Questions?
See the FAQ
or other info.

# Polytope of Type {8,12}

Atlas Canonical Name : {8,12}*1728h
if this polytope has a name.
Group : SmallGroup(1728,31623)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 72, 432, 108
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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
3-fold quotients : {8,12}*576b
4-fold quotients : {4,6}*432b
6-fold quotients : {4,12}*288
9-fold quotients : {8,12}*192b
12-fold quotients : {4,6}*144
18-fold quotients : {4,12}*96a
24-fold quotients : {4,6}*72
27-fold quotients : {8,4}*64b
36-fold quotients : {2,12}*48, {4,6}*48a
54-fold quotients : {4,4}*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)( 55,703)( 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 := (  1,392)(  2,391)(  3,393)(  4,389)(  5,388)(  6,390)(  7,395)(  8,394)
(  9,396)( 10,383)( 11,382)( 12,384)( 13,380)( 14,379)( 15,381)( 16,386)
( 17,385)( 18,387)( 19,401)( 20,400)( 21,402)( 22,398)( 23,397)( 24,399)
( 25,404)( 26,403)( 27,405)( 28,419)( 29,418)( 30,420)( 31,416)( 32,415)
( 33,417)( 34,422)( 35,421)( 36,423)( 37,410)( 38,409)( 39,411)( 40,407)
( 41,406)( 42,408)( 43,413)( 44,412)( 45,414)( 46,428)( 47,427)( 48,429)
( 49,425)( 50,424)( 51,426)( 52,431)( 53,430)( 54,432)( 55,338)( 56,337)
( 57,339)( 58,335)( 59,334)( 60,336)( 61,341)( 62,340)( 63,342)( 64,329)
( 65,328)( 66,330)( 67,326)( 68,325)( 69,327)( 70,332)( 71,331)( 72,333)
( 73,347)( 74,346)( 75,348)( 76,344)( 77,343)( 78,345)( 79,350)( 80,349)
( 81,351)( 82,365)( 83,364)( 84,366)( 85,362)( 86,361)( 87,363)( 88,368)
( 89,367)( 90,369)( 91,356)( 92,355)( 93,357)( 94,353)( 95,352)( 96,354)
( 97,359)( 98,358)( 99,360)(100,374)(101,373)(102,375)(103,371)(104,370)
(105,372)(106,377)(107,376)(108,378)(109,284)(110,283)(111,285)(112,281)
(113,280)(114,282)(115,287)(116,286)(117,288)(118,275)(119,274)(120,276)
(121,272)(122,271)(123,273)(124,278)(125,277)(126,279)(127,293)(128,292)
(129,294)(130,290)(131,289)(132,291)(133,296)(134,295)(135,297)(136,311)
(137,310)(138,312)(139,308)(140,307)(141,309)(142,314)(143,313)(144,315)
(145,302)(146,301)(147,303)(148,299)(149,298)(150,300)(151,305)(152,304)
(153,306)(154,320)(155,319)(156,321)(157,317)(158,316)(159,318)(160,323)
(161,322)(162,324)(163,230)(164,229)(165,231)(166,227)(167,226)(168,228)
(169,233)(170,232)(171,234)(172,221)(173,220)(174,222)(175,218)(176,217)
(177,219)(178,224)(179,223)(180,225)(181,239)(182,238)(183,240)(184,236)
(185,235)(186,237)(187,242)(188,241)(189,243)(190,257)(191,256)(192,258)
(193,254)(194,253)(195,255)(196,260)(197,259)(198,261)(199,248)(200,247)
(201,249)(202,245)(203,244)(204,246)(205,251)(206,250)(207,252)(208,266)
(209,265)(210,267)(211,263)(212,262)(213,264)(214,269)(215,268)(216,270)
(433,824)(434,823)(435,825)(436,821)(437,820)(438,822)(439,827)(440,826)
(441,828)(442,815)(443,814)(444,816)(445,812)(446,811)(447,813)(448,818)
(449,817)(450,819)(451,833)(452,832)(453,834)(454,830)(455,829)(456,831)
(457,836)(458,835)(459,837)(460,851)(461,850)(462,852)(463,848)(464,847)
(465,849)(466,854)(467,853)(468,855)(469,842)(470,841)(471,843)(472,839)
(473,838)(474,840)(475,845)(476,844)(477,846)(478,860)(479,859)(480,861)
(481,857)(482,856)(483,858)(484,863)(485,862)(486,864)(487,770)(488,769)
(489,771)(490,767)(491,766)(492,768)(493,773)(494,772)(495,774)(496,761)
(497,760)(498,762)(499,758)(500,757)(501,759)(502,764)(503,763)(504,765)
(505,779)(506,778)(507,780)(508,776)(509,775)(510,777)(511,782)(512,781)
(513,783)(514,797)(515,796)(516,798)(517,794)(518,793)(519,795)(520,800)
(521,799)(522,801)(523,788)(524,787)(525,789)(526,785)(527,784)(528,786)
(529,791)(530,790)(531,792)(532,806)(533,805)(534,807)(535,803)(536,802)
(537,804)(538,809)(539,808)(540,810)(541,716)(542,715)(543,717)(544,713)
(545,712)(546,714)(547,719)(548,718)(549,720)(550,707)(551,706)(552,708)
(553,704)(554,703)(555,705)(556,710)(557,709)(558,711)(559,725)(560,724)
(561,726)(562,722)(563,721)(564,723)(565,728)(566,727)(567,729)(568,743)
(569,742)(570,744)(571,740)(572,739)(573,741)(574,746)(575,745)(576,747)
(577,734)(578,733)(579,735)(580,731)(581,730)(582,732)(583,737)(584,736)
(585,738)(586,752)(587,751)(588,753)(589,749)(590,748)(591,750)(592,755)
(593,754)(594,756)(595,662)(596,661)(597,663)(598,659)(599,658)(600,660)
(601,665)(602,664)(603,666)(604,653)(605,652)(606,654)(607,650)(608,649)
(609,651)(610,656)(611,655)(612,657)(613,671)(614,670)(615,672)(616,668)
(617,667)(618,669)(619,674)(620,673)(621,675)(622,689)(623,688)(624,690)
(625,686)(626,685)(627,687)(628,692)(629,691)(630,693)(631,680)(632,679)
(633,681)(634,677)(635,676)(636,678)(637,683)(638,682)(639,684)(640,698)
(641,697)(642,699)(643,695)(644,694)(645,696)(646,701)(647,700)(648,702);;
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,
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0 ];;
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)( 55,703)
( 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)!(  1,392)(  2,391)(  3,393)(  4,389)(  5,388)(  6,390)(  7,395)
(  8,394)(  9,396)( 10,383)( 11,382)( 12,384)( 13,380)( 14,379)( 15,381)
( 16,386)( 17,385)( 18,387)( 19,401)( 20,400)( 21,402)( 22,398)( 23,397)
( 24,399)( 25,404)( 26,403)( 27,405)( 28,419)( 29,418)( 30,420)( 31,416)
( 32,415)( 33,417)( 34,422)( 35,421)( 36,423)( 37,410)( 38,409)( 39,411)
( 40,407)( 41,406)( 42,408)( 43,413)( 44,412)( 45,414)( 46,428)( 47,427)
( 48,429)( 49,425)( 50,424)( 51,426)( 52,431)( 53,430)( 54,432)( 55,338)
( 56,337)( 57,339)( 58,335)( 59,334)( 60,336)( 61,341)( 62,340)( 63,342)
( 64,329)( 65,328)( 66,330)( 67,326)( 68,325)( 69,327)( 70,332)( 71,331)
( 72,333)( 73,347)( 74,346)( 75,348)( 76,344)( 77,343)( 78,345)( 79,350)
( 80,349)( 81,351)( 82,365)( 83,364)( 84,366)( 85,362)( 86,361)( 87,363)
( 88,368)( 89,367)( 90,369)( 91,356)( 92,355)( 93,357)( 94,353)( 95,352)
( 96,354)( 97,359)( 98,358)( 99,360)(100,374)(101,373)(102,375)(103,371)
(104,370)(105,372)(106,377)(107,376)(108,378)(109,284)(110,283)(111,285)
(112,281)(113,280)(114,282)(115,287)(116,286)(117,288)(118,275)(119,274)
(120,276)(121,272)(122,271)(123,273)(124,278)(125,277)(126,279)(127,293)
(128,292)(129,294)(130,290)(131,289)(132,291)(133,296)(134,295)(135,297)
(136,311)(137,310)(138,312)(139,308)(140,307)(141,309)(142,314)(143,313)
(144,315)(145,302)(146,301)(147,303)(148,299)(149,298)(150,300)(151,305)
(152,304)(153,306)(154,320)(155,319)(156,321)(157,317)(158,316)(159,318)
(160,323)(161,322)(162,324)(163,230)(164,229)(165,231)(166,227)(167,226)
(168,228)(169,233)(170,232)(171,234)(172,221)(173,220)(174,222)(175,218)
(176,217)(177,219)(178,224)(179,223)(180,225)(181,239)(182,238)(183,240)
(184,236)(185,235)(186,237)(187,242)(188,241)(189,243)(190,257)(191,256)
(192,258)(193,254)(194,253)(195,255)(196,260)(197,259)(198,261)(199,248)
(200,247)(201,249)(202,245)(203,244)(204,246)(205,251)(206,250)(207,252)
(208,266)(209,265)(210,267)(211,263)(212,262)(213,264)(214,269)(215,268)
(216,270)(433,824)(434,823)(435,825)(436,821)(437,820)(438,822)(439,827)
(440,826)(441,828)(442,815)(443,814)(444,816)(445,812)(446,811)(447,813)
(448,818)(449,817)(450,819)(451,833)(452,832)(453,834)(454,830)(455,829)
(456,831)(457,836)(458,835)(459,837)(460,851)(461,850)(462,852)(463,848)
(464,847)(465,849)(466,854)(467,853)(468,855)(469,842)(470,841)(471,843)
(472,839)(473,838)(474,840)(475,845)(476,844)(477,846)(478,860)(479,859)
(480,861)(481,857)(482,856)(483,858)(484,863)(485,862)(486,864)(487,770)
(488,769)(489,771)(490,767)(491,766)(492,768)(493,773)(494,772)(495,774)
(496,761)(497,760)(498,762)(499,758)(500,757)(501,759)(502,764)(503,763)
(504,765)(505,779)(506,778)(507,780)(508,776)(509,775)(510,777)(511,782)
(512,781)(513,783)(514,797)(515,796)(516,798)(517,794)(518,793)(519,795)
(520,800)(521,799)(522,801)(523,788)(524,787)(525,789)(526,785)(527,784)
(528,786)(529,791)(530,790)(531,792)(532,806)(533,805)(534,807)(535,803)
(536,802)(537,804)(538,809)(539,808)(540,810)(541,716)(542,715)(543,717)
(544,713)(545,712)(546,714)(547,719)(548,718)(549,720)(550,707)(551,706)
(552,708)(553,704)(554,703)(555,705)(556,710)(557,709)(558,711)(559,725)
(560,724)(561,726)(562,722)(563,721)(564,723)(565,728)(566,727)(567,729)
(568,743)(569,742)(570,744)(571,740)(572,739)(573,741)(574,746)(575,745)
(576,747)(577,734)(578,733)(579,735)(580,731)(581,730)(582,732)(583,737)
(584,736)(585,738)(586,752)(587,751)(588,753)(589,749)(590,748)(591,750)
(592,755)(593,754)(594,756)(595,662)(596,661)(597,663)(598,659)(599,658)
(600,660)(601,665)(602,664)(603,666)(604,653)(605,652)(606,654)(607,650)
(608,649)(609,651)(610,656)(611,655)(612,657)(613,671)(614,670)(615,672)
(616,668)(617,667)(618,669)(619,674)(620,673)(621,675)(622,689)(623,688)
(624,690)(625,686)(626,685)(627,687)(628,692)(629,691)(630,693)(631,680)
(632,679)(633,681)(634,677)(635,676)(636,678)(637,683)(638,682)(639,684)
(640,698)(641,697)(642,699)(643,695)(644,694)(645,696)(646,701)(647,700)
(648,702);
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,
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0 >;

```
References : None.
to this polytope