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# Polytope of Type {6,48}

Atlas Canonical Name : {6,48}*1728e
if this polytope has a name.
Group : SmallGroup(1728,12518)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 18, 432, 144
Order of s0s1s2 : 16
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}*864e
3-fold quotients : {6,16}*576
4-fold quotients : {6,12}*432f
6-fold quotients : {6,8}*288
8-fold quotients : {6,12}*216b
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {2,16}*64
54-fold quotients : {2,8}*32
108-fold quotients : {2,4}*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)(109,298)(110,299)(111,300)(112,306)
(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)(120,317)
(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)(128,309)
(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)(136,271)
(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)(144,274)
(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)(152,293)
(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)(160,285)
(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)(168,224)
(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)(176,243)
(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)(184,232)
(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)(192,246)
(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)(200,262)
(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)(208,254)
(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)(216,257)
(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)(541,730)(542,731)(543,732)(544,738)
(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)(552,749)
(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)(560,741)
(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)(568,703)
(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)(576,706)
(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)(584,725)
(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)(592,717)
(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)(600,656)
(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)(608,675)
(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)(616,664)
(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)(624,678)
(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)(632,694)
(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)(640,686)
(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)(648,689);;
s1 := (  1, 10)(  2, 12)(  3, 11)(  4,  5)(  7, 26)(  8, 25)(  9, 27)( 13, 23)
( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)( 31, 32)
( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)( 47, 48)
( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)( 62,106)
( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)( 70, 98)
( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)( 78, 96)
( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)(113,166)
(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)(121,185)
(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)(129,182)
(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)(137,201)
(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)(145,190)
(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)(153,207)
(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)(161,196)
(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)(223,323)
(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)(231,321)
(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)(239,310)
(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)(247,275)
(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)(255,272)
(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)(263,291)
(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)(325,334)
(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)(338,346)
(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)(358,377)
(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)(379,415)
(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)(387,432)
(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)(395,421)
(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)(403,413)
(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)(438,546)
(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)(446,562)
(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)(454,554)
(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)(462,578)
(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)(470,570)
(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)(478,586)
(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)(486,576)
(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)(494,646)
(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)(502,638)
(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)(510,636)
(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)(518,598)
(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)(526,617)
(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)(534,614)
(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)(650,849)
(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)(658,838)
(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)(666,855)
(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)(674,844)
(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)(682,836)
(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)(690,834)
(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)(698,823)
(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)(706,788)
(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)(714,785)
(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)(722,804)
(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)(730,766)
(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)(738,783)
(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)(746,772)
(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)(754,764)
(755,763)(756,765);;
s2 := (  1,541)(  2,543)(  3,542)(  4,547)(  5,549)(  6,548)(  7,544)(  8,546)
(  9,545)( 10,555)( 11,554)( 12,553)( 13,552)( 14,551)( 15,550)( 16,558)
( 17,557)( 18,556)( 19,567)( 20,566)( 21,565)( 22,564)( 23,563)( 24,562)
( 25,561)( 26,560)( 27,559)( 28,568)( 29,570)( 30,569)( 31,574)( 32,576)
( 33,575)( 34,571)( 35,573)( 36,572)( 37,582)( 38,581)( 39,580)( 40,579)
( 41,578)( 42,577)( 43,585)( 44,584)( 45,583)( 46,594)( 47,593)( 48,592)
( 49,591)( 50,590)( 51,589)( 52,588)( 53,587)( 54,586)( 55,622)( 56,624)
( 57,623)( 58,628)( 59,630)( 60,629)( 61,625)( 62,627)( 63,626)( 64,636)
( 65,635)( 66,634)( 67,633)( 68,632)( 69,631)( 70,639)( 71,638)( 72,637)
( 73,648)( 74,647)( 75,646)( 76,645)( 77,644)( 78,643)( 79,642)( 80,641)
( 81,640)( 82,595)( 83,597)( 84,596)( 85,601)( 86,603)( 87,602)( 88,598)
( 89,600)( 90,599)( 91,609)( 92,608)( 93,607)( 94,606)( 95,605)( 96,604)
( 97,612)( 98,611)( 99,610)(100,621)(101,620)(102,619)(103,618)(104,617)
(105,616)(106,615)(107,614)(108,613)(109,433)(110,435)(111,434)(112,439)
(113,441)(114,440)(115,436)(116,438)(117,437)(118,447)(119,446)(120,445)
(121,444)(122,443)(123,442)(124,450)(125,449)(126,448)(127,459)(128,458)
(129,457)(130,456)(131,455)(132,454)(133,453)(134,452)(135,451)(136,460)
(137,462)(138,461)(139,466)(140,468)(141,467)(142,463)(143,465)(144,464)
(145,474)(146,473)(147,472)(148,471)(149,470)(150,469)(151,477)(152,476)
(153,475)(154,486)(155,485)(156,484)(157,483)(158,482)(159,481)(160,480)
(161,479)(162,478)(163,514)(164,516)(165,515)(166,520)(167,522)(168,521)
(169,517)(170,519)(171,518)(172,528)(173,527)(174,526)(175,525)(176,524)
(177,523)(178,531)(179,530)(180,529)(181,540)(182,539)(183,538)(184,537)
(185,536)(186,535)(187,534)(188,533)(189,532)(190,487)(191,489)(192,488)
(193,493)(194,495)(195,494)(196,490)(197,492)(198,491)(199,501)(200,500)
(201,499)(202,498)(203,497)(204,496)(205,504)(206,503)(207,502)(208,513)
(209,512)(210,511)(211,510)(212,509)(213,508)(214,507)(215,506)(216,505)
(217,838)(218,840)(219,839)(220,844)(221,846)(222,845)(223,841)(224,843)
(225,842)(226,852)(227,851)(228,850)(229,849)(230,848)(231,847)(232,855)
(233,854)(234,853)(235,864)(236,863)(237,862)(238,861)(239,860)(240,859)
(241,858)(242,857)(243,856)(244,811)(245,813)(246,812)(247,817)(248,819)
(249,818)(250,814)(251,816)(252,815)(253,825)(254,824)(255,823)(256,822)
(257,821)(258,820)(259,828)(260,827)(261,826)(262,837)(263,836)(264,835)
(265,834)(266,833)(267,832)(268,831)(269,830)(270,829)(271,784)(272,786)
(273,785)(274,790)(275,792)(276,791)(277,787)(278,789)(279,788)(280,798)
(281,797)(282,796)(283,795)(284,794)(285,793)(286,801)(287,800)(288,799)
(289,810)(290,809)(291,808)(292,807)(293,806)(294,805)(295,804)(296,803)
(297,802)(298,757)(299,759)(300,758)(301,763)(302,765)(303,764)(304,760)
(305,762)(306,761)(307,771)(308,770)(309,769)(310,768)(311,767)(312,766)
(313,774)(314,773)(315,772)(316,783)(317,782)(318,781)(319,780)(320,779)
(321,778)(322,777)(323,776)(324,775)(325,730)(326,732)(327,731)(328,736)
(329,738)(330,737)(331,733)(332,735)(333,734)(334,744)(335,743)(336,742)
(337,741)(338,740)(339,739)(340,747)(341,746)(342,745)(343,756)(344,755)
(345,754)(346,753)(347,752)(348,751)(349,750)(350,749)(351,748)(352,703)
(353,705)(354,704)(355,709)(356,711)(357,710)(358,706)(359,708)(360,707)
(361,717)(362,716)(363,715)(364,714)(365,713)(366,712)(367,720)(368,719)
(369,718)(370,729)(371,728)(372,727)(373,726)(374,725)(375,724)(376,723)
(377,722)(378,721)(379,676)(380,678)(381,677)(382,682)(383,684)(384,683)
(385,679)(386,681)(387,680)(388,690)(389,689)(390,688)(391,687)(392,686)
(393,685)(394,693)(395,692)(396,691)(397,702)(398,701)(399,700)(400,699)
(401,698)(402,697)(403,696)(404,695)(405,694)(406,649)(407,651)(408,650)
(409,655)(410,657)(411,656)(412,652)(413,654)(414,653)(415,663)(416,662)
(417,661)(418,660)(419,659)(420,658)(421,666)(422,665)(423,664)(424,675)
(425,674)(426,673)(427,672)(428,671)(429,670)(430,669)(431,668)(432,667);;
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
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)(109,298)(110,299)(111,300)
(112,306)(113,304)(114,305)(115,302)(116,303)(117,301)(118,318)(119,316)
(120,317)(121,323)(122,324)(123,322)(124,319)(125,320)(126,321)(127,308)
(128,309)(129,307)(130,313)(131,314)(132,315)(133,312)(134,310)(135,311)
(136,271)(137,272)(138,273)(139,279)(140,277)(141,278)(142,275)(143,276)
(144,274)(145,291)(146,289)(147,290)(148,296)(149,297)(150,295)(151,292)
(152,293)(153,294)(154,281)(155,282)(156,280)(157,286)(158,287)(159,288)
(160,285)(161,283)(162,284)(163,217)(164,218)(165,219)(166,225)(167,223)
(168,224)(169,221)(170,222)(171,220)(172,237)(173,235)(174,236)(175,242)
(176,243)(177,241)(178,238)(179,239)(180,240)(181,227)(182,228)(183,226)
(184,232)(185,233)(186,234)(187,231)(188,229)(189,230)(190,244)(191,245)
(192,246)(193,252)(194,250)(195,251)(196,248)(197,249)(198,247)(199,264)
(200,262)(201,263)(202,269)(203,270)(204,268)(205,265)(206,266)(207,267)
(208,254)(209,255)(210,253)(211,259)(212,260)(213,261)(214,258)(215,256)
(216,257)(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)(541,730)(542,731)(543,732)
(544,738)(545,736)(546,737)(547,734)(548,735)(549,733)(550,750)(551,748)
(552,749)(553,755)(554,756)(555,754)(556,751)(557,752)(558,753)(559,740)
(560,741)(561,739)(562,745)(563,746)(564,747)(565,744)(566,742)(567,743)
(568,703)(569,704)(570,705)(571,711)(572,709)(573,710)(574,707)(575,708)
(576,706)(577,723)(578,721)(579,722)(580,728)(581,729)(582,727)(583,724)
(584,725)(585,726)(586,713)(587,714)(588,712)(589,718)(590,719)(591,720)
(592,717)(593,715)(594,716)(595,649)(596,650)(597,651)(598,657)(599,655)
(600,656)(601,653)(602,654)(603,652)(604,669)(605,667)(606,668)(607,674)
(608,675)(609,673)(610,670)(611,671)(612,672)(613,659)(614,660)(615,658)
(616,664)(617,665)(618,666)(619,663)(620,661)(621,662)(622,676)(623,677)
(624,678)(625,684)(626,682)(627,683)(628,680)(629,681)(630,679)(631,696)
(632,694)(633,695)(634,701)(635,702)(636,700)(637,697)(638,698)(639,699)
(640,686)(641,687)(642,685)(643,691)(644,692)(645,693)(646,690)(647,688)
(648,689);
s1 := Sym(864)!(  1, 10)(  2, 12)(  3, 11)(  4,  5)(  7, 26)(  8, 25)(  9, 27)
( 13, 23)( 14, 22)( 15, 24)( 16, 17)( 20, 21)( 28, 37)( 29, 39)( 30, 38)
( 31, 32)( 34, 53)( 35, 52)( 36, 54)( 40, 50)( 41, 49)( 42, 51)( 43, 44)
( 47, 48)( 55, 91)( 56, 93)( 57, 92)( 58, 86)( 59, 85)( 60, 87)( 61,107)
( 62,106)( 63,108)( 64, 82)( 65, 84)( 66, 83)( 67,104)( 68,103)( 69,105)
( 70, 98)( 71, 97)( 72, 99)( 73,100)( 74,102)( 75,101)( 76, 95)( 77, 94)
( 78, 96)( 79, 89)( 80, 88)( 81, 90)(109,172)(110,174)(111,173)(112,167)
(113,166)(114,168)(115,188)(116,187)(117,189)(118,163)(119,165)(120,164)
(121,185)(122,184)(123,186)(124,179)(125,178)(126,180)(127,181)(128,183)
(129,182)(130,176)(131,175)(132,177)(133,170)(134,169)(135,171)(136,199)
(137,201)(138,200)(139,194)(140,193)(141,195)(142,215)(143,214)(144,216)
(145,190)(146,192)(147,191)(148,212)(149,211)(150,213)(151,206)(152,205)
(153,207)(154,208)(155,210)(156,209)(157,203)(158,202)(159,204)(160,197)
(161,196)(162,198)(217,307)(218,309)(219,308)(220,302)(221,301)(222,303)
(223,323)(224,322)(225,324)(226,298)(227,300)(228,299)(229,320)(230,319)
(231,321)(232,314)(233,313)(234,315)(235,316)(236,318)(237,317)(238,311)
(239,310)(240,312)(241,305)(242,304)(243,306)(244,280)(245,282)(246,281)
(247,275)(248,274)(249,276)(250,296)(251,295)(252,297)(253,271)(254,273)
(255,272)(256,293)(257,292)(258,294)(259,287)(260,286)(261,288)(262,289)
(263,291)(264,290)(265,284)(266,283)(267,285)(268,278)(269,277)(270,279)
(325,334)(326,336)(327,335)(328,329)(331,350)(332,349)(333,351)(337,347)
(338,346)(339,348)(340,341)(344,345)(352,361)(353,363)(354,362)(355,356)
(358,377)(359,376)(360,378)(364,374)(365,373)(366,375)(367,368)(371,372)
(379,415)(380,417)(381,416)(382,410)(383,409)(384,411)(385,431)(386,430)
(387,432)(388,406)(389,408)(390,407)(391,428)(392,427)(393,429)(394,422)
(395,421)(396,423)(397,424)(398,426)(399,425)(400,419)(401,418)(402,420)
(403,413)(404,412)(405,414)(433,550)(434,552)(435,551)(436,545)(437,544)
(438,546)(439,566)(440,565)(441,567)(442,541)(443,543)(444,542)(445,563)
(446,562)(447,564)(448,557)(449,556)(450,558)(451,559)(452,561)(453,560)
(454,554)(455,553)(456,555)(457,548)(458,547)(459,549)(460,577)(461,579)
(462,578)(463,572)(464,571)(465,573)(466,593)(467,592)(468,594)(469,568)
(470,570)(471,569)(472,590)(473,589)(474,591)(475,584)(476,583)(477,585)
(478,586)(479,588)(480,587)(481,581)(482,580)(483,582)(484,575)(485,574)
(486,576)(487,631)(488,633)(489,632)(490,626)(491,625)(492,627)(493,647)
(494,646)(495,648)(496,622)(497,624)(498,623)(499,644)(500,643)(501,645)
(502,638)(503,637)(504,639)(505,640)(506,642)(507,641)(508,635)(509,634)
(510,636)(511,629)(512,628)(513,630)(514,604)(515,606)(516,605)(517,599)
(518,598)(519,600)(520,620)(521,619)(522,621)(523,595)(524,597)(525,596)
(526,617)(527,616)(528,618)(529,611)(530,610)(531,612)(532,613)(533,615)
(534,614)(535,608)(536,607)(537,609)(538,602)(539,601)(540,603)(649,847)
(650,849)(651,848)(652,842)(653,841)(654,843)(655,863)(656,862)(657,864)
(658,838)(659,840)(660,839)(661,860)(662,859)(663,861)(664,854)(665,853)
(666,855)(667,856)(668,858)(669,857)(670,851)(671,850)(672,852)(673,845)
(674,844)(675,846)(676,820)(677,822)(678,821)(679,815)(680,814)(681,816)
(682,836)(683,835)(684,837)(685,811)(686,813)(687,812)(688,833)(689,832)
(690,834)(691,827)(692,826)(693,828)(694,829)(695,831)(696,830)(697,824)
(698,823)(699,825)(700,818)(701,817)(702,819)(703,793)(704,795)(705,794)
(706,788)(707,787)(708,789)(709,809)(710,808)(711,810)(712,784)(713,786)
(714,785)(715,806)(716,805)(717,807)(718,800)(719,799)(720,801)(721,802)
(722,804)(723,803)(724,797)(725,796)(726,798)(727,791)(728,790)(729,792)
(730,766)(731,768)(732,767)(733,761)(734,760)(735,762)(736,782)(737,781)
(738,783)(739,757)(740,759)(741,758)(742,779)(743,778)(744,780)(745,773)
(746,772)(747,774)(748,775)(749,777)(750,776)(751,770)(752,769)(753,771)
(754,764)(755,763)(756,765);
s2 := Sym(864)!(  1,541)(  2,543)(  3,542)(  4,547)(  5,549)(  6,548)(  7,544)
(  8,546)(  9,545)( 10,555)( 11,554)( 12,553)( 13,552)( 14,551)( 15,550)
( 16,558)( 17,557)( 18,556)( 19,567)( 20,566)( 21,565)( 22,564)( 23,563)
( 24,562)( 25,561)( 26,560)( 27,559)( 28,568)( 29,570)( 30,569)( 31,574)
( 32,576)( 33,575)( 34,571)( 35,573)( 36,572)( 37,582)( 38,581)( 39,580)
( 40,579)( 41,578)( 42,577)( 43,585)( 44,584)( 45,583)( 46,594)( 47,593)
( 48,592)( 49,591)( 50,590)( 51,589)( 52,588)( 53,587)( 54,586)( 55,622)
( 56,624)( 57,623)( 58,628)( 59,630)( 60,629)( 61,625)( 62,627)( 63,626)
( 64,636)( 65,635)( 66,634)( 67,633)( 68,632)( 69,631)( 70,639)( 71,638)
( 72,637)( 73,648)( 74,647)( 75,646)( 76,645)( 77,644)( 78,643)( 79,642)
( 80,641)( 81,640)( 82,595)( 83,597)( 84,596)( 85,601)( 86,603)( 87,602)
( 88,598)( 89,600)( 90,599)( 91,609)( 92,608)( 93,607)( 94,606)( 95,605)
( 96,604)( 97,612)( 98,611)( 99,610)(100,621)(101,620)(102,619)(103,618)
(104,617)(105,616)(106,615)(107,614)(108,613)(109,433)(110,435)(111,434)
(112,439)(113,441)(114,440)(115,436)(116,438)(117,437)(118,447)(119,446)
(120,445)(121,444)(122,443)(123,442)(124,450)(125,449)(126,448)(127,459)
(128,458)(129,457)(130,456)(131,455)(132,454)(133,453)(134,452)(135,451)
(136,460)(137,462)(138,461)(139,466)(140,468)(141,467)(142,463)(143,465)
(144,464)(145,474)(146,473)(147,472)(148,471)(149,470)(150,469)(151,477)
(152,476)(153,475)(154,486)(155,485)(156,484)(157,483)(158,482)(159,481)
(160,480)(161,479)(162,478)(163,514)(164,516)(165,515)(166,520)(167,522)
(168,521)(169,517)(170,519)(171,518)(172,528)(173,527)(174,526)(175,525)
(176,524)(177,523)(178,531)(179,530)(180,529)(181,540)(182,539)(183,538)
(184,537)(185,536)(186,535)(187,534)(188,533)(189,532)(190,487)(191,489)
(192,488)(193,493)(194,495)(195,494)(196,490)(197,492)(198,491)(199,501)
(200,500)(201,499)(202,498)(203,497)(204,496)(205,504)(206,503)(207,502)
(208,513)(209,512)(210,511)(211,510)(212,509)(213,508)(214,507)(215,506)
(216,505)(217,838)(218,840)(219,839)(220,844)(221,846)(222,845)(223,841)
(224,843)(225,842)(226,852)(227,851)(228,850)(229,849)(230,848)(231,847)
(232,855)(233,854)(234,853)(235,864)(236,863)(237,862)(238,861)(239,860)
(240,859)(241,858)(242,857)(243,856)(244,811)(245,813)(246,812)(247,817)
(248,819)(249,818)(250,814)(251,816)(252,815)(253,825)(254,824)(255,823)
(256,822)(257,821)(258,820)(259,828)(260,827)(261,826)(262,837)(263,836)
(264,835)(265,834)(266,833)(267,832)(268,831)(269,830)(270,829)(271,784)
(272,786)(273,785)(274,790)(275,792)(276,791)(277,787)(278,789)(279,788)
(280,798)(281,797)(282,796)(283,795)(284,794)(285,793)(286,801)(287,800)
(288,799)(289,810)(290,809)(291,808)(292,807)(293,806)(294,805)(295,804)
(296,803)(297,802)(298,757)(299,759)(300,758)(301,763)(302,765)(303,764)
(304,760)(305,762)(306,761)(307,771)(308,770)(309,769)(310,768)(311,767)
(312,766)(313,774)(314,773)(315,772)(316,783)(317,782)(318,781)(319,780)
(320,779)(321,778)(322,777)(323,776)(324,775)(325,730)(326,732)(327,731)
(328,736)(329,738)(330,737)(331,733)(332,735)(333,734)(334,744)(335,743)
(336,742)(337,741)(338,740)(339,739)(340,747)(341,746)(342,745)(343,756)
(344,755)(345,754)(346,753)(347,752)(348,751)(349,750)(350,749)(351,748)
(352,703)(353,705)(354,704)(355,709)(356,711)(357,710)(358,706)(359,708)
(360,707)(361,717)(362,716)(363,715)(364,714)(365,713)(366,712)(367,720)
(368,719)(369,718)(370,729)(371,728)(372,727)(373,726)(374,725)(375,724)
(376,723)(377,722)(378,721)(379,676)(380,678)(381,677)(382,682)(383,684)
(384,683)(385,679)(386,681)(387,680)(388,690)(389,689)(390,688)(391,687)
(392,686)(393,685)(394,693)(395,692)(396,691)(397,702)(398,701)(399,700)
(400,699)(401,698)(402,697)(403,696)(404,695)(405,694)(406,649)(407,651)
(408,650)(409,655)(410,657)(411,656)(412,652)(413,654)(414,653)(415,663)
(416,662)(417,661)(418,660)(419,659)(420,658)(421,666)(422,665)(423,664)
(424,675)(425,674)(426,673)(427,672)(428,671)(429,670)(430,669)(431,668)
(432,667);
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;

References : None.
to this polytope