Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728e
if this polytope has a name.
Group : SmallGroup(1728,12518)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 144, 432, 18
Order of s₀s₁s₂ : 48
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}*864d
   3-fold quotients : {16,6}*576
   4-fold quotients : {12,6}*432e
   6-fold quotients : {8,6}*288
   8-fold quotients : {12,6}*216b
   12-fold quotients : {4,6}*144
   24-fold quotients : {4,6}*72
   27-fold quotients : {16,2}*64
   54-fold quotients : {8,2}*32
   108-fold quotients : {4,2}*16
   216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope