Polytope of Type {6,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*1728d
if this polytope has a name.
Group : SmallGroup(1728,12518)
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}*864d
3-fold quotients : {6,16}*576
4-fold quotients : {6,12}*432e
6-fold quotients : {6,8}*288
8-fold quotients : {6,12}*216a
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {2,16}*64
54-fold quotients : {2,8}*32
108-fold quotients : {2,4}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)( 8,330)
( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)( 16,346)
( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)( 24,342)
( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)( 32,358)
( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)( 40,377)
( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)( 48,361)
( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)( 56,380)
( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)( 64,399)
( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)( 72,402)
( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)( 80,391)
( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)( 88,410)
( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)( 96,430)
( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)(104,422)
(105,423)(106,420)(107,418)(108,419)(109,298)(110,299)(111,300)(112,306)
(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)(120,317)
(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)(128,309)
(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)(136,271)
(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)(144,274)
(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)(152,293)
(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)(160,285)
(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)(168,224)
(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)(176,243)
(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)(184,232)
(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)(192,246)
(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)(200,262)
(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)(208,254)
(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)(216,257)
(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)(440,762)
(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)(448,778)
(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)(456,774)
(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)(464,790)
(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)(472,809)
(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)(480,793)
(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)(488,812)
(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)(496,831)
(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)(504,834)
(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)(512,823)
(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)(520,842)
(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)(528,862)
(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)(536,854)
(537,855)(538,852)(539,850)(540,851)(541,730)(542,731)(543,732)(544,738)
(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)(552,749)
(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)(560,741)
(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)(568,703)
(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)(576,706)
(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)(584,725)
(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)(592,717)
(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)(600,656)
(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)(608,675)
(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)(616,664)
(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)(624,678)
(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)(632,694)
(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)(640,686)
(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)(648,689);;
s1 := ( 1, 10)( 2, 12)( 3, 11)( 4, 5)( 7, 26)( 8, 25)( 9, 27)( 13, 23)
( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)( 31, 32)
( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)( 47, 48)
( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)( 62,106)
( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)( 70, 98)
( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)( 78, 96)
( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)(113,166)
(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)(121,185)
(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)(129,182)
(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)(137,201)
(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)(145,190)
(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)(153,207)
(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)(161,196)
(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)(223,323)
(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)(231,321)
(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)(239,310)
(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)(247,275)
(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)(255,272)
(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)(263,291)
(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)(325,334)
(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)(338,346)
(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)(358,377)
(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)(379,415)
(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)(387,432)
(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)(395,421)
(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)(403,413)
(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)(438,546)
(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)(446,562)
(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)(454,554)
(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)(462,578)
(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)(470,570)
(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)(478,586)
(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)(486,576)
(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)(494,646)
(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)(502,638)
(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)(510,636)
(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)(518,598)
(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)(526,617)
(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)(534,614)
(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)(650,849)
(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)(658,838)
(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)(666,855)
(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)(674,844)
(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)(682,836)
(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)(690,834)
(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)(698,823)
(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)(706,788)
(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)(714,785)
(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)(722,804)
(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)(730,766)
(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)(738,783)
(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)(746,772)
(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)(754,764)
(755,763)(756,765);;
s2 := ( 1,434)( 2,433)( 3,435)( 4,438)( 5,437)( 6,436)( 7,439)( 8,441)
( 9,440)( 10,458)( 11,457)( 12,459)( 13,453)( 14,452)( 15,451)( 16,454)
( 17,456)( 18,455)( 19,447)( 20,446)( 21,445)( 22,448)( 23,450)( 24,449)
( 25,443)( 26,442)( 27,444)( 28,461)( 29,460)( 30,462)( 31,465)( 32,464)
( 33,463)( 34,466)( 35,468)( 36,467)( 37,485)( 38,484)( 39,486)( 40,480)
( 41,479)( 42,478)( 43,481)( 44,483)( 45,482)( 46,474)( 47,473)( 48,472)
( 49,475)( 50,477)( 51,476)( 52,470)( 53,469)( 54,471)( 55,515)( 56,514)
( 57,516)( 58,519)( 59,518)( 60,517)( 61,520)( 62,522)( 63,521)( 64,539)
( 65,538)( 66,540)( 67,534)( 68,533)( 69,532)( 70,535)( 71,537)( 72,536)
( 73,528)( 74,527)( 75,526)( 76,529)( 77,531)( 78,530)( 79,524)( 80,523)
( 81,525)( 82,488)( 83,487)( 84,489)( 85,492)( 86,491)( 87,490)( 88,493)
( 89,495)( 90,494)( 91,512)( 92,511)( 93,513)( 94,507)( 95,506)( 96,505)
( 97,508)( 98,510)( 99,509)(100,501)(101,500)(102,499)(103,502)(104,504)
(105,503)(106,497)(107,496)(108,498)(109,596)(110,595)(111,597)(112,600)
(113,599)(114,598)(115,601)(116,603)(117,602)(118,620)(119,619)(120,621)
(121,615)(122,614)(123,613)(124,616)(125,618)(126,617)(127,609)(128,608)
(129,607)(130,610)(131,612)(132,611)(133,605)(134,604)(135,606)(136,623)
(137,622)(138,624)(139,627)(140,626)(141,625)(142,628)(143,630)(144,629)
(145,647)(146,646)(147,648)(148,642)(149,641)(150,640)(151,643)(152,645)
(153,644)(154,636)(155,635)(156,634)(157,637)(158,639)(159,638)(160,632)
(161,631)(162,633)(163,542)(164,541)(165,543)(166,546)(167,545)(168,544)
(169,547)(170,549)(171,548)(172,566)(173,565)(174,567)(175,561)(176,560)
(177,559)(178,562)(179,564)(180,563)(181,555)(182,554)(183,553)(184,556)
(185,558)(186,557)(187,551)(188,550)(189,552)(190,569)(191,568)(192,570)
(193,573)(194,572)(195,571)(196,574)(197,576)(198,575)(199,593)(200,592)
(201,594)(202,588)(203,587)(204,586)(205,589)(206,591)(207,590)(208,582)
(209,581)(210,580)(211,583)(212,585)(213,584)(214,578)(215,577)(216,579)
(217,731)(218,730)(219,732)(220,735)(221,734)(222,733)(223,736)(224,738)
(225,737)(226,755)(227,754)(228,756)(229,750)(230,749)(231,748)(232,751)
(233,753)(234,752)(235,744)(236,743)(237,742)(238,745)(239,747)(240,746)
(241,740)(242,739)(243,741)(244,704)(245,703)(246,705)(247,708)(248,707)
(249,706)(250,709)(251,711)(252,710)(253,728)(254,727)(255,729)(256,723)
(257,722)(258,721)(259,724)(260,726)(261,725)(262,717)(263,716)(264,715)
(265,718)(266,720)(267,719)(268,713)(269,712)(270,714)(271,677)(272,676)
(273,678)(274,681)(275,680)(276,679)(277,682)(278,684)(279,683)(280,701)
(281,700)(282,702)(283,696)(284,695)(285,694)(286,697)(287,699)(288,698)
(289,690)(290,689)(291,688)(292,691)(293,693)(294,692)(295,686)(296,685)
(297,687)(298,650)(299,649)(300,651)(301,654)(302,653)(303,652)(304,655)
(305,657)(306,656)(307,674)(308,673)(309,675)(310,669)(311,668)(312,667)
(313,670)(314,672)(315,671)(316,663)(317,662)(318,661)(319,664)(320,666)
(321,665)(322,659)(323,658)(324,660)(325,758)(326,757)(327,759)(328,762)
(329,761)(330,760)(331,763)(332,765)(333,764)(334,782)(335,781)(336,783)
(337,777)(338,776)(339,775)(340,778)(341,780)(342,779)(343,771)(344,770)
(345,769)(346,772)(347,774)(348,773)(349,767)(350,766)(351,768)(352,785)
(353,784)(354,786)(355,789)(356,788)(357,787)(358,790)(359,792)(360,791)
(361,809)(362,808)(363,810)(364,804)(365,803)(366,802)(367,805)(368,807)
(369,806)(370,798)(371,797)(372,796)(373,799)(374,801)(375,800)(376,794)
(377,793)(378,795)(379,839)(380,838)(381,840)(382,843)(383,842)(384,841)
(385,844)(386,846)(387,845)(388,863)(389,862)(390,864)(391,858)(392,857)
(393,856)(394,859)(395,861)(396,860)(397,852)(398,851)(399,850)(400,853)
(401,855)(402,854)(403,848)(404,847)(405,849)(406,812)(407,811)(408,813)
(409,816)(410,815)(411,814)(412,817)(413,819)(414,818)(415,836)(416,835)
(417,837)(418,831)(419,830)(420,829)(421,832)(422,834)(423,833)(424,825)
(425,824)(426,823)(427,826)(428,828)(429,827)(430,821)(431,820)(432,822);;
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,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)
( 8,330)( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)
( 16,346)( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)
( 24,342)( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)
( 32,358)( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)
( 40,377)( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)
( 48,361)( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)
( 56,380)( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)
( 64,399)( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)
( 72,402)( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)
( 80,391)( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)
( 88,410)( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)
( 96,430)( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)
(104,422)(105,423)(106,420)(107,418)(108,419)(109,298)(110,299)(111,300)
(112,306)(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)
(120,317)(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)
(128,309)(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)
(136,271)(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)
(144,274)(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)
(152,293)(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)
(160,285)(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)
(168,224)(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)
(176,243)(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)
(184,232)(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)
(192,246)(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)
(200,262)(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)
(208,254)(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)
(216,257)(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)
(440,762)(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)
(448,778)(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)
(456,774)(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)
(464,790)(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)
(472,809)(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)
(480,793)(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)
(488,812)(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)
(496,831)(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)
(504,834)(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)
(512,823)(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)
(520,842)(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)
(528,862)(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)
(536,854)(537,855)(538,852)(539,850)(540,851)(541,730)(542,731)(543,732)
(544,738)(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)
(552,749)(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)
(560,741)(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)
(568,703)(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)
(576,706)(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)
(584,725)(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)
(592,717)(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)
(600,656)(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)
(608,675)(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)
(616,664)(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)
(624,678)(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)
(632,694)(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)
(640,686)(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)
(648,689);
s1 := Sym(864)!( 1, 10)( 2, 12)( 3, 11)( 4, 5)( 7, 26)( 8, 25)( 9, 27)
( 13, 23)( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)
( 31, 32)( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)
( 47, 48)( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)
( 62,106)( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)
( 70, 98)( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)
( 78, 96)( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)
(113,166)(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)
(121,185)(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)
(129,182)(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)
(137,201)(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)
(145,190)(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)
(153,207)(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)
(161,196)(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)
(223,323)(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)
(231,321)(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)
(239,310)(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)
(247,275)(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)
(255,272)(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)
(263,291)(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)
(325,334)(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)
(338,346)(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)
(358,377)(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)
(379,415)(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)
(387,432)(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)
(395,421)(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)
(403,413)(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)
(438,546)(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)
(446,562)(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)
(454,554)(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)
(462,578)(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)
(470,570)(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)
(478,586)(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)
(486,576)(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)
(494,646)(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)
(502,638)(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)
(510,636)(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)
(518,598)(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)
(526,617)(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)
(534,614)(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)
(650,849)(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)
(658,838)(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)
(666,855)(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)
(674,844)(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)
(682,836)(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)
(690,834)(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)
(698,823)(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)
(706,788)(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)
(714,785)(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)
(722,804)(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)
(730,766)(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)
(738,783)(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)
(746,772)(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)
(754,764)(755,763)(756,765);
s2 := Sym(864)!( 1,434)( 2,433)( 3,435)( 4,438)( 5,437)( 6,436)( 7,439)
( 8,441)( 9,440)( 10,458)( 11,457)( 12,459)( 13,453)( 14,452)( 15,451)
( 16,454)( 17,456)( 18,455)( 19,447)( 20,446)( 21,445)( 22,448)( 23,450)
( 24,449)( 25,443)( 26,442)( 27,444)( 28,461)( 29,460)( 30,462)( 31,465)
( 32,464)( 33,463)( 34,466)( 35,468)( 36,467)( 37,485)( 38,484)( 39,486)
( 40,480)( 41,479)( 42,478)( 43,481)( 44,483)( 45,482)( 46,474)( 47,473)
( 48,472)( 49,475)( 50,477)( 51,476)( 52,470)( 53,469)( 54,471)( 55,515)
( 56,514)( 57,516)( 58,519)( 59,518)( 60,517)( 61,520)( 62,522)( 63,521)
( 64,539)( 65,538)( 66,540)( 67,534)( 68,533)( 69,532)( 70,535)( 71,537)
( 72,536)( 73,528)( 74,527)( 75,526)( 76,529)( 77,531)( 78,530)( 79,524)
( 80,523)( 81,525)( 82,488)( 83,487)( 84,489)( 85,492)( 86,491)( 87,490)
( 88,493)( 89,495)( 90,494)( 91,512)( 92,511)( 93,513)( 94,507)( 95,506)
( 96,505)( 97,508)( 98,510)( 99,509)(100,501)(101,500)(102,499)(103,502)
(104,504)(105,503)(106,497)(107,496)(108,498)(109,596)(110,595)(111,597)
(112,600)(113,599)(114,598)(115,601)(116,603)(117,602)(118,620)(119,619)
(120,621)(121,615)(122,614)(123,613)(124,616)(125,618)(126,617)(127,609)
(128,608)(129,607)(130,610)(131,612)(132,611)(133,605)(134,604)(135,606)
(136,623)(137,622)(138,624)(139,627)(140,626)(141,625)(142,628)(143,630)
(144,629)(145,647)(146,646)(147,648)(148,642)(149,641)(150,640)(151,643)
(152,645)(153,644)(154,636)(155,635)(156,634)(157,637)(158,639)(159,638)
(160,632)(161,631)(162,633)(163,542)(164,541)(165,543)(166,546)(167,545)
(168,544)(169,547)(170,549)(171,548)(172,566)(173,565)(174,567)(175,561)
(176,560)(177,559)(178,562)(179,564)(180,563)(181,555)(182,554)(183,553)
(184,556)(185,558)(186,557)(187,551)(188,550)(189,552)(190,569)(191,568)
(192,570)(193,573)(194,572)(195,571)(196,574)(197,576)(198,575)(199,593)
(200,592)(201,594)(202,588)(203,587)(204,586)(205,589)(206,591)(207,590)
(208,582)(209,581)(210,580)(211,583)(212,585)(213,584)(214,578)(215,577)
(216,579)(217,731)(218,730)(219,732)(220,735)(221,734)(222,733)(223,736)
(224,738)(225,737)(226,755)(227,754)(228,756)(229,750)(230,749)(231,748)
(232,751)(233,753)(234,752)(235,744)(236,743)(237,742)(238,745)(239,747)
(240,746)(241,740)(242,739)(243,741)(244,704)(245,703)(246,705)(247,708)
(248,707)(249,706)(250,709)(251,711)(252,710)(253,728)(254,727)(255,729)
(256,723)(257,722)(258,721)(259,724)(260,726)(261,725)(262,717)(263,716)
(264,715)(265,718)(266,720)(267,719)(268,713)(269,712)(270,714)(271,677)
(272,676)(273,678)(274,681)(275,680)(276,679)(277,682)(278,684)(279,683)
(280,701)(281,700)(282,702)(283,696)(284,695)(285,694)(286,697)(287,699)
(288,698)(289,690)(290,689)(291,688)(292,691)(293,693)(294,692)(295,686)
(296,685)(297,687)(298,650)(299,649)(300,651)(301,654)(302,653)(303,652)
(304,655)(305,657)(306,656)(307,674)(308,673)(309,675)(310,669)(311,668)
(312,667)(313,670)(314,672)(315,671)(316,663)(317,662)(318,661)(319,664)
(320,666)(321,665)(322,659)(323,658)(324,660)(325,758)(326,757)(327,759)
(328,762)(329,761)(330,760)(331,763)(332,765)(333,764)(334,782)(335,781)
(336,783)(337,777)(338,776)(339,775)(340,778)(341,780)(342,779)(343,771)
(344,770)(345,769)(346,772)(347,774)(348,773)(349,767)(350,766)(351,768)
(352,785)(353,784)(354,786)(355,789)(356,788)(357,787)(358,790)(359,792)
(360,791)(361,809)(362,808)(363,810)(364,804)(365,803)(366,802)(367,805)
(368,807)(369,806)(370,798)(371,797)(372,796)(373,799)(374,801)(375,800)
(376,794)(377,793)(378,795)(379,839)(380,838)(381,840)(382,843)(383,842)
(384,841)(385,844)(386,846)(387,845)(388,863)(389,862)(390,864)(391,858)
(392,857)(393,856)(394,859)(395,861)(396,860)(397,852)(398,851)(399,850)
(400,853)(401,855)(402,854)(403,848)(404,847)(405,849)(406,812)(407,811)
(408,813)(409,816)(410,815)(411,814)(412,817)(413,819)(414,818)(415,836)
(416,835)(417,837)(418,831)(419,830)(420,829)(421,832)(422,834)(423,833)
(424,825)(425,824)(426,823)(427,826)(428,828)(429,827)(430,821)(431,820)
(432,822);
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,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope