372)(379,409)
(380,407)(381,414)(382,406)(383,413)(384,411)(385,412)(386,410)(387,408)
(388,427)(389,425)(390,432)(391,424)(392,431)(393,429)(394,430)(395,428)
(396,426)(397,418)(398,416)(399,423)(400,415)(401,422)(402,420)(403,421)
(404,419)(405,417)(433,544)(434,542)(435,549)(436,541)(437,548)(438,546)
(439,547)(440,545)(441,543)(442,562)(443,560)(444,567)(445,559)(446,566)
(447,564)(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)
(455,557)(456,555)(457,556)(458,554)(459,552)(460,571)(461,569)(462,576)
(463,568)(464,575)(465,573)(466,574)(467,572)(468,570)(469,589)(470,587)
(471,594)(472,586)(473,593)(474,591)(475,592)(476,590)(477,588)(478,580)
(479,578)(480,585)(481,577)(482,584)(483,582)(484,583)(485,581)(486,579)
(487,625)(488,623)(489,630)(490,622)(491,629)(492,627)(493,628)(494,626)
(495,624)(496,643)(497,641)(498,648)(499,640)(500,647)(501,645)(502,646)
(503,644)(504,642)(505,634)(506,632)(507,639)(508,631)(509,638)(510,636)
(511,637)(512,635)(513,633)(514,598)(515,596)(516,603)(517,595)(518,602)
(519,600)(520,601)(521,599)(522,597)(523,616)(524,614)(525,621)(526,613)
(527,620)(528,618)(529,619)(530,617)(531,615)(532,607)(533,605)(534,612)
(535,604)(536,611)(537,609)(538,610)(539,608)(540,606)(649,841)(650,839)
(651,846)(652,838)(653,845)(654,843)(655,844)(656,842)(657,840)(658,859)
(659,857)(660,864)(661,856)(662,863)(663,861)(664,862)(665,860)(666,858)
(667,850)(668,848)(669,855)(670,847)(671,854)(672,852)(673,853)(674,851)
(675,849)(676,814)(677,812)(678,819)(679,811)(680,818)(681,816)(682,817)
(683,815)(684,813)(685,832)(686,830)(687,837)(688,829)(689,836)(690,834)
(691,835)(692,833)(693,831)(694,823)(695,821)(696,828)(697,820)(698,827)
(699,825)(700,826)(701,824)(702,822)(703,787)(704,785)(705,792)(706,784)
(707,791)(708,789)(709,790)(710,788)(711,786)(712,805)(713,803)(714,810)
(715,802)(716,809)(717,807)(718,808)(719,806)(720,804)(721,796)(722,794)
(723,801)(724,793)(725,800)(726,798)(727,799)(728,797)(729,795)(730,760)
(731,758)(732,765)(733,757)(734,764)(735,762)(736,763)(737,761)(738,759)
(739,778)(740,776)(741,783)(742,775)(743,782)(744,780)(745,781)(746,779)
(747,777)(748,769)(749,767)(750,774)(751,766)(752,773)(753,771)(754,772)
(755,770)(756,768);;
s2 := ( 1,442)( 2,443)( 3,444)( 4,450)( 5,448)( 6,449)( 7,446)( 8,447)
( 9,445)( 10,433)( 11,434)( 12,435)( 13,441)( 14,439)( 15,440)( 16,437)
( 17,438)( 18,436)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)
( 25,455)( 26,456)( 27,454)( 28,469)( 29,470)( 30,471)( 31,477)( 32,475)
( 33,476)( 34,473)( 35,474)( 36,472)( 37,460)( 38,461)( 39,462)( 40,468)
( 41,466)( 42,467)( 43,464)( 44,465)( 45,463)( 46,478)( 47,479)( 48,480)
( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,523)( 56,524)
( 57,525)( 58,531)( 59,529)( 60,530)( 61,527)( 62,528)( 63,526)( 64,514)
( 65,515)( 66,516)( 67,522)( 68,520)( 69,521)( 70,518)( 71,519)( 72,517)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,496)( 83,497)( 84,498)( 85,504)( 86,502)( 87,503)( 88,500)
( 89,501)( 90,499)( 91,487)( 92,488)( 93,489)( 94,495)( 95,493)( 96,494)
( 97,491)( 98,492)( 99,490)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,604)(110,605)(111,606)(112,612)
(113,610)(114,611)(115,608)(116,609)(117,607)(118,595)(119,596)(120,597)
(121,603)(122,601)(123,602)(124,599)(125,600)(126,598)(127,613)(128,614)
(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,631)
(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)(144,634)
(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)(152,627)
(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)
(161,645)(162,643)(163,550)(164,551)(165,552)(166,558)(167,556)(168,557)
(169,554)(170,555)(171,553)(172,541)(173,542)(174,543)(175,549)(176,547)
(177,548)(178,545)(179,546)(180,544)(181,559)(182,560)(183,561)(184,567)
(185,565)(186,566)(187,563)(188,564)(189,562)(190,577)(191,578)(192,579)
(193,585)(194,583)(195,584)(196,581)(197,582)(198,580)(199,568)(200,569)
(201,570)(202,576)(203,574)(204,575)(205,572)(206,573)(207,571)(208,586)
(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)
(217,739)(218,740)(219,741)(220,747)(221,745)(222,746)(223,743)(224,744)
(225,742)(226,730)(227,731)(228,732)(229,738)(230,736)(231,737)(232,734)
(233,735)(234,733)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)
(241,752)(242,753)(243,751)(244,712)(245,713)(246,714)(247,720)(248,718)
(249,719)(250,716)(251,717)(252,715)(253,703)(254,704)(255,705)(256,711)
(257,709)(258,710)(259,707)(260,708)(261,706)(262,721)(263,722)(264,723)
(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,685)(272,686)
(273,687)(274,693)(275,691)(276,692)(277,689)(278,690)(279,688)(280,676)
(281,677)(282,678)(283,684)(284,682)(285,683)(286,680)(287,681)(288,679)
(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)
(297,697)(298,658)(299,659)(300,660)(301,666)(302,664)(303,665)(304,662)
(305,663)(306,661)(307,649)(308,650)(309,651)(310,657)(311,655)(312,656)
(313,653)(314,654)(315,652)(316,667)(317,668)(318,669)(319,675)(320,673)
(321,674)(322,671)(323,672)(324,670)(325,766)(326,767)(327,768)(328,774)
(329,772)(330,773)(331,770)(332,771)(333,769)(334,757)(335,758)(336,759)
(337,765)(338,763)(339,764)(340,761)(341,762)(342,760)(343,775)(344,776)
(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,793)
(353,794)(354,795)(355,801)(356,799)(357,800)(358,797)(359,798)(360,796)
(361,784)(362,785)(363,786)(364,792)(365,790)(366,791)(367,788)(368,789)
(369,787)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)
(377,807)(378,805)(379,847)(380,848)(381,849)(382,855)(383,853)(384,854)
(385,851)(386,852)(387,850)(388,838)(389,839)(390,840)(391,846)(392,844)
(393,845)(394,842)(395,843)(396,841)(397,856)(398,857)(399,858)(400,864)
(401,862)(402,863)(403,860)(404,861)(405,859)(406,820)(407,821)(408,822)
(409,828)(410,826)(411,827)(412,824)(413,825)(414,823)(415,811)(416,812)
(417,813)(418,819)(419,817)(420,818)(421,815)(422,816)(423,814)(424,829)
(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832);;
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*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)
( 16,337)( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)
( 24,350)( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,361)( 38,363)( 39,362)
( 40,367)( 41,369)( 42,368)( 43,364)( 44,366)( 45,365)( 46,370)( 47,372)
( 48,371)( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,379)
( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)
( 64,388)( 65,390)( 66,389)( 67,394)( 68,396)( 69,395)( 70,391)( 71,393)
( 72,392)( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)
( 80,402)( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)
( 88,409)( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)
( 96,422)( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)
(104,432)(105,431)(106,427)(107,429)(108,428)(109,298)(110,300)(111,299)
(112,304)(113,306)(114,305)(115,301)(116,303)(117,302)(118,307)(119,309)
(120,308)(121,313)(122,315)(123,314)(124,310)(125,312)(126,311)(127,316)
(128,318)(129,317)(130,322)(131,324)(132,323)(133,319)(134,321)(135,320)
(136,271)(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)
(144,275)(145,280)(146,282)(147,281)(148,286)(149,288)(150,287)(151,283)
(152,285)(153,284)(154,289)(155,291)(156,290)(157,295)(158,297)(159,296)
(160,292)(161,294)(162,293)(163,217)(164,219)(165,218)(166,223)(167,225)
(168,224)(169,220)(170,222)(171,221)(172,226)(173,228)(174,227)(175,232)
(176,234)(177,233)(178,229)(179,231)(180,230)(181,235)(182,237)(183,236)
(184,241)(185,243)(186,242)(187,238)(188,240)(189,239)(190,244)(191,246)
(192,245)(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,253)
(200,255)(201,254)(202,259)(203,261)(204,260)(205,256)(206,258)(207,257)
(208,262)(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)
(216,266)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)
(440,762)(441,761)(442,766)(443,768)(444,767)(445,772)(446,774)(447,773)
(448,769)(449,771)(450,770)(451,775)(452,777)(453,776)(454,781)(455,783)
(456,782)(457,778)(458,780)(459,779)(460,784)(461,786)(462,785)(463,790)
(464,792)(465,791)(466,787)(467,789)(468,788)(469,793)(470,795)(471,794)
(472,799)(473,801)(474,800)(475,796)(476,798)(477,797)(478,802)(479,804)
(480,803)(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,811)
(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)
(496,820)(497,822)(498,821)(499,826)(500,828)(501,827)(502,823)(503,825)
(504,824)(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)
(512,834)(513,833)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)
(520,841)(521,843)(522,842)(523,847)(524,849)(525,848)(526,853)(527,855)
(528,854)(529,850)(530,852)(531,851)(532,856)(533,858)(534,857)(535,862)
(536,864)(537,863)(538,859)(539,861)(540,860)(541,730)(542,732)(543,731)
(544,736)(545,738)(546,737)(547,733)(548,735)(549,734)(550,739)(551,741)
(552,740)(553,745)(554,747)(555,746)(556,742)(557,744)(558,743)(559,748)
(560,750)(561,749)(562,754)(563,756)(564,755)(565,751)(566,753)(567,752)
(568,703)(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)
(576,707)(577,712)(578,714)(579,713)(580,718)(581,720)(582,719)(583,715)
(584,717)(585,716)(586,721)(587,723)(588,722)(589,727)(590,729)(591,728)
(592,724)(593,726)(594,725)(595,649)(596,651)(597,650)(598,655)(599,657)
(600,656)(601,652)(602,654)(603,653)(604,658)(605,660)(606,659)(607,664)
(608,666)(609,665)(610,661)(611,663)(612,662)(613,667)(614,669)(615,668)
(616,673)(617,675)(618,674)(619,670)(620,672)(621,671)(622,676)(623,678)
(624,677)(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,685)
(632,687)(633,686)(634,691)(635,693)(636,692)(637,688)(638,690)(639,689)
(640,694)(641,696)(642,695)(643,700)(644,702)(645,701)(646,697)(647,699)
(648,698);
s1 := Sym(864)!( 1, 4)( 3, 9)( 5, 8)( 10, 22)( 11, 20)( 12, 27)( 13, 19)
( 14, 26)( 15, 24)( 16, 25)( 17, 23)( 18, 21)( 28, 31)( 30, 36)( 32, 35)
( 37, 49)( 38, 47)( 39, 54)( 40, 46)( 41, 53)( 42, 51)( 43, 52)( 44, 50)
( 45, 48)( 55, 85)( 56, 83)( 57, 90)( 58, 82)( 59, 89)( 60, 87)( 61, 88)
( 62, 86)( 63, 84)( 64,103)( 65,101)( 66,108)( 67,100)( 68,107)( 69,105)
( 70,106)( 71,104)( 72,102)( 73, 94)( 74, 92)( 75, 99)( 76, 91)( 77, 98)
( 78, 96)( 79, 97)( 80, 95)( 81, 93)(109,166)(110,164)(111,171)(112,163)
(113,170)(114,168)(115,169)(116,167)(117,165)(118,184)(119,182)(120,189)
(121,181)(122,188)(123,186)(124,187)(125,185)(126,183)(127,175)(128,173)
(129,180)(130,172)(131,179)(132,177)(133,178)(134,176)(135,174)(136,193)
(137,191)(138,198)(139,190)(140,197)(141,195)(142,196)(143,194)(144,192)
(145,211)(146,209)(147,216)(148,208)(149,215)(150,213)(151,214)(152,212)
(153,210)(154,202)(155,200)(156,207)(157,199)(158,206)(159,204)(160,205)
(161,203)(162,201)(217,301)(218,299)(219,306)(220,298)(221,305)(222,303)
(223,304)(224,302)(225,300)(226,319)(227,317)(228,324)(229,316)(230,323)
(231,321)(232,322)(233,320)(234,318)(235,310)(236,308)(237,315)(238,307)
(239,314)(240,312)(241,313)(242,311)(243,309)(244,274)(245,272)(246,279)
(247,271)(248,278)(249,276)(250,277)(251,275)(252,273)(253,292)(254,290)
(255,297)(256,289)(257,296)(258,294)(259,295)(260,293)(261,291)(262,283)
(263,281)(264,288)(265,280)(266,287)(267,285)(268,286)(269,284)(270,282)
(325,328)(327,333)(329,332)(334,346)(335,344)(336,351)(337,343)(338,350)
(339,348)(340,349)(341,347)(342,345)(352,355)(354,360)(356,359)(361,373)
(362,371)(363,378)(364,370)(365,377)(366,375)(367,376)(368,374)(369,372)
(379,409)(380,407)(381,414)(382,406)(383,413)(384,411)(385,412)(386,410)
(387,408)(388,427)(389,425)(390,432)(391,424)(392,431)(393,429)(394,430)
(395,428)(396,426)(397,418)(398,416)(399,423)(400,415)(401,422)(402,420)
(403,421)(404,419)(405,417)(433,544)(434,542)(435,549)(436,541)(437,548)
(438,546)(439,547)(440,545)(441,543)(442,562)(443,560)(444,567)(445,559)
(446,566)(447,564)(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)
(454,550)(455,557)(456,555)(457,556)(458,554)(459,552)(460,571)(461,569)
(462,576)(463,568)(464,575)(465,573)(466,574)(467,572)(468,570)(469,589)
(470,587)(471,594)(472,586)(473,593)(474,591)(475,592)(476,590)(477,588)
(478,580)(479,578)(480,585)(481,577)(482,584)(483,582)(484,583)(485,581)
(486,579)(487,625)(488,623)(489,630)(490,622)(491,629)(492,627)(493,628)
(494,626)(495,624)(496,643)(497,641)(498,648)(499,640)(500,647)(501,645)
(502,646)(503,644)(504,642)(505,634)(506,632)(507,639)(508,631)(509,638)
(510,636)(511,637)(512,635)(513,633)(514,598)(515,596)(516,603)(517,595)
(518,602)(519,600)(520,601)(521,599)(522,597)(523,616)(524,614)(525,621)
(526,613)(527,620)(528,618)(529,619)(530,617)(531,615)(532,607)(533,605)
(534,612)(535,604)(536,611)(537,609)(538,610)(539,608)(540,606)(649,841)
(650,839)(651,846)(652,838)(653,845)(654,843)(655,844)(656,842)(657,840)
(658,859)(659,857)(660,864)(661,856)(662,863)(663,861)(664,862)(665,860)
(666,858)(667,850)(668,848)(669,855)(670,847)(671,854)(672,852)(673,853)
(674,851)(675,849)(676,814)(677,812)(678,819)(679,811)(680,818)(681,816)
(682,817)(683,815)(684,813)(685,832)(686,830)(687,837)(688,829)(689,836)
(690,834)(691,835)(692,833)(693,831)(694,823)(695,821)(696,828)(697,820)
(698,827)(699,825)(700,826)(701,824)(702,822)(703,787)(704,785)(705,792)
(706,784)(707,791)(708,789)(709,790)(710,788)(711,786)(712,805)(713,803)
(714,810)(715,802)(716,809)(717,807)(718,808)(719,806)(720,804)(721,796)
(722,794)(723,801)(724,793)(725,800)(726,798)(727,799)(728,797)(729,795)
(730,760)(731,758)(732,765)(733,757)(734,764)(735,762)(736,763)(737,761)
(738,759)(739,778)(740,776)(741,783)(742,775)(743,782)(744,780)(745,781)
(746,779)(747,777)(748,769)(749,767)(750,774)(751,766)(752,773)(753,771)
(754,772)(755,770)(756,768);
s2 := Sym(864)!( 1,442)( 2,443)( 3,444)( 4,450)( 5,448)( 6,449)( 7,446)
( 8,447)( 9,445)( 10,433)( 11,434)( 12,435)( 13,441)( 14,439)( 15,440)
( 16,437)( 17,438)( 18,436)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)
( 24,458)( 25,455)( 26,456)( 27,454)( 28,469)( 29,470)( 30,471)( 31,477)
( 32,475)( 33,476)( 34,473)( 35,474)( 36,472)( 37,460)( 38,461)( 39,462)
( 40,468)( 41,466)( 42,467)( 43,464)( 44,465)( 45,463)( 46,478)( 47,479)
( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,523)
( 56,524)( 57,525)( 58,531)( 59,529)( 60,530)( 61,527)( 62,528)( 63,526)
( 64,514)( 65,515)( 66,516)( 67,522)( 68,520)( 69,521)( 70,518)( 71,519)
( 72,517)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,496)( 83,497)( 84,498)( 85,504)( 86,502)( 87,503)
( 88,500)( 89,501)( 90,499)( 91,487)( 92,488)( 93,489)( 94,495)( 95,493)
( 96,494)( 97,491)( 98,492)( 99,490)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,604)(110,605)(111,606)
(112,612)(113,610)(114,611)(115,608)(116,609)(117,607)(118,595)(119,596)
(120,597)(121,603)(122,601)(123,602)(124,599)(125,600)(126,598)(127,613)
(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)
(136,631)(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)
(144,634)(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)
(152,627)(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)
(160,644)(161,645)(162,643)(163,550)(164,551)(165,552)(166,558)(167,556)
(168,557)(169,554)(170,555)(171,553)(172,541)(173,542)(174,543)(175,549)
(176,547)(177,548)(178,545)(179,546)(180,544)(181,559)(182,560)(183,561)
(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,577)(191,578)
(192,579)(193,585)(194,583)(195,584)(196,581)(197,582)(198,580)(199,568)
(200,569)(201,570)(202,576)(203,574)(204,575)(205,572)(206,573)(207,571)
(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)
(216,589)(217,739)(218,740)(219,741)(220,747)(221,745)(222,746)(223,743)
(224,744)(225,742)(226,730)(227,731)(228,732)(229,738)(230,736)(231,737)
(232,734)(233,735)(234,733)(235,748)(236,749)(237,750)(238,756)(239,754)
(240,755)(241,752)(242,753)(243,751)(244,712)(245,713)(246,714)(247,720)
(248,718)(249,719)(250,716)(251,717)(252,715)(253,703)(254,704)(255,705)
(256,711)(257,709)(258,710)(259,707)(260,708)(261,706)(262,721)(263,722)
(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,685)
(272,686)(273,687)(274,693)(275,691)(276,692)(277,689)(278,690)(279,688)
(280,676)(281,677)(282,678)(283,684)(284,682)(285,683)(286,680)(287,681)
(288,679)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)
(296,699)(297,697)(298,658)(299,659)(300,660)(301,666)(302,664)(303,665)
(304,662)(305,663)(306,661)(307,649)(308,650)(309,651)(310,657)(311,655)
(312,656)(313,653)(314,654)(315,652)(316,667)(317,668)(318,669)(319,675)
(320,673)(321,674)(322,671)(323,672)(324,670)(325,766)(326,767)(327,768)
(328,774)(329,772)(330,773)(331,770)(332,771)(333,769)(334,757)(335,758)
(336,759)(337,765)(338,763)(339,764)(340,761)(341,762)(342,760)(343,775)
(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)
(352,793)(353,794)(354,795)(355,801)(356,799)(357,800)(358,797)(359,798)
(360,796)(361,784)(362,785)(363,786)(364,792)(365,790)(366,791)(367,788)
(368,789)(369,787)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)
(376,806)(377,807)(378,805)(379,847)(380,848)(381,849)(382,855)(383,853)
(384,854)(385,851)(386,852)(387,850)(388,838)(389,839)(390,840)(391,846)
(392,844)(393,845)(394,842)(395,843)(396,841)(397,856)(398,857)(399,858)
(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,820)(407,821)
(408,822)(409,828)(410,826)(411,827)(412,824)(413,825)(414,823)(415,811)
(416,812)(417,813)(418,819)(419,817)(420,818)(421,815)(422,816)(423,814)
(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)
(432,832);
poly := sub<Sym(864)|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*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*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 >;
References : None.
to this polytope