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# Polytope of Type {12,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1728h
if this polytope has a name.
Group : SmallGroup(1728,12653)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 36, 432, 72
Order of s0s1s2 : 24
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, {12,12}*864g
3-fold quotients : {12,8}*576a
4-fold quotients : {6,12}*432e
6-fold quotients : {6,8}*288, {12,4}*288
8-fold quotients : {6,12}*216a
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {4,8}*64a
54-fold quotients : {4,4}*32, {2,8}*32
108-fold quotients : {2,4}*16, {4,2}*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)(109,244)(110,245)(111,246)(112,252)
(113,250)(114,251)(115,248)(116,249)(117,247)(118,264)(119,262)(120,263)
(121,269)(122,270)(123,268)(124,265)(125,266)(126,267)(127,254)(128,255)
(129,253)(130,259)(131,260)(132,261)(133,258)(134,256)(135,257)(136,217)
(137,218)(138,219)(139,225)(140,223)(141,224)(142,221)(143,222)(144,220)
(145,237)(146,235)(147,236)(148,242)(149,243)(150,241)(151,238)(152,239)
(153,240)(154,227)(155,228)(156,226)(157,232)(158,233)(159,234)(160,231)
(161,229)(162,230)(163,298)(164,299)(165,300)(166,306)(167,304)(168,305)
(169,302)(170,303)(171,301)(172,318)(173,316)(174,317)(175,323)(176,324)
(177,322)(178,319)(179,320)(180,321)(181,308)(182,309)(183,307)(184,313)
(185,314)(186,315)(187,312)(188,310)(189,311)(190,271)(191,272)(192,273)
(193,279)(194,277)(195,278)(196,275)(197,276)(198,274)(199,291)(200,289)
(201,290)(202,296)(203,297)(204,295)(205,292)(206,293)(207,294)(208,281)
(209,282)(210,280)(211,286)(212,287)(213,288)(214,285)(215,283)(216,284)
(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)(541,676)(542,677)(543,678)(544,684)
(545,682)(546,683)(547,680)(548,681)(549,679)(550,696)(551,694)(552,695)
(553,701)(554,702)(555,700)(556,697)(557,698)(558,699)(559,686)(560,687)
(561,685)(562,691)(563,692)(564,693)(565,690)(566,688)(567,689)(568,649)
(569,650)(570,651)(571,657)(572,655)(573,656)(574,653)(575,654)(576,652)
(577,669)(578,667)(579,668)(580,674)(581,675)(582,673)(583,670)(584,671)
(585,672)(586,659)(587,660)(588,658)(589,664)(590,665)(591,666)(592,663)
(593,661)(594,662)(595,730)(596,731)(597,732)(598,738)(599,736)(600,737)
(601,734)(602,735)(603,733)(604,750)(605,748)(606,749)(607,755)(608,756)
(609,754)(610,751)(611,752)(612,753)(613,740)(614,741)(615,739)(616,745)
(617,746)(618,747)(619,744)(620,742)(621,743)(622,703)(623,704)(624,705)
(625,711)(626,709)(627,710)(628,707)(629,708)(630,706)(631,723)(632,721)
(633,722)(634,728)(635,729)(636,727)(637,724)(638,725)(639,726)(640,713)
(641,714)(642,712)(643,718)(644,719)(645,720)(646,717)(647,715)(648,716);;
s1 := (  1,544)(  2,546)(  3,545)(  4,541)(  5,543)(  6,542)(  7,547)(  8,549)
(  9,548)( 10,558)( 11,557)( 12,556)( 13,555)( 14,554)( 15,553)( 16,552)
( 17,551)( 18,550)( 19,561)( 20,560)( 21,559)( 22,567)( 23,566)( 24,565)
( 25,564)( 26,563)( 27,562)( 28,571)( 29,573)( 30,572)( 31,568)( 32,570)
( 33,569)( 34,574)( 35,576)( 36,575)( 37,585)( 38,584)( 39,583)( 40,582)
( 41,581)( 42,580)( 43,579)( 44,578)( 45,577)( 46,588)( 47,587)( 48,586)
( 49,594)( 50,593)( 51,592)( 52,591)( 53,590)( 54,589)( 55,598)( 56,600)
( 57,599)( 58,595)( 59,597)( 60,596)( 61,601)( 62,603)( 63,602)( 64,612)
( 65,611)( 66,610)( 67,609)( 68,608)( 69,607)( 70,606)( 71,605)( 72,604)
( 73,615)( 74,614)( 75,613)( 76,621)( 77,620)( 78,619)( 79,618)( 80,617)
( 81,616)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)( 88,628)
( 89,630)( 90,629)( 91,639)( 92,638)( 93,637)( 94,636)( 95,635)( 96,634)
( 97,633)( 98,632)( 99,631)(100,642)(101,641)(102,640)(103,648)(104,647)
(105,646)(106,645)(107,644)(108,643)(109,436)(110,438)(111,437)(112,433)
(113,435)(114,434)(115,439)(116,441)(117,440)(118,450)(119,449)(120,448)
(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,453)(128,452)
(129,451)(130,459)(131,458)(132,457)(133,456)(134,455)(135,454)(136,463)
(137,465)(138,464)(139,460)(140,462)(141,461)(142,466)(143,468)(144,467)
(145,477)(146,476)(147,475)(148,474)(149,473)(150,472)(151,471)(152,470)
(153,469)(154,480)(155,479)(156,478)(157,486)(158,485)(159,484)(160,483)
(161,482)(162,481)(163,490)(164,492)(165,491)(166,487)(167,489)(168,488)
(169,493)(170,495)(171,494)(172,504)(173,503)(174,502)(175,501)(176,500)
(177,499)(178,498)(179,497)(180,496)(181,507)(182,506)(183,505)(184,513)
(185,512)(186,511)(187,510)(188,509)(189,508)(190,517)(191,519)(192,518)
(193,514)(194,516)(195,515)(196,520)(197,522)(198,521)(199,531)(200,530)
(201,529)(202,528)(203,527)(204,526)(205,525)(206,524)(207,523)(208,534)
(209,533)(210,532)(211,540)(212,539)(213,538)(214,537)(215,536)(216,535)
(217,814)(218,816)(219,815)(220,811)(221,813)(222,812)(223,817)(224,819)
(225,818)(226,828)(227,827)(228,826)(229,825)(230,824)(231,823)(232,822)
(233,821)(234,820)(235,831)(236,830)(237,829)(238,837)(239,836)(240,835)
(241,834)(242,833)(243,832)(244,841)(245,843)(246,842)(247,838)(248,840)
(249,839)(250,844)(251,846)(252,845)(253,855)(254,854)(255,853)(256,852)
(257,851)(258,850)(259,849)(260,848)(261,847)(262,858)(263,857)(264,856)
(265,864)(266,863)(267,862)(268,861)(269,860)(270,859)(271,760)(272,762)
(273,761)(274,757)(275,759)(276,758)(277,763)(278,765)(279,764)(280,774)
(281,773)(282,772)(283,771)(284,770)(285,769)(286,768)(287,767)(288,766)
(289,777)(290,776)(291,775)(292,783)(293,782)(294,781)(295,780)(296,779)
(297,778)(298,787)(299,789)(300,788)(301,784)(302,786)(303,785)(304,790)
(305,792)(306,791)(307,801)(308,800)(309,799)(310,798)(311,797)(312,796)
(313,795)(314,794)(315,793)(316,804)(317,803)(318,802)(319,810)(320,809)
(321,808)(322,807)(323,806)(324,805)(325,706)(326,708)(327,707)(328,703)
(329,705)(330,704)(331,709)(332,711)(333,710)(334,720)(335,719)(336,718)
(337,717)(338,716)(339,715)(340,714)(341,713)(342,712)(343,723)(344,722)
(345,721)(346,729)(347,728)(348,727)(349,726)(350,725)(351,724)(352,733)
(353,735)(354,734)(355,730)(356,732)(357,731)(358,736)(359,738)(360,737)
(361,747)(362,746)(363,745)(364,744)(365,743)(366,742)(367,741)(368,740)
(369,739)(370,750)(371,749)(372,748)(373,756)(374,755)(375,754)(376,753)
(377,752)(378,751)(379,652)(380,654)(381,653)(382,649)(383,651)(384,650)
(385,655)(386,657)(387,656)(388,666)(389,665)(390,664)(391,663)(392,662)
(393,661)(394,660)(395,659)(396,658)(397,669)(398,668)(399,667)(400,675)
(401,674)(402,673)(403,672)(404,671)(405,670)(406,679)(407,681)(408,680)
(409,676)(410,678)(411,677)(412,682)(413,684)(414,683)(415,693)(416,692)
(417,691)(418,690)(419,689)(420,688)(421,687)(422,686)(423,685)(424,696)
(425,695)(426,694)(427,702)(428,701)(429,700)(430,699)(431,698)(432,697);;
s2 := (  1,  2)(  4, 23)(  5, 22)(  6, 24)(  7, 16)(  8, 18)(  9, 17)( 10, 20)
( 11, 19)( 12, 21)( 13, 14)( 26, 27)( 28, 29)( 31, 50)( 32, 49)( 33, 51)
( 34, 43)( 35, 45)( 36, 44)( 37, 47)( 38, 46)( 39, 48)( 40, 41)( 53, 54)
( 55, 56)( 58, 77)( 59, 76)( 60, 78)( 61, 70)( 62, 72)( 63, 71)( 64, 74)
( 65, 73)( 66, 75)( 67, 68)( 80, 81)( 82, 83)( 85,104)( 86,103)( 87,105)
( 88, 97)( 89, 99)( 90, 98)( 91,101)( 92,100)( 93,102)( 94, 95)(107,108)
(109,137)(110,136)(111,138)(112,158)(113,157)(114,159)(115,151)(116,153)
(117,152)(118,155)(119,154)(120,156)(121,149)(122,148)(123,150)(124,142)
(125,144)(126,143)(127,146)(128,145)(129,147)(130,140)(131,139)(132,141)
(133,160)(134,162)(135,161)(163,191)(164,190)(165,192)(166,212)(167,211)
(168,213)(169,205)(170,207)(171,206)(172,209)(173,208)(174,210)(175,203)
(176,202)(177,204)(178,196)(179,198)(180,197)(181,200)(182,199)(183,201)
(184,194)(185,193)(186,195)(187,214)(188,216)(189,215)(217,245)(218,244)
(219,246)(220,266)(221,265)(222,267)(223,259)(224,261)(225,260)(226,263)
(227,262)(228,264)(229,257)(230,256)(231,258)(232,250)(233,252)(234,251)
(235,254)(236,253)(237,255)(238,248)(239,247)(240,249)(241,268)(242,270)
(243,269)(271,299)(272,298)(273,300)(274,320)(275,319)(276,321)(277,313)
(278,315)(279,314)(280,317)(281,316)(282,318)(283,311)(284,310)(285,312)
(286,304)(287,306)(288,305)(289,308)(290,307)(291,309)(292,302)(293,301)
(294,303)(295,322)(296,324)(297,323)(325,326)(328,347)(329,346)(330,348)
(331,340)(332,342)(333,341)(334,344)(335,343)(336,345)(337,338)(350,351)
(352,353)(355,374)(356,373)(357,375)(358,367)(359,369)(360,368)(361,371)
(362,370)(363,372)(364,365)(377,378)(379,380)(382,401)(383,400)(384,402)
(385,394)(386,396)(387,395)(388,398)(389,397)(390,399)(391,392)(404,405)
(406,407)(409,428)(410,427)(411,429)(412,421)(413,423)(414,422)(415,425)
(416,424)(417,426)(418,419)(431,432)(433,542)(434,541)(435,543)(436,563)
(437,562)(438,564)(439,556)(440,558)(441,557)(442,560)(443,559)(444,561)
(445,554)(446,553)(447,555)(448,547)(449,549)(450,548)(451,551)(452,550)
(453,552)(454,545)(455,544)(456,546)(457,565)(458,567)(459,566)(460,569)
(461,568)(462,570)(463,590)(464,589)(465,591)(466,583)(467,585)(468,584)
(469,587)(470,586)(471,588)(472,581)(473,580)(474,582)(475,574)(476,576)
(477,575)(478,578)(479,577)(480,579)(481,572)(482,571)(483,573)(484,592)
(485,594)(486,593)(487,596)(488,595)(489,597)(490,617)(491,616)(492,618)
(493,610)(494,612)(495,611)(496,614)(497,613)(498,615)(499,608)(500,607)
(501,609)(502,601)(503,603)(504,602)(505,605)(506,604)(507,606)(508,599)
(509,598)(510,600)(511,619)(512,621)(513,620)(514,623)(515,622)(516,624)
(517,644)(518,643)(519,645)(520,637)(521,639)(522,638)(523,641)(524,640)
(525,642)(526,635)(527,634)(528,636)(529,628)(530,630)(531,629)(532,632)
(533,631)(534,633)(535,626)(536,625)(537,627)(538,646)(539,648)(540,647)
(649,785)(650,784)(651,786)(652,806)(653,805)(654,807)(655,799)(656,801)
(657,800)(658,803)(659,802)(660,804)(661,797)(662,796)(663,798)(664,790)
(665,792)(666,791)(667,794)(668,793)(669,795)(670,788)(671,787)(672,789)
(673,808)(674,810)(675,809)(676,758)(677,757)(678,759)(679,779)(680,778)
(681,780)(682,772)(683,774)(684,773)(685,776)(686,775)(687,777)(688,770)
(689,769)(690,771)(691,763)(692,765)(693,764)(694,767)(695,766)(696,768)
(697,761)(698,760)(699,762)(700,781)(701,783)(702,782)(703,839)(704,838)
(705,840)(706,860)(707,859)(708,861)(709,853)(710,855)(711,854)(712,857)
(713,856)(714,858)(715,851)(716,850)(717,852)(718,844)(719,846)(720,845)
(721,848)(722,847)(723,849)(724,842)(725,841)(726,843)(727,862)(728,864)
(729,863)(730,812)(731,811)(732,813)(733,833)(734,832)(735,834)(736,826)
(737,828)(738,827)(739,830)(740,829)(741,831)(742,824)(743,823)(744,825)
(745,817)(746,819)(747,818)(748,821)(749,820)(750,822)(751,815)(752,814)
(753,816)(754,835)(755,837)(756,836);;
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*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)(109,244)(110,245)(111,246)
(112,252)(113,250)(114,251)(115,248)(116,249)(117,247)(118,264)(119,262)
(120,263)(121,269)(122,270)(123,268)(124,265)(125,266)(126,267)(127,254)
(128,255)(129,253)(130,259)(131,260)(132,261)(133,258)(134,256)(135,257)
(136,217)(137,218)(138,219)(139,225)(140,223)(141,224)(142,221)(143,222)
(144,220)(145,237)(146,235)(147,236)(148,242)(149,243)(150,241)(151,238)
(152,239)(153,240)(154,227)(155,228)(156,226)(157,232)(158,233)(159,234)
(160,231)(161,229)(162,230)(163,298)(164,299)(165,300)(166,306)(167,304)
(168,305)(169,302)(170,303)(171,301)(172,318)(173,316)(174,317)(175,323)
(176,324)(177,322)(178,319)(179,320)(180,321)(181,308)(182,309)(183,307)
(184,313)(185,314)(186,315)(187,312)(188,310)(189,311)(190,271)(191,272)
(192,273)(193,279)(194,277)(195,278)(196,275)(197,276)(198,274)(199,291)
(200,289)(201,290)(202,296)(203,297)(204,295)(205,292)(206,293)(207,294)
(208,281)(209,282)(210,280)(211,286)(212,287)(213,288)(214,285)(215,283)
(216,284)(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)(541,676)(542,677)(543,678)
(544,684)(545,682)(546,683)(547,680)(548,681)(549,679)(550,696)(551,694)
(552,695)(553,701)(554,702)(555,700)(556,697)(557,698)(558,699)(559,686)
(560,687)(561,685)(562,691)(563,692)(564,693)(565,690)(566,688)(567,689)
(568,649)(569,650)(570,651)(571,657)(572,655)(573,656)(574,653)(575,654)
(576,652)(577,669)(578,667)(579,668)(580,674)(581,675)(582,673)(583,670)
(584,671)(585,672)(586,659)(587,660)(588,658)(589,664)(590,665)(591,666)
(592,663)(593,661)(594,662)(595,730)(596,731)(597,732)(598,738)(599,736)
(600,737)(601,734)(602,735)(603,733)(604,750)(605,748)(606,749)(607,755)
(608,756)(609,754)(610,751)(611,752)(612,753)(613,740)(614,741)(615,739)
(616,745)(617,746)(618,747)(619,744)(620,742)(621,743)(622,703)(623,704)
(624,705)(625,711)(626,709)(627,710)(628,707)(629,708)(630,706)(631,723)
(632,721)(633,722)(634,728)(635,729)(636,727)(637,724)(638,725)(639,726)
(640,713)(641,714)(642,712)(643,718)(644,719)(645,720)(646,717)(647,715)
(648,716);
s1 := Sym(864)!(  1,544)(  2,546)(  3,545)(  4,541)(  5,543)(  6,542)(  7,547)
(  8,549)(  9,548)( 10,558)( 11,557)( 12,556)( 13,555)( 14,554)( 15,553)
( 16,552)( 17,551)( 18,550)( 19,561)( 20,560)( 21,559)( 22,567)( 23,566)
( 24,565)( 25,564)( 26,563)( 27,562)( 28,571)( 29,573)( 30,572)( 31,568)
( 32,570)( 33,569)( 34,574)( 35,576)( 36,575)( 37,585)( 38,584)( 39,583)
( 40,582)( 41,581)( 42,580)( 43,579)( 44,578)( 45,577)( 46,588)( 47,587)
( 48,586)( 49,594)( 50,593)( 51,592)( 52,591)( 53,590)( 54,589)( 55,598)
( 56,600)( 57,599)( 58,595)( 59,597)( 60,596)( 61,601)( 62,603)( 63,602)
( 64,612)( 65,611)( 66,610)( 67,609)( 68,608)( 69,607)( 70,606)( 71,605)
( 72,604)( 73,615)( 74,614)( 75,613)( 76,621)( 77,620)( 78,619)( 79,618)
( 80,617)( 81,616)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)
( 88,628)( 89,630)( 90,629)( 91,639)( 92,638)( 93,637)( 94,636)( 95,635)
( 96,634)( 97,633)( 98,632)( 99,631)(100,642)(101,641)(102,640)(103,648)
(104,647)(105,646)(106,645)(107,644)(108,643)(109,436)(110,438)(111,437)
(112,433)(113,435)(114,434)(115,439)(116,441)(117,440)(118,450)(119,449)
(120,448)(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,453)
(128,452)(129,451)(130,459)(131,458)(132,457)(133,456)(134,455)(135,454)
(136,463)(137,465)(138,464)(139,460)(140,462)(141,461)(142,466)(143,468)
(144,467)(145,477)(146,476)(147,475)(148,474)(149,473)(150,472)(151,471)
(152,470)(153,469)(154,480)(155,479)(156,478)(157,486)(158,485)(159,484)
(160,483)(161,482)(162,481)(163,490)(164,492)(165,491)(166,487)(167,489)
(168,488)(169,493)(170,495)(171,494)(172,504)(173,503)(174,502)(175,501)
(176,500)(177,499)(178,498)(179,497)(180,496)(181,507)(182,506)(183,505)
(184,513)(185,512)(186,511)(187,510)(188,509)(189,508)(190,517)(191,519)
(192,518)(193,514)(194,516)(195,515)(196,520)(197,522)(198,521)(199,531)
(200,530)(201,529)(202,528)(203,527)(204,526)(205,525)(206,524)(207,523)
(208,534)(209,533)(210,532)(211,540)(212,539)(213,538)(214,537)(215,536)
(216,535)(217,814)(218,816)(219,815)(220,811)(221,813)(222,812)(223,817)
(224,819)(225,818)(226,828)(227,827)(228,826)(229,825)(230,824)(231,823)
(232,822)(233,821)(234,820)(235,831)(236,830)(237,829)(238,837)(239,836)
(240,835)(241,834)(242,833)(243,832)(244,841)(245,843)(246,842)(247,838)
(248,840)(249,839)(250,844)(251,846)(252,845)(253,855)(254,854)(255,853)
(256,852)(257,851)(258,850)(259,849)(260,848)(261,847)(262,858)(263,857)
(264,856)(265,864)(266,863)(267,862)(268,861)(269,860)(270,859)(271,760)
(272,762)(273,761)(274,757)(275,759)(276,758)(277,763)(278,765)(279,764)
(280,774)(281,773)(282,772)(283,771)(284,770)(285,769)(286,768)(287,767)
(288,766)(289,777)(290,776)(291,775)(292,783)(293,782)(294,781)(295,780)
(296,779)(297,778)(298,787)(299,789)(300,788)(301,784)(302,786)(303,785)
(304,790)(305,792)(306,791)(307,801)(308,800)(309,799)(310,798)(311,797)
(312,796)(313,795)(314,794)(315,793)(316,804)(317,803)(318,802)(319,810)
(320,809)(321,808)(322,807)(323,806)(324,805)(325,706)(326,708)(327,707)
(328,703)(329,705)(330,704)(331,709)(332,711)(333,710)(334,720)(335,719)
(336,718)(337,717)(338,716)(339,715)(340,714)(341,713)(342,712)(343,723)
(344,722)(345,721)(346,729)(347,728)(348,727)(349,726)(350,725)(351,724)
(352,733)(353,735)(354,734)(355,730)(356,732)(357,731)(358,736)(359,738)
(360,737)(361,747)(362,746)(363,745)(364,744)(365,743)(366,742)(367,741)
(368,740)(369,739)(370,750)(371,749)(372,748)(373,756)(374,755)(375,754)
(376,753)(377,752)(378,751)(379,652)(380,654)(381,653)(382,649)(383,651)
(384,650)(385,655)(386,657)(387,656)(388,666)(389,665)(390,664)(391,663)
(392,662)(393,661)(394,660)(395,659)(396,658)(397,669)(398,668)(399,667)
(400,675)(401,674)(402,673)(403,672)(404,671)(405,670)(406,679)(407,681)
(408,680)(409,676)(410,678)(411,677)(412,682)(413,684)(414,683)(415,693)
(416,692)(417,691)(418,690)(419,689)(420,688)(421,687)(422,686)(423,685)
(424,696)(425,695)(426,694)(427,702)(428,701)(429,700)(430,699)(431,698)
(432,697);
s2 := Sym(864)!(  1,  2)(  4, 23)(  5, 22)(  6, 24)(  7, 16)(  8, 18)(  9, 17)
( 10, 20)( 11, 19)( 12, 21)( 13, 14)( 26, 27)( 28, 29)( 31, 50)( 32, 49)
( 33, 51)( 34, 43)( 35, 45)( 36, 44)( 37, 47)( 38, 46)( 39, 48)( 40, 41)
( 53, 54)( 55, 56)( 58, 77)( 59, 76)( 60, 78)( 61, 70)( 62, 72)( 63, 71)
( 64, 74)( 65, 73)( 66, 75)( 67, 68)( 80, 81)( 82, 83)( 85,104)( 86,103)
( 87,105)( 88, 97)( 89, 99)( 90, 98)( 91,101)( 92,100)( 93,102)( 94, 95)
(107,108)(109,137)(110,136)(111,138)(112,158)(113,157)(114,159)(115,151)
(116,153)(117,152)(118,155)(119,154)(120,156)(121,149)(122,148)(123,150)
(124,142)(125,144)(126,143)(127,146)(128,145)(129,147)(130,140)(131,139)
(132,141)(133,160)(134,162)(135,161)(163,191)(164,190)(165,192)(166,212)
(167,211)(168,213)(169,205)(170,207)(171,206)(172,209)(173,208)(174,210)
(175,203)(176,202)(177,204)(178,196)(179,198)(180,197)(181,200)(182,199)
(183,201)(184,194)(185,193)(186,195)(187,214)(188,216)(189,215)(217,245)
