Polytope of Type {48,6}

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

References : None.
to this polytope