Polytope of Type {8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1728e
if this polytope has a name.
Group : SmallGroup(1728,31258)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 72, 432, 108
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
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 : {4,12}*864d
3-fold quotients : {8,4}*576a
4-fold quotients : {4,12}*432b
6-fold quotients : {4,4}*288
9-fold quotients : {8,12}*192a
12-fold quotients : {4,4}*144
18-fold quotients : {4,12}*96a, {8,6}*96
24-fold quotients : {4,4}*72
27-fold quotients : {8,4}*64a
36-fold quotients : {2,12}*48, {4,6}*48a
54-fold quotients : {4,4}*32, {8,2}*32
72-fold quotients : {2,6}*24
108-fold quotients : {2,4}*16, {4,2}*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 := ( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)
( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)
( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)
( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)
( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)( 76,106)
( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(109,136)(110,143)(111,141)
(112,142)(113,140)(114,138)(115,139)(116,137)(117,144)(118,145)(119,152)
(120,150)(121,151)(122,149)(123,147)(124,148)(125,146)(126,153)(127,154)
(128,161)(129,159)(130,160)(131,158)(132,156)(133,157)(134,155)(135,162)
(164,170)(165,168)(166,169)(173,179)(174,177)(175,178)(182,188)(183,186)
(184,187)(191,197)(192,195)(193,196)(200,206)(201,204)(202,205)(209,215)
(210,213)(211,214)(218,224)(219,222)(220,223)(227,233)(228,231)(229,232)
(236,242)(237,240)(238,241)(245,251)(246,249)(247,250)(254,260)(255,258)
(256,259)(263,269)(264,267)(265,268)(271,298)(272,305)(273,303)(274,304)
(275,302)(276,300)(277,301)(278,299)(279,306)(280,307)(281,314)(282,312)
(283,313)(284,311)(285,309)(286,310)(287,308)(288,315)(289,316)(290,323)
(291,321)(292,322)(293,320)(294,318)(295,319)(296,317)(297,324)(325,352)
(326,359)(327,357)(328,358)(329,356)(330,354)(331,355)(332,353)(333,360)
(334,361)(335,368)(336,366)(337,367)(338,365)(339,363)(340,364)(341,362)
(342,369)(343,370)(344,377)(345,375)(346,376)(347,374)(348,372)(349,373)
(350,371)(351,378)(380,386)(381,384)(382,385)(389,395)(390,393)(391,394)
(398,404)(399,402)(400,403)(407,413)(408,411)(409,412)(416,422)(417,420)
(418,421)(425,431)(426,429)(427,430)(433,541)(434,548)(435,546)(436,547)
(437,545)(438,543)(439,544)(440,542)(441,549)(442,550)(443,557)(444,555)
(445,556)(446,554)(447,552)(448,553)(449,551)(450,558)(451,559)(452,566)
(453,564)(454,565)(455,563)(456,561)(457,562)(458,560)(459,567)(460,568)
(461,575)(462,573)(463,574)(464,572)(465,570)(466,571)(467,569)(468,576)
(469,577)(470,584)(471,582)(472,583)(473,581)(474,579)(475,580)(476,578)
(477,585)(478,586)(479,593)(480,591)(481,592)(482,590)(483,588)(484,589)
(485,587)(486,594)(487,622)(488,629)(489,627)(490,628)(491,626)(492,624)
(493,625)(494,623)(495,630)(496,631)(497,638)(498,636)(499,637)(500,635)