(218,244)(219,246)(220,266)(221,265)(222,267)(223,259)(224,261)(225,260)
(226,263)(227,262)(228,264)(229,257)(230,256)(231,258)(232,250)(233,252)
(234,251)(235,254)(236,253)(237,255)(238,248)(239,247)(240,249)(241,268)
(242,270)(243,269)(271,299)(272,298)(273,300)(274,320)(275,319)(276,321)
(277,313)(278,315)(279,314)(280,317)(281,316)(282,318)(283,311)(284,310)
(285,312)(286,304)(287,306)(288,305)(289,308)(290,307)(291,309)(292,302)
(293,301)(294,303)(295,322)(296,324)(297,323)(325,326)(328,347)(329,346)
(330,348)(331,340)(332,342)(333,341)(334,344)(335,343)(336,345)(337,338)
(350,351)(352,353)(355,374)(356,373)(357,375)(358,367)(359,369)(360,368)
(361,371)(362,370)(363,372)(364,365)(377,378)(379,380)(382,401)(383,400)
(384,402)(385,394)(386,396)(387,395)(388,398)(389,397)(390,399)(391,392)
(404,405)(406,407)(409,428)(410,427)(411,429)(412,421)(413,423)(414,422)
(415,425)(416,424)(417,426)(418,419)(431,432)(433,542)(434,541)(435,543)
(436,563)(437,562)(438,564)(439,556)(440,558)(441,557)(442,560)(443,559)
(444,561)(445,554)(446,553)(447,555)(448,547)(449,549)(450,548)(451,551)
(452,550)(453,552)(454,545)(455,544)(456,546)(457,565)(458,567)(459,566)
(460,569)(461,568)(462,570)(463,590)(464,589)(465,591)(466,583)(467,585)
(468,584)(469,587)(470,586)(471,588)(472,581)(473,580)(474,582)(475,574)
(476,576)(477,575)(478,578)(479,577)(480,579)(481,572)(482,571)(483,573)
(484,592)(485,594)(486,593)(487,596)(488,595)(489,597)(490,617)(491,616)
(492,618)(493,610)(494,612)(495,611)(496,614)(497,613)(498,615)(499,608)
(500,607)(501,609)(502,601)(503,603)(504,602)(505,605)(506,604)(507,606)
(508,599)(509,598)(510,600)(511,619)(512,621)(513,620)(514,623)(515,622)
(516,624)(517,644)(518,643)(519,645)(520,637)(521,639)(522,638)(523,641)
(524,640)(525,642)(526,635)(527,634)(528,636)(529,628)(530,630)(531,629)
(532,632)(533,631)(534,633)(535,626)(536,625)(537,627)(538,646)(539,648)
(540,647)(649,785)(650,784)(651,786)(652,806)(653,805)(654,807)(655,799)
(656,801)(657,800)(658,803)(659,802)(660,804)(661,797)(662,796)(663,798)
(664,790)(665,792)(666,791)(667,794)(668,793)(669,795)(670,788)(671,787)
(672,789)(673,808)(674,810)(675,809)(676,758)(677,757)(678,759)(679,779)
(680,778)(681,780)(682,772)(683,774)(684,773)(685,776)(686,775)(687,777)
(688,770)(689,769)(690,771)(691,763)(692,765)(693,764)(694,767)(695,766)
(696,768)(697,761)(698,760)(699,762)(700,781)(701,783)(702,782)(703,839)
(704,838)(705,840)(706,860)(707,859)(708,861)(709,853)(710,855)(711,854)
(712,857)(713,856)(714,858)(715,851)(716,850)(717,852)(718,844)(719,846)
(720,845)(721,848)(722,847)(723,849)(724,842)(725,841)(726,843)(727,862)
(728,864)(729,863)(730,812)(731,811)(732,813)(733,833)(734,832)(735,834)
(736,826)(737,828)(738,827)(739,830)(740,829)(741,831)(742,824)(743,823)
(744,825)(745,817)(746,819)(747,818)(748,821)(749,820)(750,822)(751,815)
(752,814)(753,816)(754,835)(755,837)(756,836);
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope