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Polytope of Type {24,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1728u
if this polytope has a name.
Group : SmallGroup(1728,33554)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 72, 432, 36
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {24,6}*864h, {12,12}*864k
   3-fold quotients : {8,12}*576a
   4-fold quotients : {12,6}*432i
   6-fold quotients : {8,6}*288, {4,12}*288
   8-fold quotients : {12,6}*216c
   9-fold quotients : {24,4}*192a
   12-fold quotients : {4,6}*144
   18-fold quotients : {12,4}*96a, {24,2}*96
   24-fold quotients : {4,6}*72
   27-fold quotients : {8,4}*64a
   36-fold quotients : {12,2}*48, {6,4}*48a
   54-fold quotients : {4,4}*32, {8,2}*32
   72-fold quotients : {6,2}*24
   108-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {3,2}*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)( 10, 19)( 11, 26)( 12, 24)( 13, 25)( 14, 23)
( 15, 21)( 16, 22)( 17, 20)( 18, 27)( 29, 35)( 30, 33)( 31, 34)( 37, 46)
( 38, 53)( 39, 51)( 40, 52)( 41, 50)( 42, 48)( 43, 49)( 44, 47)( 45, 54)
( 56, 62)( 57, 60)( 58, 61)( 64, 73)( 65, 80)( 66, 78)( 67, 79)( 68, 77)
( 69, 75)( 70, 76)( 71, 74)( 72, 81)( 83, 89)( 84, 87)( 85, 88)( 91,100)
( 92,107)( 93,105)( 94,106)( 95,104)( 96,102)( 97,103)( 98,101)( 99,108)
(109,136)(110,143)(111,141)(112,142)(113,140)(114,138)(115,139)(116,137)
(117,144)(118,154)(119,161)(120,159)(121,160)(122,158)(123,156)(124,157)
(125,155)(126,162)(127,145)(128,152)(129,150)(130,151)(131,149)(132,147)
(133,148)(134,146)(135,153)(163,190)(164,197)(165,195)(166,196)(167,194)
(168,192)(169,193)(170,191)(171,198)(172,208)(173,215)(174,213)(175,214)
(176,212)(177,210)(178,211)(179,209)(180,216)(181,199)(182,206)(183,204)
(184,205)(185,203)(186,201)(187,202)(188,200)(189,207)(217,244)(218,251)
(219,249)(220,250)(221,248)(222,246)(223,247)(224,245)(225,252)(226,262)
(227,269)(228,267)(229,268)(230,266)(231,264)(232,265)(233,263)(234,270)
(235,253)(236,260)(237,258)(238,259)(239,257)(240,255)(241,256)(242,254)
(243,261)(271,298)(272,305)(273,303)(274,304)(275,302)(276,300)(277,301)
(278,299)(279,306)(280,316)(281,323)(282,321)(283,322)(284,320)(285,318)
(286,319)(287,317)(288,324)(289,307)(290,314)(291,312)(292,313)(293,311)
(294,309)(295,310)(296,308)(297,315)(326,332)(327,330)(328,331)(334,343)
(335,350)(336,348)(337,349)(338,347)(339,345)(340,346)(341,344)(342,351)
(353,359)(354,357)(355,358)(361,370)(362,377)(363,375)(364,376)(365,374)
(366,372)(367,373)(368,371)(369,378)(380,386)(381,384)(382,385)(388,397)
(389,404)(390,402)(391,403)(392,401)(393,399)(394,400)(395,398)(396,405)
(407,413)(408,411)(409,412)(415,424)(416,431)(417,429)(418,430)(419,428)
(420,426)(421,427)(422,425)(423,432)(433,541)(434,548)(435,546)(436,547)
(437,545)(438,543)(439,544)(440,542)(441,549)(442,559)(443,566)(444,564)
(445,565)(446,563)(447,561)(448,562)(449,560)(450,567)(451,550)(452,557)
(453,555)(454,556)(455,554)(456,552)(457,553)(458,551)(459,558)(460,568)
(461,575)(462,573)(463,574)(464,572)(465,570)(466,571)(467,569)(468,576)
