Polytope of Type {8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1728g
if this polytope has a name.
Group : SmallGroup(1728,31593)
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}*864c, {8,6}*864b
3-fold quotients : {8,12}*576a
4-fold quotients : {4,6}*432b
6-fold quotients : {8,6}*288, {4,12}*288
9-fold quotients : {8,12}*192a
12-fold quotients : {4,6}*144
18-fold quotients : {4,12}*96a, {8,6}*96
24-fold quotients : {4,6}*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)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)( 67, 70)
( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)( 93, 96)
( 94, 97)(101,107)(102,105)(103,106)(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)(163,190)
(164,197)(165,195)(166,196)(167,194)(168,192)(169,193)(170,191)(171,198)
(172,199)(173,206)(174,204)(175,205)(176,203)(177,201)(178,202)(179,200)
(180,207)(181,208)(182,215)(183,213)(184,214)(185,212)(186,210)(187,211)
(188,209)(189,216)(217,244)(218,251)(219,249)(220,250)(221,248)(222,246)
(223,247)(224,245)(225,252)(226,253)(227,260)(228,258)(229,259)(230,257)
(231,255)(232,256)(233,254)(234,261)(235,262)(236,269)(237,267)(238,268)
(239,266)(240,264)(241,265)(242,263)(243,270)(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)
(326,332)(327,330)(328,331)(335,341)(336,339)(337,340)(344,350)(345,348)
(346,349)(353,359)(354,357)(355,358)(362,368)(363,366)(364,367)(371,377)
(372,375)(373,376)(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)(487,595)(488,602)(489,600)(490,601)(491,599)(492,597)
(493,598)(494,596)(495,603)(496,604)(497,611)(498,609)(499,610)(500,608)
(501,606)(502,607)(503,605)(504,612)(505,613)(506,620)(507,618)(508,619)
(509,617)(510,615)(511,616)(512,614)(513,621)(514,622)(515,629)(516,627)
(517,628)(518,626)(519,624)(520,625)(521,623)(522,630)(523,631)(524,638)
(525,636)(526,637)(527,635)(528,633)(529,634)(530,632)(531,639)(532,640)
(533,647)(534,645)(535,646)(536,644)(537,642)(538,643)(539,641)(540,648)
(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)(703,838)(704,845)
(705,843)(706,844)(707,842)(708,840)(709,841)(710,839)(711,846)(712,847)
(713,854)(714,852)(715,853)(716,851)(717,849)(718,850)(719,848)(720,855)
(721,856)(722,863)(723,861)(724,862)(725,860)(726,858)(727,859)(728,857)
(729,864)(730,811)(731,818)(732,816)(733,817)(734,815)(735,813)(736,814)
(737,812)(738,819)(739,820)(740,827)(741,825)(742,826)(743,824)(744,822)
(745,823)(746,821)(747,828)(748,829)(749,836)(750,834)(751,835)(752,833)
(753,831)(754,832)(755,830)(756,837);;
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)( 55,703)( 56,704)
( 57,705)( 58,711)( 59,709)( 60,710)( 61,707)( 62,708)( 63,706)( 64,721)
( 65,722)( 66,723)( 67,729)( 68,727)( 69,728)( 70,725)( 71,726)( 72,724)
( 73,712)( 74,713)( 75,714)( 76,720)( 77,718)( 78,719)( 79,716)( 80,717)
( 81,715)( 82,730)( 83,731)( 84,732)( 85,738)( 86,736)( 87,737)( 88,734)
( 89,735)( 90,733)( 91,748)( 92,749)( 93,750)( 94,756)( 95,754)( 96,755)
( 97,752)( 98,753)( 99,751)(100,739)(101,740)(102,741)(103,747)(104,745)
(105,746)(106,743)(107,744)(108,742)(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)(163,838)(164,839)(165,840)(166,846)(167,844)(168,845)
(169,842)(170,843)(171,841)(172,856)(173,857)(174,858)(175,864)(176,862)
(177,863)(178,860)(179,861)(180,859)(181,847)(182,848)(183,849)(184,855)
(185,853)(186,854)(187,851)(188,852)(189,850)(190,811)(191,812)(192,813)
(193,819)(194,817)(195,818)(196,815)(197,816)(198,814)(199,829)(200,830)
(201,831)(202,837)(203,835)(204,836)(205,833)(206,834)(207,832)(208,820)
(209,821)(210,822)(211,828)(212,826)(213,827)(214,824)(215,825)(216,823)
(217,487)(218,488)(219,489)(220,495)(221,493)(222,494)(223,491)(224,492)
(225,490)(226,505)(227,506)(228,507)(229,513)(230,511)(231,512)(232,509)
(233,510)(234,508)(235,496)(236,497)(237,498)(238,504)(239,502)(240,503)
(241,500)(242,501)(243,499)(244,514)(245,515)(246,516)(247,522)(248,520)
(249,521)(250,518)(251,519)(252,517)(253,532)(254,533)(255,534)(256,540)
(257,538)(258,539)(259,536)(260,537)(261,535)(262,523)(263,524)(264,525)
(265,531)(266,529)(267,530)(268,527)(269,528)(270,526)(271,433)(272,434)
(273,435)(274,441)(275,439)(276,440)(277,437)(278,438)(279,436)(280,451)
(281,452)(282,453)(283,459)(284,457)(285,458)(286,455)(287,456)(288,454)
(289,442)(290,443)(291,444)(292,450)(293,448)(294,449)(295,446)(296,447)
(297,445)(298,460)(299,461)(300,462)(301,468)(302,466)(303,467)(304,464)
(305,465)(306,463)(307,478)(308,479)(309,480)(310,486)(311,484)(312,485)
(313,482)(314,483)(315,481)(316,469)(317,470)(318,471)(319,477)(320,475)
(321,476)(322,473)(323,474)(324,472)(325,622)(326,623)(327,624)(328,630)
(329,628)(330,629)(331,626)(332,627)(333,625)(334,640)(335,641)(336,642)
(337,648)(338,646)(339,647)(340,644)(341,645)(342,643)(343,631)(344,632)
(345,633)(346,639)(347,637)(348,638)(349,635)(350,636)(351,634)(352,595)
(353,596)(354,597)(355,603)(356,601)(357,602)(358,599)(359,600)(360,598)
(361,613)(362,614)(363,615)(364,621)(365,619)(366,620)(367,617)(368,618)
(369,616)(370,604)(371,605)(372,606)(373,612)(374,610)(375,611)(376,608)
(377,609)(378,607)(379,568)(380,569)(381,570)(382,576)(383,574)(384,575)
(385,572)(386,573)(387,571)(388,586)(389,587)(390,588)(391,594)(392,592)
(393,593)(394,590)(395,591)(396,589)(397,577)(398,578)(399,579)(400,585)
(401,583)(402,584)(403,581)(404,582)(405,580)(406,541)(407,542)(408,543)
(409,549)(410,547)(411,548)(412,545)(413,546)(414,544)(415,559)(416,560)
(417,561)(418,567)(419,565)(420,566)(421,563)(422,564)(423,562)(424,550)
(425,551)(426,552)(427,558)(428,556)(429,557)(430,554)(431,555)(432,553);;
s2 := ( 1,338)( 2,337)( 3,339)( 4,335)( 5,334)( 6,336)( 7,341)( 8,340)
( 9,342)( 10,329)( 11,328)( 12,330)( 13,326)( 14,325)( 15,327)( 16,332)
( 17,331)( 18,333)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)( 24,345)
( 25,350)( 26,349)( 27,351)( 28,365)( 29,364)( 30,366)( 31,362)( 32,361)
( 33,363)( 34,368)( 35,367)( 36,369)( 37,356)( 38,355)( 39,357)( 40,353)
( 41,352)( 42,354)( 43,359)( 44,358)( 45,360)( 46,374)( 47,373)( 48,375)
( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,392)( 56,391)
( 57,393)( 58,389)( 59,388)( 60,390)( 61,395)( 62,394)( 63,396)( 64,383)
( 65,382)( 66,384)( 67,380)( 68,379)( 69,381)( 70,386)( 71,385)( 72,387)
( 73,401)( 74,400)( 75,402)( 76,398)( 77,397)( 78,399)( 79,404)( 80,403)
( 81,405)( 82,419)( 83,418)( 84,420)( 85,416)( 86,415)( 87,417)( 88,422)
( 89,421)( 90,423)( 91,410)( 92,409)( 93,411)( 94,407)( 95,406)( 96,408)
( 97,413)( 98,412)( 99,414)(100,428)(101,427)(102,429)(103,425)(104,424)
(105,426)(106,431)(107,430)(108,432)(109,257)(110,256)(111,258)(112,254)
(113,253)(114,255)(115,260)(116,259)(117,261)(118,248)(119,247)(120,249)
(121,245)(122,244)(123,246)(124,251)(125,250)(126,252)(127,266)(128,265)
(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)(136,230)
(137,229)(138,231)(139,227)(140,226)(141,228)(142,233)(143,232)(144,234)
(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)(152,223)
(153,225)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)(160,242)
(161,241)(162,243)(163,311)(164,310)(165,312)(166,308)(167,307)(168,309)
(169,314)(170,313)(171,315)(172,302)(173,301)(174,303)(175,299)(176,298)
(177,300)(178,305)(179,304)(180,306)(181,320)(182,319)(183,321)(184,317)
(185,316)(186,318)(187,323)(188,322)(189,324)(190,284)(191,283)(192,285)
(193,281)(194,280)(195,282)(196,287)(197,286)(198,288)(199,275)(200,274)
(201,276)(202,272)(203,271)(204,273)(205,278)(206,277)(207,279)(208,293)
(209,292)(210,294)(211,290)(212,289)(213,291)(214,296)(215,295)(216,297)
(433,770)(434,769)(435,771)(436,767)(437,766)(438,768)(439,773)(440,772)
(441,774)(442,761)(443,760)(444,762)(445,758)(446,757)(447,759)(448,764)
(449,763)(450,765)(451,779)(452,778)(453,780)(454,776)(455,775)(456,777)
(457,782)(458,781)(459,783)(460,797)(461,796)(462,798)(463,794)(464,793)
(465,795)(466,800)(467,799)(468,801)(469,788)(470,787)(471,789)(472,785)
(473,784)(474,786)(475,791)(476,790)(477,792)(478,806)(479,805)(480,807)
(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,824)(488,823)
(489,825)(490,821)(491,820)(492,822)(493,827)(494,826)(495,828)(496,815)
(497,814)(498,816)(499,812)(500,811)(501,813)(502,818)(503,817)(504,819)
(505,833)(506,832)(507,834)(508,830)(509,829)(510,831)(511,836)(512,835)
(513,837)(514,851)(515,850)(516,852)(517,848)(518,847)(519,849)(520,854)
(521,853)(522,855)(523,842)(524,841)(525,843)(526,839)(527,838)(528,840)
(529,845)(530,844)(531,846)(532,860)(533,859)(534,861)(535,857)(536,856)
(537,858)(538,863)(539,862)(540,864)(541,689)(542,688)(543,690)(544,686)
(545,685)(546,687)(547,692)(548,691)(549,693)(550,680)(551,679)(552,681)
(553,677)(554,676)(555,678)(556,683)(557,682)(558,684)(559,698)(560,697)
(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)(568,662)
(569,661)(570,663)(571,659)(572,658)(573,660)(574,665)(575,664)(576,666)
(577,653)(578,652)(579,654)(580,650)(581,649)(582,651)(583,656)(584,655)
(585,657)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)(592,674)
(593,673)(594,675)(595,743)(596,742)(597,744)(598,740)(599,739)(600,741)
(601,746)(602,745)(603,747)(604,734)(605,733)(606,735)(607,731)(608,730)
(609,732)(610,737)(611,736)(612,738)(613,752)(614,751)(615,753)(616,749)
(617,748)(618,750)(619,755)(620,754)(621,756)(622,716)(623,715)(624,717)
(625,713)(626,712)(627,714)(628,719)(629,718)(630,720)(631,707)(632,706)
(633,708)(634,704)(635,703)(636,705)(637,710)(638,709)(639,711)(640,725)
(641,724)(642,726)(643,722)(644,721)(645,723)(646,728)(647,727)(648,729);;
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*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*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)( 56, 62)( 57, 60)( 58, 61)( 65, 71)( 66, 69)
( 67, 70)( 74, 80)( 75, 78)( 76, 79)( 83, 89)( 84, 87)( 85, 88)( 92, 98)
( 93, 96)( 94, 97)(101,107)(102,105)(103,106)(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)
(163,190)(164,197)(165,195)(166,196)(167,194)(168,192)(169,193)(170,191)
(171,198)(172,199)(173,206)(174,204)(175,205)(176,203)(177,201)(178,202)
(179,200)(180,207)(181,208)(182,215)(183,213)(184,214)(185,212)(186,210)
(187,211)(188,209)(189,216)(217,244)(218,251)(219,249)(220,250)(221,248)
(222,246)(223,247)(224,245)(225,252)(226,253)(227,260)(228,258)(229,259)
(230,257)(231,255)(232,256)(233,254)(234,261)(235,262)(236,269)(237,267)
(238,268)(239,266)(240,264)(241,265)(242,263)(243,270)(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)(326,332)(327,330)(328,331)(335,341)(336,339)(337,340)(344,350)
(345,348)(346,349)(353,359)(354,357)(355,358)(362,368)(363,366)(364,367)
(371,377)(372,375)(373,376)(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)(487,595)(488,602)(489,600)(490,601)(491,599)
(492,597)(493,598)(494,596)(495,603)(496,604)(497,611)(498,609)(499,610)
(500,608)(501,606)(502,607)(503,605)(504,612)(505,613)(506,620)(507,618)
(508,619)(509,617)(510,615)(511,616)(512,614)(513,621)(514,622)(515,629)
(516,627)(517,628)(518,626)(519,624)(520,625)(521,623)(522,630)(523,631)
(524,638)(525,636)(526,637)(527,635)(528,633)(529,634)(530,632)(531,639)
(532,640)(533,647)(534,645)(535,646)(536,644)(537,642)(538,643)(539,641)
(540,648)(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)(703,838)
(704,845)(705,843)(706,844)(707,842)(708,840)(709,841)(710,839)(711,846)
(712,847)(713,854)(714,852)(715,853)(716,851)(717,849)(718,850)(719,848)
(720,855)(721,856)(722,863)(723,861)(724,862)(725,860)(726,858)(727,859)
(728,857)(729,864)(730,811)(731,818)(732,816)(733,817)(734,815)(735,813)
(736,814)(737,812)(738,819)(739,820)(740,827)(741,825)(742,826)(743,824)
(744,822)(745,823)(746,821)(747,828)(748,829)(749,836)(750,834)(751,835)
(752,833)(753,831)(754,832)(755,830)(756,837);
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)( 55,703)
( 56,704)( 57,705)( 58,711)( 59,709)( 60,710)( 61,707)( 62,708)( 63,706)
( 64,721)( 65,722)( 66,723)( 67,729)( 68,727)( 69,728)( 70,725)( 71,726)
( 72,724)( 73,712)( 74,713)( 75,714)( 76,720)( 77,718)( 78,719)( 79,716)
( 80,717)( 81,715)( 82,730)( 83,731)( 84,732)( 85,738)( 86,736)( 87,737)
( 88,734)( 89,735)( 90,733)( 91,748)( 92,749)( 93,750)( 94,756)( 95,754)
( 96,755)( 97,752)( 98,753)( 99,751)(100,739)(101,740)(102,741)(103,747)
(104,745)(105,746)(106,743)(107,744)(108,742)(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)(163,838)(164,839)(165,840)(166,846)(167,844)
(168,845)(169,842)(170,843)(171,841)(172,856)(173,857)(174,858)(175,864)
(176,862)(177,863)(178,860)(179,861)(180,859)(181,847)(182,848)(183,849)
(184,855)(185,853)(186,854)(187,851)(188,852)(189,850)(190,811)(191,812)
(192,813)(193,819)(194,817)(195,818)(196,815)(197,816)(198,814)(199,829)
(200,830)(201,831)(202,837)(203,835)(204,836)(205,833)(206,834)(207,832)
(208,820)(209,821)(210,822)(211,828)(212,826)(213,827)(214,824)(215,825)
(216,823)(217,487)(218,488)(219,489)(220,495)(221,493)(222,494)(223,491)
(224,492)(225,490)(226,505)(227,506)(228,507)(229,513)(230,511)(231,512)
(232,509)(233,510)(234,508)(235,496)(236,497)(237,498)(238,504)(239,502)
(240,503)(241,500)(242,501)(243,499)(244,514)(245,515)(246,516)(247,522)
(248,520)(249,521)(250,518)(251,519)(252,517)(253,532)(254,533)(255,534)
(256,540)(257,538)(258,539)(259,536)(260,537)(261,535)(262,523)(263,524)
(264,525)(265,531)(266,529)(267,530)(268,527)(269,528)(270,526)(271,433)
(272,434)(273,435)(274,441)(275,439)(276,440)(277,437)(278,438)(279,436)
(280,451)(281,452)(282,453)(283,459)(284,457)(285,458)(286,455)(287,456)
(288,454)(289,442)(290,443)(291,444)(292,450)(293,448)(294,449)(295,446)
(296,447)(297,445)(298,460)(299,461)(300,462)(301,468)(302,466)(303,467)
(304,464)(305,465)(306,463)(307,478)(308,479)(309,480)(310,486)(311,484)
(312,485)(313,482)(314,483)(315,481)(316,469)(317,470)(318,471)(319,477)
(320,475)(321,476)(322,473)(323,474)(324,472)(325,622)(326,623)(327,624)
(328,630)(329,628)(330,629)(331,626)(332,627)(333,625)(334,640)(335,641)
(336,642)(337,648)(338,646)(339,647)(340,644)(341,645)(342,643)(343,631)
(344,632)(345,633)(346,639)(347,637)(348,638)(349,635)(350,636)(351,634)
(352,595)(353,596)(354,597)(355,603)(356,601)(357,602)(358,599)(359,600)
(360,598)(361,613)(362,614)(363,615)(364,621)(365,619)(366,620)(367,617)
(368,618)(369,616)(370,604)(371,605)(372,606)(373,612)(374,610)(375,611)
(376,608)(377,609)(378,607)(379,568)(380,569)(381,570)(382,576)(383,574)
(384,575)(385,572)(386,573)(387,571)(388,586)(389,587)(390,588)(391,594)
(392,592)(393,593)(394,590)(395,591)(396,589)(397,577)(398,578)(399,579)
(400,585)(401,583)(402,584)(403,581)(404,582)(405,580)(406,541)(407,542)
(408,543)(409,549)(410,547)(411,548)(412,545)(413,546)(414,544)(415,559)
(416,560)(417,561)(418,567)(419,565)(420,566)(421,563)(422,564)(423,562)
(424,550)(425,551)(426,552)(427,558)(428,556)(429,557)(430,554)(431,555)
(432,553);
s2 := Sym(864)!( 1,338)( 2,337)( 3,339)( 4,335)( 5,334)( 6,336)( 7,341)
( 8,340)( 9,342)( 10,329)( 11,328)( 12,330)( 13,326)( 14,325)( 15,327)
( 16,332)( 17,331)( 18,333)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)
( 24,345)( 25,350)( 26,349)( 27,351)( 28,365)( 29,364)( 30,366)( 31,362)
( 32,361)( 33,363)( 34,368)( 35,367)( 36,369)( 37,356)( 38,355)( 39,357)
( 40,353)( 41,352)( 42,354)( 43,359)( 44,358)( 45,360)( 46,374)( 47,373)
( 48,375)( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,392)
( 56,391)( 57,393)( 58,389)( 59,388)( 60,390)( 61,395)( 62,394)( 63,396)
( 64,383)( 65,382)( 66,384)( 67,380)( 68,379)( 69,381)( 70,386)( 71,385)
( 72,387)( 73,401)( 74,400)( 75,402)( 76,398)( 77,397)( 78,399)( 79,404)
( 80,403)( 81,405)( 82,419)( 83,418)( 84,420)( 85,416)( 86,415)( 87,417)
( 88,422)( 89,421)( 90,423)( 91,410)( 92,409)( 93,411)( 94,407)( 95,406)
( 96,408)( 97,413)( 98,412)( 99,414)(100,428)(101,427)(102,429)(103,425)
(104,424)(105,426)(106,431)(107,430)(108,432)(109,257)(110,256)(111,258)
(112,254)(113,253)(114,255)(115,260)(116,259)(117,261)(118,248)(119,247)
(120,249)(121,245)(122,244)(123,246)(124,251)(125,250)(126,252)(127,266)
(128,265)(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)
(136,230)(137,229)(138,231)(139,227)(140,226)(141,228)(142,233)(143,232)
(144,234)(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)
(152,223)(153,225)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)
(160,242)(161,241)(162,243)(163,311)(164,310)(165,312)(166,308)(167,307)
(168,309)(169,314)(170,313)(171,315)(172,302)(173,301)(174,303)(175,299)
(176,298)(177,300)(178,305)(179,304)(180,306)(181,320)(182,319)(183,321)
(184,317)(185,316)(186,318)(187,323)(188,322)(189,324)(190,284)(191,283)
(192,285)(193,281)(194,280)(195,282)(196,287)(197,286)(198,288)(199,275)
(200,274)(201,276)(202,272)(203,271)(204,273)(205,278)(206,277)(207,279)
(208,293)(209,292)(210,294)(211,290)(212,289)(213,291)(214,296)(215,295)
(216,297)(433,770)(434,769)(435,771)(436,767)(437,766)(438,768)(439,773)
(440,772)(441,774)(442,761)(443,760)(444,762)(445,758)(446,757)(447,759)
(448,764)(449,763)(450,765)(451,779)(452,778)(453,780)(454,776)(455,775)
(456,777)(457,782)(458,781)(459,783)(460,797)(461,796)(462,798)(463,794)
(464,793)(465,795)(466,800)(467,799)(468,801)(469,788)(470,787)(471,789)
(472,785)(473,784)(474,786)(475,791)(476,790)(477,792)(478,806)(479,805)
(480,807)(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,824)
(488,823)(489,825)(490,821)(491,820)(492,822)(493,827)(494,826)(495,828)
(496,815)(497,814)(498,816)(499,812)(500,811)(501,813)(502,818)(503,817)
(504,819)(505,833)(506,832)(507,834)(508,830)(509,829)(510,831)(511,836)
(512,835)(513,837)(514,851)(515,850)(516,852)(517,848)(518,847)(519,849)
(520,854)(521,853)(522,855)(523,842)(524,841)(525,843)(526,839)(527,838)
(528,840)(529,845)(530,844)(531,846)(532,860)(533,859)(534,861)(535,857)
(536,856)(537,858)(538,863)(539,862)(540,864)(541,689)(542,688)(543,690)
(544,686)(545,685)(546,687)(547,692)(548,691)(549,693)(550,680)(551,679)
(552,681)(553,677)(554,676)(555,678)(556,683)(557,682)(558,684)(559,698)
(560,697)(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)
(568,662)(569,661)(570,663)(571,659)(572,658)(573,660)(574,665)(575,664)
(576,666)(577,653)(578,652)(579,654)(580,650)(581,649)(582,651)(583,656)
(584,655)(585,657)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)
(592,674)(593,673)(594,675)(595,743)(596,742)(597,744)(598,740)(599,739)
(600,741)(601,746)(602,745)(603,747)(604,734)(605,733)(606,735)(607,731)
(608,730)(609,732)(610,737)(611,736)(612,738)(613,752)(614,751)(615,753)
(616,749)(617,748)(618,750)(619,755)(620,754)(621,756)(622,716)(623,715)
(624,717)(625,713)(626,712)(627,714)(628,719)(629,718)(630,720)(631,707)
(632,706)(633,708)(634,704)(635,703)(636,705)(637,710)(638,709)(639,711)
(640,725)(641,724)(642,726)(643,722)(644,721)(645,723)(646,728)(647,727)
(648,729);
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,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*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*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