(501,633)(502,634)(503,632)(504,639)(505,640)(506,647)(507,645)(508,646)
(509,644)(510,642)(511,643)(512,641)(513,648)(514,595)(515,602)(516,600)
(517,601)(518,599)(519,597)(520,598)(521,596)(522,603)(523,604)(524,611)
(525,609)(526,610)(527,608)(528,606)(529,607)(530,605)(531,612)(532,613)
(533,620)(534,618)(535,619)(536,617)(537,615)(538,616)(539,614)(540,621)
(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)(656,785)
(657,792)(658,793)(659,800)(660,798)(661,799)(662,797)(663,795)(664,796)
(665,794)(666,801)(667,802)(668,809)(669,807)(670,808)(671,806)(672,804)
(673,805)(674,803)(675,810)(676,757)(677,764)(678,762)(679,763)(680,761)
(681,759)(682,760)(683,758)(684,765)(685,766)(686,773)(687,771)(688,772)
(689,770)(690,768)(691,769)(692,767)(693,774)(694,775)(695,782)(696,780)
(697,781)(698,779)(699,777)(700,778)(701,776)(702,783)(703,811)(704,818)
(705,816)(706,817)(707,815)(708,813)(709,814)(710,812)(711,819)(712,820)
(713,827)(714,825)(715,826)(716,824)(717,822)(718,823)(719,821)(720,828)
(721,829)(722,836)(723,834)(724,835)(725,833)(726,831)(727,832)(728,830)
(729,837)(730,838)(731,845)(732,843)(733,844)(734,842)(735,840)(736,841)
(737,839)(738,846)(739,847)(740,854)(741,852)(742,853)(743,851)(744,849)
(745,850)(746,848)(747,855)(748,856)(749,863)(750,861)(751,862)(752,860)
(753,858)(754,859)(755,857)(756,864);;
s1 := ( 1,649)( 2,650)( 3,651)( 4,657)( 5,655)( 6,656)( 7,653)( 8,654)
( 9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)( 16,671)
( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)( 24,665)
( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)( 32,682)
( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)( 40,702)
( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)( 48,687)
( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)( 56,731)
( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)( 64,748)
( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)( 72,751)
( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)( 80,744)
( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)( 88,707)
( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)( 96,728)
( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)(104,718)
(105,719)(106,716)(107,717)(108,715)(109,784)(110,785)(111,786)(112,792)
(113,790)(114,791)(115,788)(116,789)(117,787)(118,802)(119,803)(120,804)
(121,810)(122,808)(123,809)(124,806)(125,807)(126,805)(127,793)(128,794)
(129,795)(130,801)(131,799)(132,800)(133,797)(134,798)(135,796)(136,757)
(137,758)(138,759)(139,765)(140,763)(141,764)(142,761)(143,762)(144,760)
(145,775)(146,776)(147,777)(148,783)(149,781)(150,782)(151,779)(152,780)
(153,778)(154,766)(155,767)(156,768)(157,774)(158,772)(159,773)(160,770)
(161,771)(162,769)(163,811)(164,812)(165,813)(166,819)(167,817)(168,818)
(169,815)(170,816)(171,814)(172,829)(173,830)(174,831)(175,837)(176,835)
(177,836)(178,833)(179,834)(180,832)(181,820)(182,821)(183,822)(184,828)
(185,826)(186,827)(187,824)(188,825)(189,823)(190,838)(191,839)(192,840)
(193,846)(194,844)(195,845)(196,842)(197,843)(198,841)(199,856)(200,857)
(201,858)(202,864)(203,862)(204,863)(205,860)(206,861)(207,859)(208,847)
(209,848)(210,849)(211,855)(212,853)(213,854)(214,851)(215,852)(216,850)
(217,514)(218,515)(219,516)(220,522)(221,520)(222,521)(223,518)(224,519)
(225,517)(226,532)(227,533)(228,534)(229,540)(230,538)(231,539)(232,536)
(233,537)(234,535)(235,523)(236,524)(237,525)(238,531)(239,529)(240,530)
(241,527)(242,528)(243,526)(244,487)(245,488)(246,489)(247,495)(248,493)
(249,494)(250,491)(251,492)(252,490)(253,505)(254,506)(255,507)(256,513)
(257,511)(258,512)(259,509)(260,510)(261,508)(262,496)(263,497)(264,498)
(265,504)(266,502)(267,503)(268,500)(269,501)(270,499)(271,460)(272,461)
(273,462)(274,468)(275,466)(276,467)(277,464)(278,465)(279,463)(280,478)
(281,479)(282,480)(283,486)(284,484)(285,485)(286,482)(287,483)(288,481)
(289,469)(290,470)(291,471)(292,477)(293,475)(294,476)(295,473)(296,474)
(297,472)(298,433)(299,434)(300,435)(301,441)(302,439)(303,440)(304,437)
(305,438)(306,436)(307,451)(308,452)(309,453)(310,459)(311,457)(312,458)
(313,455)(314,456)(315,454)(316,442)(317,443)(318,444)(319,450)(320,448)
(321,449)(322,446)(323,447)(324,445)(325,595)(326,596)(327,597)(328,603)
(329,601)(330,602)(331,599)(332,600)(333,598)(334,613)(335,614)(336,615)
(337,621)(338,619)(339,620)(340,617)(341,618)(342,616)(343,604)(344,605)
(345,606)(346,612)(347,610)(348,611)(349,608)(350,609)(351,607)(352,622)
(353,623)(354,624)(355,630)(356,628)(357,629)(358,626)(359,627)(360,625)
(361,640)(362,641)(363,642)(364,648)(365,646)(366,647)(367,644)(368,645)
(369,643)(370,631)(371,632)(372,633)(373,639)(374,637)(375,638)(376,635)
(377,636)(378,634)(379,541)(380,542)(381,543)(382,549)(383,547)(384,548)
(385,545)(386,546)(387,544)(388,559)(389,560)(390,561)(391,567)(392,565)
(393,566)(394,563)(395,564)(396,562)(397,550)(398,551)(399,552)(400,558)
(401,556)(402,557)(403,554)(404,555)(405,553)(406,568)(407,569)(408,570)
(409,576)(410,574)(411,575)(412,572)(413,573)(414,571)(415,586)(416,587)
(417,588)(418,594)(419,592)(420,593)(421,590)(422,591)(423,589)(424,577)
(425,578)(426,579)(427,585)(428,583)(429,584)(430,581)(431,582)(432,580);;
s2 := ( 1,392)( 2,394)( 3,390)( 4,395)( 5,388)( 6,393)( 7,389)( 8,391)
( 9,396)( 10,383)( 11,385)( 12,381)( 13,386)( 14,379)( 15,384)( 16,380)
( 17,382)( 18,387)( 19,401)( 20,403)( 21,399)( 22,404)( 23,397)( 24,402)
( 25,398)( 26,400)( 27,405)( 28,419)( 29,421)( 30,417)( 31,422)( 32,415)
( 33,420)( 34,416)( 35,418)( 36,423)( 37,410)( 38,412)( 39,408)( 40,413)
( 41,406)( 42,411)( 43,407)( 44,409)( 45,414)( 46,428)( 47,430)( 48,426)
( 49,431)( 50,424)( 51,429)( 52,425)( 53,427)( 54,432)( 55,365)( 56,367)
( 57,363)( 58,368)( 59,361)( 60,366)( 61,362)( 62,364)( 63,369)( 64,356)
( 65,358)( 66,354)( 67,359)( 68,352)( 69,357)( 70,353)( 71,355)( 72,360)
( 73,374)( 74,376)( 75,372)( 76,377)( 77,370)( 78,375)( 79,371)( 80,373)
( 81,378)( 82,338)( 83,340)( 84,336)( 85,341)( 86,334)( 87,339)( 88,335)
( 89,337)( 90,342)( 91,329)( 92,331)( 93,327)( 94,332)( 95,325)( 96,330)
( 97,326)( 98,328)( 99,333)(100,347)(101,349)(102,345)(103,350)(104,343)
(105,348)(106,344)(107,346)(108,351)(109,311)(110,313)(111,309)(112,314)
(113,307)(114,312)(115,308)(116,310)(117,315)(118,302)(119,304)(120,300)
(121,305)(122,298)(123,303)(124,299)(125,301)(126,306)(127,320)(128,322)
(129,318)(130,323)(131,316)(132,321)(133,317)(134,319)(135,324)(136,284)
(137,286)(138,282)(139,287)(140,280)(141,285)(142,281)(143,283)(144,288)
(145,275)(146,277)(147,273)(148,278)(149,271)(150,276)(151,272)(152,274)
(153,279)(154,293)(155,295)(156,291)(157,296)(158,289)(159,294)(160,290)
(161,292)(162,297)(163,230)(164,232)(165,228)(166,233)(167,226)(168,231)
(169,227)(170,229)(171,234)(172,221)(173,223)(174,219)(175,224)(176,217)
(177,222)(178,218)(179,220)(180,225)(181,239)(182,241)(183,237)(184,242)
(185,235)(186,240)(187,236)(188,238)(189,243)(190,257)(191,259)(192,255)
(193,260)(194,253)(195,258)(196,254)(197,256)(198,261)(199,248)(200,250)
(201,246)(202,251)(203,244)(204,249)(205,245)(206,247)(207,252)(208,266)
(209,268)(210,264)(211,269)(212,262)(213,267)(214,263)(215,265)(216,270)
(433,716)(434,718)(435,714)(436,719)(437,712)(438,717)(439,713)(440,715)
(441,720)(442,707)(443,709)(444,705)(445,710)(446,703)(447,708)(448,704)
(449,706)(450,711)(451,725)(452,727)(453,723)(454,728)(455,721)(456,726)
(457,722)(458,724)(459,729)(460,743)(461,745)(462,741)(463,746)(464,739)
(465,744)(466,740)(467,742)(468,747)(469,734)(470,736)(471,732)(472,737)
(473,730)(474,735)(475,731)(476,733)(477,738)(478,752)(479,754)(480,750)
(481,755)(482,748)(483,753)(484,749)(485,751)(486,756)(487,689)(488,691)
(489,687)(490,692)(491,685)(492,690)(493,686)(494,688)(495,693)(496,680)
(497,682)(498,678)(499,683)(500,676)(501,681)(502,677)(503,679)(504,684)
(505,698)(506,700)(507,696)(508,701)(509,694)(510,699)(511,695)(512,697)
(513,702)(514,662)(515,664)(516,660)(517,665)(518,658)(519,663)(520,659)
(521,661)(522,666)(523,653)(524,655)(525,651)(526,656)(527,649)(528,654)
(529,650)(530,652)(531,657)(532,671)(533,673)(534,669)(535,674)(536,667)
(537,672)(538,668)(539,670)(540,675)(541,824)(542,826)(543,822)(544,827)
(545,820)(546,825)(547,821)(548,823)(549,828)(550,815)(551,817)(552,813)
(553,818)(554,811)(555,816)(556,812)(557,814)(558,819)(559,833)(560,835)
(561,831)(562,836)(563,829)(564,834)(565,830)(566,832)(567,837)(568,851)
(569,853)(570,849)(571,854)(572,847)(573,852)(574,848)(575,850)(576,855)
(577,842)(578,844)(579,840)(580,845)(581,838)(582,843)(583,839)(584,841)
(585,846)(586,860)(587,862)(588,858)(589,863)(590,856)(591,861)(592,857)
(593,859)(594,864)(595,797)(596,799)(597,795)(598,800)(599,793)(600,798)
(601,794)(602,796)(603,801)(604,788)(605,790)(606,786)(607,791)(608,784)
(609,789)(610,785)(611,787)(612,792)(613,806)(614,808)(615,804)(616,809)
(617,802)(618,807)(619,803)(620,805)(621,810)(622,770)(623,772)(624,768)
(625,773)(626,766)(627,771)(628,767)(629,769)(630,774)(631,761)(632,763)
(633,759)(634,764)(635,757)(636,762)(637,758)(638,760)(639,765)(640,779)
(641,781)(642,777)(643,782)(644,775)(645,780)(646,776)(647,778)(648,783);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)
( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)
( 47, 53)( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)
( 60, 84)( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)
( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)
( 76,106)( 77,104)( 78,102)( 79,103)( 80,101)( 81,108)(109,136)(110,143)
(111,141)(112,142)(113,140)(114,138)(115,139)(116,137)(117,144)(118,145)
(119,152)(120,150)(121,151)(122,149)(123,147)(124,148)(125,146)(126,153)
(127,154)(128,161)(129,159)(130,160)(131,158)(132,156)(133,157)(134,155)
(135,162)(164,170)(165,168)(166,169)(173,179)(174,177)(175,178)(182,188)
(183,186)(184,187)(191,197)(192,195)(193,196)(200,206)(201,204)(202,205)
(209,215)(210,213)(211,214)(218,224)(219,222)(220,223)(227,233)(228,231)
(229,232)(236,242)(237,240)(238,241)(245,251)(246,249)(247,250)(254,260)
(255,258)(256,259)(263,269)(264,267)(265,268)(271,298)(272,305)(273,303)
(274,304)(275,302)(276,300)(277,301)(278,299)(279,306)(280,307)(281,314)
(282,312)(283,313)(284,311)(285,309)(286,310)(287,308)(288,315)(289,316)
(290,323)(291,321)(292,322)(293,320)(294,318)(295,319)(296,317)(297,324)
(325,352)(326,359)(327,357)(328,358)(329,356)(330,354)(331,355)(332,353)
(333,360)(334,361)(335,368)(336,366)(337,367)(338,365)(339,363)(340,364)
(341,362)(342,369)(343,370)(344,377)(345,375)(346,376)(347,374)(348,372)
(349,373)(350,371)(351,378)(380,386)(381,384)(382,385)(389,395)(390,393)
(391,394)(398,404)(399,402)(400,403)(407,413)(408,411)(409,412)(416,422)
(417,420)(418,421)(425,431)(426,429)(427,430)(433,541)(434,548)(435,546)
(436,547)(437,545)(438,543)(439,544)(440,542)(441,549)(442,550)(443,557)
(444,555)(445,556)(446,554)(447,552)(448,553)(449,551)(450,558)(451,559)
(452,566)(453,564)(454,565)(455,563)(456,561)(457,562)(458,560)(459,567)
(460,568)(461,575)(462,573)(463,574)(464,572)(465,570)(466,571)(467,569)
(468,576)(469,577)(470,584)(471,582)(472,583)(473,581)(474,579)(475,580)
(476,578)(477,585)(478,586)(479,593)(480,591)(481,592)(482,590)(483,588)
(484,589)(485,587)(486,594)(487,622)(488,629)(489,627)(490,628)(491,626)
(492,624)(493,625)(494,623)(495,630)(496,631)(497,638)(498,636)(499,637)
(500,635)(501,633)(502,634)(503,632)(504,639)(505,640)(506,647)(507,645)
(508,646)(509,644)(510,642)(511,643)(512,641)(513,648)(514,595)(515,602)
(516,600)(517,601)(518,599)(519,597)(520,598)(521,596)(522,603)(523,604)
(524,611)(525,609)(526,610)(527,608)(528,606)(529,607)(530,605)(531,612)
(532,613)(533,620)(534,618)(535,619)(536,617)(537,615)(538,616)(539,614)
(540,621)(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)
(656,785)(657,792)(658,793)(659,800)(660,798)(661,799)(662,797)(663,795)
(664,796)(665,794)(666,801)(667,802)(668,809)(669,807)(670,808)(671,806)
(672,804)(673,805)(674,803)(675,810)(676,757)(677,764)(678,762)(679,763)
(680,761)(681,759)(682,760)(683,758)(684,765)(685,766)(686,773)(687,771)
(688,772)(689,770)(690,768)(691,769)(692,767)(693,774)(694,775)(695,782)
(696,780)(697,781)(698,779)(699,777)(700,778)(701,776)(702,783)(703,811)
(704,818)(705,816)(706,817)(707,815)(708,813)(709,814)(710,812)(711,819)
(712,820)(713,827)(714,825)(715,826)(716,824)(717,822)(718,823)(719,821)
(720,828)(721,829)(722,836)(723,834)(724,835)(725,833)(726,831)(727,832)
(728,830)(729,837)(730,838)(731,845)(732,843)(733,844)(734,842)(735,840)
(736,841)(737,839)(738,846)(739,847)(740,854)(741,852)(742,853)(743,851)
(744,849)(745,850)(746,848)(747,855)(748,856)(749,863)(750,861)(751,862)
(752,860)(753,858)(754,859)(755,857)(756,864);
s1 := Sym(864)!( 1,649)( 2,650)( 3,651)( 4,657)( 5,655)( 6,656)( 7,653)
( 8,654)( 9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)
( 16,671)( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)
( 24,665)( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)
( 32,682)( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)
( 40,702)( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)
( 48,687)( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)
( 56,731)( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)
( 64,748)( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)
( 72,751)( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)
( 80,744)( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)
( 88,707)( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)
( 96,728)( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)
(104,718)(105,719)(106,716)(107,717)(108,715)(109,784)(110,785)(111,786)
(112,792)(113,790)(114,791)(115,788)(116,789)(117,787)(118,802)(119,803)
(120,804)(121,810)(122,808)(123,809)(124,806)(125,807)(126,805)(127,793)
(128,794)(129,795)(130,801)(131,799)(132,800)(133,797)(134,798)(135,796)
(136,757)(137,758)(138,759)(139,765)(140,763)(141,764)(142,761)(143,762)
(144,760)(145,775)(146,776)(147,777)(148,783)(149,781)(150,782)(151,779)
(152,780)(153,778)(154,766)(155,767)(156,768)(157,774)(158,772)(159,773)
(160,770)(161,771)(162,769)(163,811)(164,812)(165,813)(166,819)(167,817)
(168,818)(169,815)(170,816)(171,814)(172,829)(173,830)(174,831)(175,837)
(176,835)(177,836)(178,833)(179,834)(180,832)(181,820)(182,821)(183,822)
(184,828)(185,826)(186,827)(187,824)(188,825)(189,823)(190,838)(191,839)
(192,840)(193,846)(194,844)(195,845)(196,842)(197,843)(198,841)(199,856)
(200,857)(201,858)(202,864)(203,862)(204,863)(205,860)(206,861)(207,859)
(208,847)(209,848)(210,849)(211,855)(212,853)(213,854)(214,851)(215,852)
(216,850)(217,514)(218,515)(219,516)(220,522)(221,520)(222,521)(223,518)
(224,519)(225,517)(226,532)(227,533)(228,534)(229,540)(230,538)(231,539)
(232,536)(233,537)(234,535)(235,523)(236,524)(237,525)(238,531)(239,529)
(240,530)(241,527)(242,528)(243,526)(244,487)(245,488)(246,489)(247,495)
(248,493)(249,494)(250,491)(251,492)(252,490)(253,505)(254,506)(255,507)
(256,513)(257,511)(258,512)(259,509)(260,510)(261,508)(262,496)(263,497)
(264,498)(265,504)(266,502)(267,503)(268,500)(269,501)(270,499)(271,460)
(272,461)(273,462)(274,468)(275,466)(276,467)(277,464)(278,465)(279,463)
(280,478)(281,479)(282,480)(283,486)(284,484)(285,485)(286,482)(287,483)
(288,481)(289,469)(290,470)(291,471)(292,477)(293,475)(294,476)(295,473)
(296,474)(297,472)(298,433)(299,434)(300,435)(301,441)(302,439)(303,440)
(304,437)(305,438)(306,436)(307,451)(308,452)(309,453)(310,459)(311,457)
(312,458)(313,455)(314,456)(315,454)(316,442)(317,443)(318,444)(319,450)
(320,448)(321,449)(322,446)(323,447)(324,445)(325,595)(326,596)(327,597)
(328,603)(329,601)(330,602)(331,599)(332,600)(333,598)(334,613)(335,614)
(336,615)(337,621)(338,619)(339,620)(340,617)(341,618)(342,616)(343,604)
(344,605)(345,606)(346,612)(347,610)(348,611)(349,608)(350,609)(351,607)
(352,622)(353,623)(354,624)(355,630)(356,628)(357,629)(358,626)(359,627)
(360,625)(361,640)(362,641)(363,642)(364,648)(365,646)(366,647)(367,644)
(368,645)(369,643)(370,631)(371,632)(372,633)(373,639)(374,637)(375,638)
(376,635)(377,636)(378,634)(379,541)(380,542)(381,543)(382,549)(383,547)
(384,548)(385,545)(386,546)(387,544)(388,559)(389,560)(390,561)(391,567)
(392,565)(393,566)(394,563)(395,564)(396,562)(397,550)(398,551)(399,552)
(400,558)(401,556)(402,557)(403,554)(404,555)(405,553)(406,568)(407,569)
(408,570)(409,576)(410,574)(411,575)(412,572)(413,573)(414,571)(415,586)
(416,587)(417,588)(418,594)(419,592)(420,593)(421,590)(422,591)(423,589)
(424,577)(425,578)(426,579)(427,585)(428,583)(429,584)(430,581)(431,582)
(432,580);
s2 := Sym(864)!( 1,392)( 2,394)( 3,390)( 4,395)( 5,388)( 6,393)( 7,389)
( 8,391)( 9,396)( 10,383)( 11,385)( 12,381)( 13,386)( 14,379)( 15,384)
( 16,380)( 17,382)( 18,387)( 19,401)( 20,403)( 21,399)( 22,404)( 23,397)
( 24,402)( 25,398)( 26,400)( 27,405)( 28,419)( 29,421)( 30,417)( 31,422)
( 32,415)( 33,420)( 34,416)( 35,418)( 36,423)( 37,410)( 38,412)( 39,408)
( 40,413)( 41,406)( 42,411)( 43,407)( 44,409)( 45,414)( 46,428)( 47,430)
( 48,426)( 49,431)( 50,424)( 51,429)( 52,425)( 53,427)( 54,432)( 55,365)
( 56,367)( 57,363)( 58,368)( 59,361)( 60,366)( 61,362)( 62,364)( 63,369)
( 64,356)( 65,358)( 66,354)( 67,359)( 68,352)( 69,357)( 70,353)( 71,355)
( 72,360)( 73,374)( 74,376)( 75,372)( 76,377)( 77,370)( 78,375)( 79,371)
( 80,373)( 81,378)( 82,338)( 83,340)( 84,336)( 85,341)( 86,334)( 87,339)
( 88,335)( 89,337)( 90,342)( 91,329)( 92,331)( 93,327)( 94,332)( 95,325)
( 96,330)( 97,326)( 98,328)( 99,333)(100,347)(101,349)(102,345)(103,350)
(104,343)(105,348)(106,344)(107,346)(108,351)(109,311)(110,313)(111,309)
(112,314)(113,307)(114,312)(115,308)(116,310)(117,315)(118,302)(119,304)
(120,300)(121,305)(122,298)(123,303)(124,299)(125,301)(126,306)(127,320)
(128,322)(129,318)(130,323)(131,316)(132,321)(133,317)(134,319)(135,324)
(136,284)(137,286)(138,282)(139,287)(140,280)(141,285)(142,281)(143,283)
(144,288)(145,275)(146,277)(147,273)(148,278)(149,271)(150,276)(151,272)
(152,274)(153,279)(154,293)(155,295)(156,291)(157,296)(158,289)(159,294)
(160,290)(161,292)(162,297)(163,230)(164,232)(165,228)(166,233)(167,226)
(168,231)(169,227)(170,229)(171,234)(172,221)(173,223)(174,219)(175,224)
(176,217)(177,222)(178,218)(179,220)(180,225)(181,239)(182,241)(183,237)
(184,242)(185,235)(186,240)(187,236)(188,238)(189,243)(190,257)(191,259)
(192,255)(193,260)(194,253)(195,258)(196,254)(197,256)(198,261)(199,248)
(200,250)(201,246)(202,251)(203,244)(204,249)(205,245)(206,247)(207,252)
(208,266)(209,268)(210,264)(211,269)(212,262)(213,267)(214,263)(215,265)
(216,270)(433,716)(434,718)(435,714)(436,719)(437,712)(438,717)(439,713)
(440,715)(441,720)(442,707)(443,709)(444,705)(445,710)(446,703)(447,708)
(448,704)(449,706)(450,711)(451,725)(452,727)(453,723)(454,728)(455,721)
(456,726)(457,722)(458,724)(459,729)(460,743)(461,745)(462,741)(463,746)
(464,739)(465,744)(466,740)(467,742)(468,747)(469,734)(470,736)(471,732)
(472,737)(473,730)(474,735)(475,731)(476,733)(477,738)(478,752)(479,754)
(480,750)(481,755)(482,748)(483,753)(484,749)(485,751)(486,756)(487,689)
(488,691)(489,687)(490,692)(491,685)(492,690)(493,686)(494,688)(495,693)
(496,680)(497,682)(498,678)(499,683)(500,676)(501,681)(502,677)(503,679)
(504,684)(505,698)(506,700)(507,696)(508,701)(509,694)(510,699)(511,695)
(512,697)(513,702)(514,662)(515,664)(516,660)(517,665)(518,658)(519,663)
(520,659)(521,661)(522,666)(523,653)(524,655)(525,651)(526,656)(527,649)
(528,654)(529,650)(530,652)(531,657)(532,671)(533,673)(534,669)(535,674)
(536,667)(537,672)(538,668)(539,670)(540,675)(541,824)(542,826)(543,822)
(544,827)(545,820)(546,825)(547,821)(548,823)(549,828)(550,815)(551,817)
(552,813)(553,818)(554,811)(555,816)(556,812)(557,814)(558,819)(559,833)
(560,835)(561,831)(562,836)(563,829)(564,834)(565,830)(566,832)(567,837)
(568,851)(569,853)(570,849)(571,854)(572,847)(573,852)(574,848)(575,850)
(576,855)(577,842)(578,844)(579,840)(580,845)(581,838)(582,843)(583,839)
(584,841)(585,846)(586,860)(587,862)(588,858)(589,863)(590,856)(591,861)
(592,857)(593,859)(594,864)(595,797)(596,799)(597,795)(598,800)(599,793)
(600,798)(601,794)(602,796)(603,801)(604,788)(605,790)(606,786)(607,791)
(608,784)(609,789)(610,785)(611,787)(612,792)(613,806)(614,808)(615,804)
(616,809)(617,802)(618,807)(619,803)(620,805)(621,810)(622,770)(623,772)
(624,768)(625,773)(626,766)(627,771)(628,767)(629,769)(630,774)(631,761)
(632,763)(633,759)(634,764)(635,757)(636,762)(637,758)(638,760)(639,765)
(640,779)(641,781)(642,777)(643,782)(644,775)(645,780)(646,776)(647,778)
(648,783);
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*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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 >;
References : None.
to this polytope