(469,586)(470,593)(471,591)(472,592)(473,590)(474,588)(475,589)(476,587)
(477,594)(478,577)(479,584)(480,582)(481,583)(482,581)(483,579)(484,580)
(485,578)(486,585)(487,595)(488,602)(489,600)(490,601)(491,599)(492,597)
(493,598)(494,596)(495,603)(496,613)(497,620)(498,618)(499,619)(500,617)
(501,615)(502,616)(503,614)(504,621)(505,604)(506,611)(507,609)(508,610)
(509,608)(510,606)(511,607)(512,605)(513,612)(514,622)(515,629)(516,627)
(517,628)(518,626)(519,624)(520,625)(521,623)(522,630)(523,640)(524,647)
(525,645)(526,646)(527,644)(528,642)(529,643)(530,641)(531,648)(532,631)
(533,638)(534,636)(535,637)(536,635)(537,633)(538,634)(539,632)(540,639)
(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)(656,785)
(657,792)(658,802)(659,809)(660,807)(661,808)(662,806)(663,804)(664,805)
(665,803)(666,810)(667,793)(668,800)(669,798)(670,799)(671,797)(672,795)
(673,796)(674,794)(675,801)(676,757)(677,764)(678,762)(679,763)(680,761)
(681,759)(682,760)(683,758)(684,765)(685,775)(686,782)(687,780)(688,781)
(689,779)(690,777)(691,778)(692,776)(693,783)(694,766)(695,773)(696,771)
(697,772)(698,770)(699,768)(700,769)(701,767)(702,774)(703,838)(704,845)
(705,843)(706,844)(707,842)(708,840)(709,841)(710,839)(711,846)(712,856)
(713,863)(714,861)(715,862)(716,860)(717,858)(718,859)(719,857)(720,864)
(721,847)(722,854)(723,852)(724,853)(725,851)(726,849)(727,850)(728,848)
(729,855)(730,811)(731,818)(732,816)(733,817)(734,815)(735,813)(736,814)
(737,812)(738,819)(739,829)(740,836)(741,834)(742,835)(743,833)(744,831)
(745,832)(746,830)(747,837)(748,820)(749,827)(750,825)(751,826)(752,824)
(753,822)(754,823)(755,821)(756,828);;
s1 := (  1,442)(  2,443)(  3,444)(  4,450)(  5,448)(  6,449)(  7,446)(  8,447)
(  9,445)( 10,433)( 11,434)( 12,435)( 13,441)( 14,439)( 15,440)( 16,437)
( 17,438)( 18,436)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)
( 25,455)( 26,456)( 27,454)( 28,469)( 29,470)( 30,471)( 31,477)( 32,475)
( 33,476)( 34,473)( 35,474)( 36,472)( 37,460)( 38,461)( 39,462)( 40,468)
( 41,466)( 42,467)( 43,464)( 44,465)( 45,463)( 46,478)( 47,479)( 48,480)
( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,496)( 56,497)
( 57,498)( 58,504)( 59,502)( 60,503)( 61,500)( 62,501)( 63,499)( 64,487)
( 65,488)( 66,489)( 67,495)( 68,493)( 69,494)( 70,491)( 71,492)( 72,490)
( 73,505)( 74,506)( 75,507)( 76,513)( 77,511)( 78,512)( 79,509)( 80,510)
( 81,508)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)( 88,527)
( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)( 96,521)
( 97,518)( 98,519)( 99,517)(100,532)(101,533)(102,534)(103,540)(104,538)
(105,539)(106,536)(107,537)(108,535)(109,577)(110,578)(111,579)(112,585)
(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)(120,570)
(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)(128,587)
(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)(136,550)
(137,551)(138,552)(139,558)(140,556)(141,557)(142,554)(143,555)(144,553)
(145,541)(146,542)(147,543)(148,549)(149,547)(150,548)(151,545)(152,546)
(153,544)(154,559)(155,560)(156,561)(157,567)(158,565)(159,566)(160,563)
(161,564)(162,562)(163,631)(164,632)(165,633)(166,639)(167,637)(168,638)
(169,635)(170,636)(171,634)(172,622)(173,623)(174,624)(175,630)(176,628)
(177,629)(178,626)(179,627)(180,625)(181,640)(182,641)(183,642)(184,648)
(185,646)(186,647)(187,644)(188,645)(189,643)(190,604)(191,605)(192,606)
(193,612)(194,610)(195,611)(196,608)(197,609)(198,607)(199,595)(200,596)
(201,597)(202,603)(203,601)(204,602)(205,599)(206,600)(207,598)(208,613)
(209,614)(210,615)(211,621)(212,619)(213,620)(214,617)(215,618)(216,616)
(217,712)(218,713)(219,714)(220,720)(221,718)(222,719)(223,716)(224,717)
(225,715)(226,703)(227,704)(228,705)(229,711)(230,709)(231,710)(232,707)
(233,708)(234,706)(235,721)(236,722)(237,723)(238,729)(239,727)(240,728)
(241,725)(242,726)(243,724)(244,739)(245,740)(246,741)(247,747)(248,745)
(249,746)(250,743)(251,744)(252,742)(253,730)(254,731)(255,732)(256,738)
(257,736)(258,737)(259,734)(260,735)(261,733)(262,748)(263,749)(264,750)
(265,756)(266,754)(267,755)(268,752)(269,753)(270,751)(271,658)(272,659)
(273,660)(274,666)(275,664)(276,665)(277,662)(278,663)(279,661)(280,649)
(281,650)(282,651)(283,657)(284,655)(285,656)(286,653)(287,654)(288,652)
(289,667)(290,668)(291,669)(292,675)(293,673)(294,674)(295,671)(296,672)
(297,670)(298,685)(299,686)(300,687)(301,693)(302,691)(303,692)(304,689)
(305,690)(306,688)(307,676)(308,677)(309,678)(310,684)(311,682)(312,683)
(313,680)(314,681)(315,679)(316,694)(317,695)(318,696)(319,702)(320,700)
(321,701)(322,698)(323,699)(324,697)(325,847)(326,848)(327,849)(328,855)
(329,853)(330,854)(331,851)(332,852)(333,850)(334,838)(335,839)(336,840)
(337,846)(338,844)(339,845)(340,842)(341,843)(342,841)(343,856)(344,857)
(345,858)(346,864)(347,862)(348,863)(349,860)(350,861)(351,859)(352,820)
(353,821)(354,822)(355,828)(356,826)(357,827)(358,824)(359,825)(360,823)
(361,811)(362,812)(363,813)(364,819)(365,817)(366,818)(367,815)(368,816)
(369,814)(370,829)(371,830)(372,831)(373,837)(374,835)(375,836)(376,833)
(377,834)(378,832)(379,793)(380,794)(381,795)(382,801)(383,799)(384,800)
(385,797)(386,798)(387,796)(388,784)(389,785)(390,786)(391,792)(392,790)
(393,791)(394,788)(395,789)(396,787)(397,802)(398,803)(399,804)(400,810)
(401,808)(402,809)(403,806)(404,807)(405,805)(406,766)(407,767)(408,768)
(409,774)(410,772)(411,773)(412,770)(413,771)(414,769)(415,757)(416,758)
(417,759)(418,765)(419,763)(420,764)(421,761)(422,762)(423,760)(424,775)
(425,776)(426,777)(427,783)(428,781)(429,782)(430,779)(431,780)(432,778);;
s2 := (  1,329)(  2,328)(  3,330)(  4,326)(  5,325)(  6,327)(  7,332)(  8,331)
(  9,333)( 10,338)( 11,337)( 12,339)( 13,335)( 14,334)( 15,336)( 16,341)
( 17,340)( 18,342)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)( 24,345)
( 25,350)( 26,349)( 27,351)( 28,356)( 29,355)( 30,357)( 31,353)( 32,352)
( 33,354)( 34,359)( 35,358)( 36,360)( 37,365)( 38,364)( 39,366)( 40,362)
( 41,361)( 42,363)( 43,368)( 44,367)( 45,369)( 46,374)( 47,373)( 48,375)
( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,383)( 56,382)
( 57,384)( 58,380)( 59,379)( 60,381)( 61,386)( 62,385)( 63,387)( 64,392)
( 65,391)( 66,393)( 67,389)( 68,388)( 69,390)( 70,395)( 71,394)( 72,396)
( 73,401)( 74,400)( 75,402)( 76,398)( 77,397)( 78,399)( 79,404)( 80,403)
( 81,405)( 82,410)( 83,409)( 84,411)( 85,407)( 86,406)( 87,408)( 88,413)
( 89,412)( 90,414)( 91,419)( 92,418)( 93,420)( 94,416)( 95,415)( 96,417)
( 97,422)( 98,421)( 99,423)(100,428)(101,427)(102,429)(103,425)(104,424)
(105,426)(106,431)(107,430)(108,432)(109,248)(110,247)(111,249)(112,245)
(113,244)(114,246)(115,251)(116,250)(117,252)(118,257)(119,256)(120,258)
(121,254)(122,253)(123,255)(124,260)(125,259)(126,261)(127,266)(128,265)
(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)(136,221)
(137,220)(138,222)(139,218)(140,217)(141,219)(142,224)(143,223)(144,225)
(145,230)(146,229)(147,231)(148,227)(149,226)(150,228)(151,233)(152,232)
(153,234)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)(160,242)
(161,241)(162,243)(163,302)(164,301)(165,303)(166,299)(167,298)(168,300)
(169,305)(170,304)(171,306)(172,311)(173,310)(174,312)(175,308)(176,307)
(177,309)(178,314)(179,313)(180,315)(181,320)(182,319)(183,321)(184,317)
(185,316)(186,318)(187,323)(188,322)(189,324)(190,275)(191,274)(192,276)
(193,272)(194,271)(195,273)(196,278)(197,277)(198,279)(199,284)(200,283)
(201,285)(202,281)(203,280)(204,282)(205,287)(206,286)(207,288)(208,293)
(209,292)(210,294)(211,290)(212,289)(213,291)(214,296)(215,295)(216,297)
(433,761)(434,760)(435,762)(436,758)(437,757)(438,759)(439,764)(440,763)
(441,765)(442,770)(443,769)(444,771)(445,767)(446,766)(447,768)(448,773)
(449,772)(450,774)(451,779)(452,778)(453,780)(454,776)(455,775)(456,777)
(457,782)(458,781)(459,783)(460,788)(461,787)(462,789)(463,785)(464,784)
(465,786)(466,791)(467,790)(468,792)(469,797)(470,796)(471,798)(472,794)
(473,793)(474,795)(475,800)(476,799)(477,801)(478,806)(479,805)(480,807)
(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,815)(488,814)
(489,816)(490,812)(491,811)(492,813)(493,818)(494,817)(495,819)(496,824)
(497,823)(498,825)(499,821)(500,820)(501,822)(502,827)(503,826)(504,828)
(505,833)(506,832)(507,834)(508,830)(509,829)(510,831)(511,836)(512,835)
(513,837)(514,842)(515,841)(516,843)(517,839)(518,838)(519,840)(520,845)
(521,844)(522,846)(523,851)(524,850)(525,852)(526,848)(527,847)(528,849)
(529,854)(530,853)(531,855)(532,860)(533,859)(534,861)(535,857)(536,856)
(537,858)(538,863)(539,862)(540,864)(541,680)(542,679)(543,681)(544,677)
(545,676)(546,678)(547,683)(548,682)(549,684)(550,689)(551,688)(552,690)
(553,686)(554,685)(555,687)(556,692)(557,691)(558,693)(559,698)(560,697)
(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)(568,653)
(569,652)(570,654)(571,650)(572,649)(573,651)(574,656)(575,655)(576,657)
(577,662)(578,661)(579,663)(580,659)(581,658)(582,660)(583,665)(584,664)
(585,666)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)(592,674)
(593,673)(594,675)(595,734)(596,733)(597,735)(598,731)(599,730)(600,732)
(601,737)(602,736)(603,738)(604,743)(605,742)(606,744)(607,740)(608,739)
(609,741)(610,746)(611,745)(612,747)(613,752)(614,751)(615,753)(616,749)
(617,748)(618,750)(619,755)(620,754)(621,756)(622,707)(623,706)(624,708)
(625,704)(626,703)(627,705)(628,710)(629,709)(630,711)(631,716)(632,715)
(633,717)(634,713)(635,712)(636,714)(637,719)(638,718)(639,720)(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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(864)!(  2,  8)(  3,  6)(  4,  7)( 10, 19)( 11, 26)( 12, 24)( 13, 25)
( 14, 23)( 15, 21)( 16, 22)( 17, 20)( 18, 27)( 29, 35)( 30, 33)( 31, 34)
( 37, 46)( 38, 53)( 39, 51)( 40, 52)( 41, 50)( 42, 48)( 43, 49)( 44, 47)
( 45, 54)( 56, 62)( 57, 60)( 58, 61)( 64, 73)( 65, 80)( 66, 78)( 67, 79)
( 68, 77)( 69, 75)( 70, 76)( 71, 74)( 72, 81)( 83, 89)( 84, 87)( 85, 88)
( 91,100)( 92,107)( 93,105)( 94,106)( 95,104)( 96,102)( 97,103)( 98,101)
( 99,108)(109,136)(110,143)(111,141)(112,142)(113,140)(114,138)(115,139)
(116,137)(117,144)(118,154)(119,161)(120,159)(121,160)(122,158)(123,156)
(124,157)(125,155)(126,162)(127,145)(128,152)(129,150)(130,151)(131,149)
(132,147)(133,148)(134,146)(135,153)(163,190)(164,197)(165,195)(166,196)
(167,194)(168,192)(169,193)(170,191)(171,198)(172,208)(173,215)(174,213)
(175,214)(176,212)(177,210)(178,211)(179,209)(180,216)(181,199)(182,206)
(183,204)(184,205)(185,203)(186,201)(187,202)(188,200)(189,207)(217,244)
(218,251)(219,249)(220,250)(221,248)(222,246)(223,247)(224,245)(225,252)
(226,262)(227,269)(228,267)(229,268)(230,266)(231,264)(232,265)(233,263)
(234,270)(235,253)(236,260)(237,258)(238,259)(239,257)(240,255)(241,256)
(242,254)(243,261)(271,298)(272,305)(273,303)(274,304)(275,302)(276,300)
(277,301)(278,299)(279,306)(280,316)(281,323)(282,321)(283,322)(284,320)
(285,318)(286,319)(287,317)(288,324)(289,307)(290,314)(291,312)(292,313)
(293,311)(294,309)(295,310)(296,308)(297,315)(326,332)(327,330)(328,331)
(334,343)(335,350)(336,348)(337,349)(338,347)(339,345)(340,346)(341,344)
(342,351)(353,359)(354,357)(355,358)(361,370)(362,377)(363,375)(364,376)
(365,374)(366,372)(367,373)(368,371)(369,378)(380,386)(381,384)(382,385)
(388,397)(389,404)(390,402)(391,403)(392,401)(393,399)(394,400)(395,398)
(396,405)(407,413)(408,411)(409,412)(415,424)(416,431)(417,429)(418,430)
(419,428)(420,426)(421,427)(422,425)(423,432)(433,541)(434,548)(435,546)
(436,547)(437,545)(438,543)(439,544)(440,542)(441,549)(442,559)(443,566)
(444,564)(445,565)(446,563)(447,561)(448,562)(449,560)(450,567)(451,550)
(452,557)(453,555)(454,556)(455,554)(456,552)(457,553)(458,551)(459,558)
(460,568)(461,575)(462,573)(463,574)(464,572)(465,570)(466,571)(467,569)
(468,576)(469,586)(470,593)(471,591)(472,592)(473,590)(474,588)(475,589)
(476,587)(477,594)(478,577)(479,584)(480,582)(481,583)(482,581)(483,579)
(484,580)(485,578)(486,585)(487,595)(488,602)(489,600)(490,601)(491,599)
(492,597)(493,598)(494,596)(495,603)(496,613)(497,620)(498,618)(499,619)
(500,617)(501,615)(502,616)(503,614)(504,621)(505,604)(506,611)(507,609)
(508,610)(509,608)(510,606)(511,607)(512,605)(513,612)(514,622)(515,629)
(516,627)(517,628)(518,626)(519,624)(520,625)(521,623)(522,630)(523,640)
(524,647)(525,645)(526,646)(527,644)(528,642)(529,643)(530,641)(531,648)
(532,631)(533,638)(534,636)(535,637)(536,635)(537,633)(538,634)(539,632)
(540,639)(649,784)(650,791)(651,789)(652,790)(653,788)(654,786)(655,787)
(656,785)(657,792)(658,802)(659,809)(660,807)(661,808)(662,806)(663,804)
(664,805)(665,803)(666,810)(667,793)(668,800)(669,798)(670,799)(671,797)
(672,795)(673,796)(674,794)(675,801)(676,757)(677,764)(678,762)(679,763)
(680,761)(681,759)(682,760)(683,758)(684,765)(685,775)(686,782)(687,780)
(688,781)(689,779)(690,777)(691,778)(692,776)(693,783)(694,766)(695,773)
(696,771)(697,772)(698,770)(699,768)(700,769)(701,767)(702,774)(703,838)
(704,845)(705,843)(706,844)(707,842)(708,840)(709,841)(710,839)(711,846)
(712,856)(713,863)(714,861)(715,862)(716,860)(717,858)(718,859)(719,857)
(720,864)(721,847)(722,854)(723,852)(724,853)(725,851)(726,849)(727,850)
(728,848)(729,855)(730,811)(731,818)(732,816)(733,817)(734,815)(735,813)
(736,814)(737,812)(738,819)(739,829)(740,836)(741,834)(742,835)(743,833)
(744,831)(745,832)(746,830)(747,837)(748,820)(749,827)(750,825)(751,826)
(752,824)(753,822)(754,823)(755,821)(756,828);
s1 := Sym(864)!(  1,442)(  2,443)(  3,444)(  4,450)(  5,448)(  6,449)(  7,446)
(  8,447)(  9,445)( 10,433)( 11,434)( 12,435)( 13,441)( 14,439)( 15,440)
( 16,437)( 17,438)( 18,436)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)
( 24,458)( 25,455)( 26,456)( 27,454)( 28,469)( 29,470)( 30,471)( 31,477)
( 32,475)( 33,476)( 34,473)( 35,474)( 36,472)( 37,460)( 38,461)( 39,462)
( 40,468)( 41,466)( 42,467)( 43,464)( 44,465)( 45,463)( 46,478)( 47,479)
( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,496)
( 56,497)( 57,498)( 58,504)( 59,502)( 60,503)( 61,500)( 62,501)( 63,499)
( 64,487)( 65,488)( 66,489)( 67,495)( 68,493)( 69,494)( 70,491)( 71,492)
( 72,490)( 73,505)( 74,506)( 75,507)( 76,513)( 77,511)( 78,512)( 79,509)
( 80,510)( 81,508)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)
( 88,527)( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)
( 96,521)( 97,518)( 98,519)( 99,517)(100,532)(101,533)(102,534)(103,540)
(104,538)(105,539)(106,536)(107,537)(108,535)(109,577)(110,578)(111,579)
(112,585)(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)
(120,570)(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)
(128,587)(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)
(136,550)(137,551)(138,552)(139,558)(140,556)(141,557)(142,554)(143,555)
(144,553)(145,541)(146,542)(147,543)(148,549)(149,547)(150,548)(151,545)
(152,546)(153,544)(154,559)(155,560)(156,561)(157,567)(158,565)(159,566)
(160,563)(161,564)(162,562)(163,631)(164,632)(165,633)(166,639)(167,637)
(168,638)(169,635)(170,636)(171,634)(172,622)(173,623)(174,624)(175,630)
(176,628)(177,629)(178,626)(179,627)(180,625)(181,640)(182,641)(183,642)
(184,648)(185,646)(186,647)(187,644)(188,645)(189,643)(190,604)(191,605)
(192,606)(193,612)(194,610)(195,611)(196,608)(197,609)(198,607)(199,595)
(200,596)(201,597)(202,603)(203,601)(204,602)(205,599)(206,600)(207,598)
(208,613)(209,614)(210,615)(211,621)(212,619)(213,620)(214,617)(215,618)
(216,616)(217,712)(218,713)(219,714)(220,720)(221,718)(222,719)(223,716)
(224,717)(225,715)(226,703)(227,704)(228,705)(229,711)(230,709)(231,710)
(232,707)(233,708)(234,706)(235,721)(236,722)(237,723)(238,729)(239,727)
(240,728)(241,725)(242,726)(243,724)(244,739)(245,740)(246,741)(247,747)
(248,745)(249,746)(250,743)(251,744)(252,742)(253,730)(254,731)(255,732)
(256,738)(257,736)(258,737)(259,734)(260,735)(261,733)(262,748)(263,749)
(264,750)(265,756)(266,754)(267,755)(268,752)(269,753)(270,751)(271,658)
(272,659)(273,660)(274,666)(275,664)(276,665)(277,662)(278,663)(279,661)
(280,649)(281,650)(282,651)(283,657)(284,655)(285,656)(286,653)(287,654)
(288,652)(289,667)(290,668)(291,669)(292,675)(293,673)(294,674)(295,671)
(296,672)(297,670)(298,685)(299,686)(300,687)(301,693)(302,691)(303,692)
(304,689)(305,690)(306,688)(307,676)(308,677)(309,678)(310,684)(311,682)
(312,683)(313,680)(314,681)(315,679)(316,694)(317,695)(318,696)(319,702)
(320,700)(321,701)(322,698)(323,699)(324,697)(325,847)(326,848)(327,849)
(328,855)(329,853)(330,854)(331,851)(332,852)(333,850)(334,838)(335,839)
(336,840)(337,846)(338,844)(339,845)(340,842)(341,843)(342,841)(343,856)
(344,857)(345,858)(346,864)(347,862)(348,863)(349,860)(350,861)(351,859)
(352,820)(353,821)(354,822)(355,828)(356,826)(357,827)(358,824)(359,825)
(360,823)(361,811)(362,812)(363,813)(364,819)(365,817)(366,818)(367,815)
(368,816)(369,814)(370,829)(371,830)(372,831)(373,837)(374,835)(375,836)
(376,833)(377,834)(378,832)(379,793)(380,794)(381,795)(382,801)(383,799)
(384,800)(385,797)(386,798)(387,796)(388,784)(389,785)(390,786)(391,792)
(392,790)(393,791)(394,788)(395,789)(396,787)(397,802)(398,803)(399,804)
(400,810)(401,808)(402,809)(403,806)(404,807)(405,805)(406,766)(407,767)
(408,768)(409,774)(410,772)(411,773)(412,770)(413,771)(414,769)(415,757)
(416,758)(417,759)(418,765)(419,763)(420,764)(421,761)(422,762)(423,760)
(424,775)(425,776)(426,777)(427,783)(428,781)(429,782)(430,779)(431,780)
(432,778);
s2 := Sym(864)!(  1,329)(  2,328)(  3,330)(  4,326)(  5,325)(  6,327)(  7,332)
(  8,331)(  9,333)( 10,338)( 11,337)( 12,339)( 13,335)( 14,334)( 15,336)
( 16,341)( 17,340)( 18,342)( 19,347)( 20,346)( 21,348)( 22,344)( 23,343)
( 24,345)( 25,350)( 26,349)( 27,351)( 28,356)( 29,355)( 30,357)( 31,353)
( 32,352)( 33,354)( 34,359)( 35,358)( 36,360)( 37,365)( 38,364)( 39,366)
( 40,362)( 41,361)( 42,363)( 43,368)( 44,367)( 45,369)( 46,374)( 47,373)
( 48,375)( 49,371)( 50,370)( 51,372)( 52,377)( 53,376)( 54,378)( 55,383)
( 56,382)( 57,384)( 58,380)( 59,379)( 60,381)( 61,386)( 62,385)( 63,387)
( 64,392)( 65,391)( 66,393)( 67,389)( 68,388)( 69,390)( 70,395)( 71,394)
( 72,396)( 73,401)( 74,400)( 75,402)( 76,398)( 77,397)( 78,399)( 79,404)
( 80,403)( 81,405)( 82,410)( 83,409)( 84,411)( 85,407)( 86,406)( 87,408)
( 88,413)( 89,412)( 90,414)( 91,419)( 92,418)( 93,420)( 94,416)( 95,415)
( 96,417)( 97,422)( 98,421)( 99,423)(100,428)(101,427)(102,429)(103,425)
(104,424)(105,426)(106,431)(107,430)(108,432)(109,248)(110,247)(111,249)
(112,245)(113,244)(114,246)(115,251)(116,250)(117,252)(118,257)(119,256)
(120,258)(121,254)(122,253)(123,255)(124,260)(125,259)(126,261)(127,266)
(128,265)(129,267)(130,263)(131,262)(132,264)(133,269)(134,268)(135,270)
(136,221)(137,220)(138,222)(139,218)(140,217)(141,219)(142,224)(143,223)
(144,225)(145,230)(146,229)(147,231)(148,227)(149,226)(150,228)(151,233)
(152,232)(153,234)(154,239)(155,238)(156,240)(157,236)(158,235)(159,237)
(160,242)(161,241)(162,243)(163,302)(164,301)(165,303)(166,299)(167,298)
(168,300)(169,305)(170,304)(171,306)(172,311)(173,310)(174,312)(175,308)
(176,307)(177,309)(178,314)(179,313)(180,315)(181,320)(182,319)(183,321)
(184,317)(185,316)(186,318)(187,323)(188,322)(189,324)(190,275)(191,274)
(192,276)(193,272)(194,271)(195,273)(196,278)(197,277)(198,279)(199,284)
(200,283)(201,285)(202,281)(203,280)(204,282)(205,287)(206,286)(207,288)
(208,293)(209,292)(210,294)(211,290)(212,289)(213,291)(214,296)(215,295)
(216,297)(433,761)(434,760)(435,762)(436,758)(437,757)(438,759)(439,764)
(440,763)(441,765)(442,770)(443,769)(444,771)(445,767)(446,766)(447,768)
(448,773)(449,772)(450,774)(451,779)(452,778)(453,780)(454,776)(455,775)
(456,777)(457,782)(458,781)(459,783)(460,788)(461,787)(462,789)(463,785)
(464,784)(465,786)(466,791)(467,790)(468,792)(469,797)(470,796)(471,798)
(472,794)(473,793)(474,795)(475,800)(476,799)(477,801)(478,806)(479,805)
(480,807)(481,803)(482,802)(483,804)(484,809)(485,808)(486,810)(487,815)
(488,814)(489,816)(490,812)(491,811)(492,813)(493,818)(494,817)(495,819)
(496,824)(497,823)(498,825)(499,821)(500,820)(501,822)(502,827)(503,826)
(504,828)(505,833)(506,832)(507,834)(508,830)(509,829)(510,831)(511,836)
(512,835)(513,837)(514,842)(515,841)(516,843)(517,839)(518,838)(519,840)
(520,845)(521,844)(522,846)(523,851)(524,850)(525,852)(526,848)(527,847)
(528,849)(529,854)(530,853)(531,855)(532,860)(533,859)(534,861)(535,857)
(536,856)(537,858)(538,863)(539,862)(540,864)(541,680)(542,679)(543,681)
(544,677)(545,676)(546,678)(547,683)(548,682)(549,684)(550,689)(551,688)
(552,690)(553,686)(554,685)(555,687)(556,692)(557,691)(558,693)(559,698)
(560,697)(561,699)(562,695)(563,694)(564,696)(565,701)(566,700)(567,702)
(568,653)(569,652)(570,654)(571,650)(572,649)(573,651)(574,656)(575,655)
(576,657)(577,662)(578,661)(579,663)(580,659)(581,658)(582,660)(583,665)
(584,664)(585,666)(586,671)(587,670)(588,672)(589,668)(590,667)(591,669)
(592,674)(593,673)(594,675)(595,734)(596,733)(597,735)(598,731)(599,730)
(600,732)(601,737)(602,736)(603,738)(604,743)(605,742)(606,744)(607,740)
(608,739)(609,741)(610,746)(611,745)(612,747)(613,752)(614,751)(615,753)
(616,749)(617,748)(618,750)(619,755)(620,754)(621,756)(622,707)(623,706)
(624,708)(625,704)(626,703)(627,705)(628,710)(629,709)(630,711)(631,716)
(632,715)(633,717)(634,713)(635,712)(636,714)(637,719)(638,718)(639,720)
(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*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope