Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728h
if this polytope has a name.
Group : SmallGroup(1728,33416)
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}*864h
   3-fold quotients : {16,6}*576
   4-fold quotients : {12,6}*432i
   6-fold quotients : {8,6}*288
   8-fold quotients : {12,6}*216c
   9-fold quotients : {48,2}*192
   12-fold quotients : {4,6}*144
   18-fold quotients : {24,2}*96
   24-fold quotients : {4,6}*72
   27-fold quotients : {16,2}*64
   36-fold quotients : {12,2}*48
   54-fold quotients : {8,2}*32
   72-fold quotients : {6,2}*24
   108-fold quotients : {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)
( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)( 61, 85)( 62, 83)
( 63, 90)( 64,100)( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)
( 71,101)( 72,108)( 73, 91)( 74, 98)( 75, 96)( 76, 97)( 77, 95)( 78, 93)
( 79, 94)( 80, 92)( 81, 99)(109,163)(110,170)(111,168)(112,169)(113,167)
(114,165)(115,166)(116,164)(117,171)(118,181)(119,188)(120,186)(121,187)
(122,185)(123,183)(124,184)(125,182)(126,189)(127,172)(128,179)(129,177)
(130,178)(131,176)(132,174)(133,175)(134,173)(135,180)(136,190)(137,197)
(138,195)(139,196)(140,194)(141,192)(142,193)(143,191)(144,198)(145,208)
(146,215)(147,213)(148,214)(149,212)(150,210)(151,211)(152,209)(153,216)
(154,199)(155,206)(156,204)(157,205)(158,203)(159,201)(160,202)(161,200)
(162,207)(217,298)(218,305)(219,303)(220,304)(221,302)(222,300)(223,301)
(224,299)(225,306)(226,316)(227,323)(228,321)(229,322)(230,320)(231,318)
(232,319)(233,317)(234,324)(235,307)(236,314)(237,312)(238,313)(239,311)
(240,309)(241,310)(242,308)(243,315)(244,271)(245,278)(246,276)(247,277)
(248,275)(249,273)(250,274)(251,272)(252,279)(253,289)(254,296)(255,294)
(256,295)(257,293)(258,291)(259,292)(260,290)(261,297)(262,280)(263,287)
(264,285)(265,286)(266,284)(267,282)(268,283)(269,281)(270,288)(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)(379,406)
(380,413)(381,411)(382,412)(383,410)(384,408)(385,409)(386,407)(387,414)
(388,424)(389,431)(390,429)(391,430)(392,428)(393,426)(394,427)(395,425)
(396,432)(397,415)(398,422)(399,420)(400,421)(401,419)(402,417)(403,418)
(404,416)(405,423)(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)
(487,622)(488,629)(489,627)(490,628)(491,626)(492,624)(493,625)(494,623)
(495,630)(496,640)(497,647)(498,645)(499,646)(500,644)(501,642)(502,643)
(503,641)(504,648)(505,631)(506,638)(507,636)(508,637)(509,635)(510,633)
(511,634)(512,632)(513,639)(514,595)(515,602)(516,600)(517,601)(518,599)
(519,597)(520,598)(521,596)(522,603)(523,613)(524,620)(525,618)(526,619)
(527,617)(528,615)(529,616)(530,614)(531,621)(532,604)(533,611)(534,609)
(535,610)(536,608)(537,606)(538,607)(539,605)(540,612)(649,838)(650,845)
(651,843)(652,844)(653,842)(654,840)(655,841)(656,839)(657,846)(658,856)
(659,863)(660,861)(661,862)(662,860)(663,858)(664,859)(665,857)(666,864)
(667,847)(668,854)(669,852)(670,853)(671,851)(672,849)(673,850)(674,848)
(675,855)(676,811)(677,818)(678,816)(679,817)(680,815)(681,813)(682,814)
(683,812)(684,819)(685,829)(686,836)(687,834)(688,835)(689,833)(690,831)
(691,832)(692,830)(693,837)(694,820)(695,827)(696,825)(697,826)(698,824)
(699,822)(700,823)(701,821)(702,828)(703,784)(704,791)(705,789)(706,790)
(707,788)(708,786)(709,787)(710,785)(711,792)(712,802)(713,809)(714,807)
(715,808)(716,806)(717,804)(718,805)(719,803)(720,810)(721,793)(722,800)
(723,798)(724,799)(725,797)(726,795)(727,796)(728,794)(729,801)(730,757)
(731,764)(732,762)(733,763)(734,761)(735,759)(736,760)(737,758)(738,765)
(739,775)(740,782)(741,780)(742,781)(743,779)(744,777)(745,778)(746,776)
(747,783)(748,766)(749,773)(750,771)(751,772)(752,770)(753,768)(754,769)
(755,767)(756,774);;
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)( 55,523)( 56,524)
( 57,525)( 58,531)( 59,529)( 60,530)( 61,527)( 62,528)( 63,526)( 64,514)
( 65,515)( 66,516)( 67,522)( 68,520)( 69,521)( 70,518)( 71,519)( 72,517)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,496)( 83,497)( 84,498)( 85,504)( 86,502)( 87,503)( 88,500)
( 89,501)( 90,499)( 91,487)( 92,488)( 93,489)( 94,495)( 95,493)( 96,494)
( 97,491)( 98,492)( 99,490)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,604)(110,605)(111,606)(112,612)
(113,610)(114,611)(115,608)(116,609)(117,607)(118,595)(119,596)(120,597)
(121,603)(122,601)(123,602)(124,599)(125,600)(126,598)(127,613)(128,614)
(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,631)
(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)(144,634)
(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)(152,627)
(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)
(161,645)(162,643)(163,550)(164,551)(165,552)(166,558)(167,556)(168,557)
(169,554)(170,555)(171,553)(172,541)(173,542)(174,543)(175,549)(176,547)
(177,548)(178,545)(179,546)(180,544)(181,559)(182,560)(183,561)(184,567)
(185,565)(186,566)(187,563)(188,564)(189,562)(190,577)(191,578)(192,579)
(193,585)(194,583)(195,584)(196,581)(197,582)(198,580)(199,568)(200,569)
(201,570)(202,576)(203,574)(204,575)(205,572)(206,573)(207,571)(208,586)
(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)
(217,739)(218,740)(219,741)(220,747)(221,745)(222,746)(223,743)(224,744)
(225,742)(226,730)(227,731)(228,732)(229,738)(230,736)(231,737)(232,734)
(233,735)(234,733)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)
(241,752)(242,753)(243,751)(244,712)(245,713)(246,714)(247,720)(248,718)
(249,719)(250,716)(251,717)(252,715)(253,703)(254,704)(255,705)(256,711)
(257,709)(258,710)(259,707)(260,708)(261,706)(262,721)(263,722)(264,723)
(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,685)(272,686)
(273,687)(274,693)(275,691)(276,692)(277,689)(278,690)(279,688)(280,676)
(281,677)(282,678)(283,684)(284,682)(285,683)(286,680)(287,681)(288,679)
(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)
(297,697)(298,658)(299,659)(300,660)(301,666)(302,664)(303,665)(304,662)
(305,663)(306,661)(307,649)(308,650)(309,651)(310,657)(311,655)(312,656)
(313,653)(314,654)(315,652)(316,667)(317,668)(318,669)(319,675)(320,673)
(321,674)(322,671)(323,672)(324,670)(325,766)(326,767)(327,768)(328,774)
(329,772)(330,773)(331,770)(332,771)(333,769)(334,757)(335,758)(336,759)
(337,765)(338,763)(339,764)(340,761)(341,762)(342,760)(343,775)(344,776)
(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,793)
(353,794)(354,795)(355,801)(356,799)(357,800)(358,797)(359,798)(360,796)
(361,784)(362,785)(363,786)(364,792)(365,790)(366,791)(367,788)(368,789)
(369,787)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)
(377,807)(378,805)(379,847)(380,848)(381,849)(382,855)(383,853)(384,854)
(385,851)(386,852)(387,850)(388,838)(389,839)(390,840)(391,846)(392,844)
(393,845)(394,842)(395,843)(396,841)(397,856)(398,857)(399,858)(400,864)
(401,862)(402,863)(403,860)(404,861)(405,859)(406,820)(407,821)(408,822)
(409,828)(410,826)(411,827)(412,824)(413,825)(414,823)(415,811)(416,812)
(417,813)(418,819)(419,817)(420,818)(421,815)(422,816)(423,814)(424,829)
(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832);;
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)(109,302)(110,301)(111,303)(112,299)
(113,298)(114,300)(115,305)(116,304)(117,306)(118,311)(119,310)(120,312)
(121,308)(122,307)(123,309)(124,314)(125,313)(126,315)(127,320)(128,319)
(129,321)(130,317)(131,316)(132,318)(133,323)(134,322)(135,324)(136,275)
(137,274)(138,276)(139,272)(140,271)(141,273)(142,278)(143,277)(144,279)
(145,284)(146,283)(147,285)(148,281)(149,280)(150,282)(151,287)(152,286)
(153,288)(154,293)(155,292)(156,294)(157,290)(158,289)(159,291)(160,296)
(161,295)(162,297)(163,221)(164,220)(165,222)(166,218)(167,217)(168,219)
(169,224)(170,223)(171,225)(172,230)(173,229)(174,231)(175,227)(176,226)
(177,228)(178,233)(179,232)(180,234)(181,239)(182,238)(183,240)(184,236)
(185,235)(186,237)(187,242)(188,241)(189,243)(190,248)(191,247)(192,249)
(193,245)(194,244)(195,246)(196,251)(197,250)(198,252)(199,257)(200,256)
(201,258)(202,254)(203,253)(204,255)(205,260)(206,259)(207,261)(208,266)
(209,265)(210,267)(211,263)(212,262)(213,264)(214,269)(215,268)(216,270)
(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)(541,734)(542,733)(543,735)(544,731)
(545,730)(546,732)(547,737)(548,736)(549,738)(550,743)(551,742)(552,744)
(553,740)(554,739)(555,741)(556,746)(557,745)(558,747)(559,752)(560,751)
(561,753)(562,749)(563,748)(564,750)(565,755)(566,754)(567,756)(568,707)
(569,706)(570,708)(571,704)(572,703)(573,705)(574,710)(575,709)(576,711)
(577,716)(578,715)(579,717)(580,713)(581,712)(582,714)(583,719)(584,718)
(585,720)(586,725)(587,724)(588,726)(589,722)(590,721)(591,723)(592,728)
(593,727)(594,729)(595,653)(596,652)(597,654)(598,650)(599,649)(600,651)
(601,656)(602,655)(603,657)(604,662)(605,661)(606,663)(607,659)(608,658)
(609,660)(610,665)(611,664)(612,666)(613,671)(614,670)(615,672)(616,668)
(617,667)(618,669)(619,674)(620,673)(621,675)(622,680)(623,679)(624,681)
(625,677)(626,676)(627,678)(628,683)(629,682)(630,684)(631,689)(632,688)
(633,690)(634,686)(635,685)(636,687)(637,692)(638,691)(639,693)(640,698)
(641,697)(642,699)(643,695)(644,694)(645,696)(646,701)(647,700)(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*s2*s0*s1*s2*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*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*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)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)( 61, 85)
( 62, 83)( 63, 90)( 64,100)( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)
( 70,103)( 71,101)( 72,108)( 73, 91)( 74, 98)( 75, 96)( 76, 97)( 77, 95)
( 78, 93)( 79, 94)( 80, 92)( 81, 99)(109,163)(110,170)(111,168)(112,169)
(113,167)(114,165)(115,166)(116,164)(117,171)(118,181)(119,188)(120,186)
(121,187)(122,185)(123,183)(124,184)(125,182)(126,189)(127,172)(128,179)
(129,177)(130,178)(131,176)(132,174)(133,175)(134,173)(135,180)(136,190)
(137,197)(138,195)(139,196)(140,194)(141,192)(142,193)(143,191)(144,198)
(145,208)(146,215)(147,213)(148,214)(149,212)(150,210)(151,211)(152,209)
(153,216)(154,199)(155,206)(156,204)(157,205)(158,203)(159,201)(160,202)
(161,200)(162,207)(217,298)(218,305)(219,303)(220,304)(221,302)(222,300)
(223,301)(224,299)(225,306)(226,316)(227,323)(228,321)(229,322)(230,320)
(231,318)(232,319)(233,317)(234,324)(235,307)(236,314)(237,312)(238,313)
(239,311)(240,309)(241,310)(242,308)(243,315)(244,271)(245,278)(246,276)
(247,277)(248,275)(249,273)(250,274)(251,272)(252,279)(253,289)(254,296)
(255,294)(256,295)(257,293)(258,291)(259,292)(260,290)(261,297)(262,280)
(263,287)(264,285)(265,286)(266,284)(267,282)(268,283)(269,281)(270,288)
(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)
(379,406)(380,413)(381,411)(382,412)(383,410)(384,408)(385,409)(386,407)
(387,414)(388,424)(389,431)(390,429)(391,430)(392,428)(393,426)(394,427)
(395,425)(396,432)(397,415)(398,422)(399,420)(400,421)(401,419)(402,417)
(403,418)(404,416)(405,423)(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)(487,622)(488,629)(489,627)(490,628)(491,626)(492,624)(493,625)
(494,623)(495,630)(496,640)(497,647)(498,645)(499,646)(500,644)(501,642)
(502,643)(503,641)(504,648)(505,631)(506,638)(507,636)(508,637)(509,635)
(510,633)(511,634)(512,632)(513,639)(514,595)(515,602)(516,600)(517,601)
(518,599)(519,597)(520,598)(521,596)(522,603)(523,613)(524,620)(525,618)
(526,619)(527,617)(528,615)(529,616)(530,614)(531,621)(532,604)(533,611)
(534,609)(535,610)(536,608)(537,606)(538,607)(539,605)(540,612)(649,838)
(650,845)(651,843)(652,844)(653,842)(654,840)(655,841)(656,839)(657,846)
(658,856)(659,863)(660,861)(661,862)(662,860)(663,858)(664,859)(665,857)
(666,864)(667,847)(668,854)(669,852)(670,853)(671,851)(672,849)(673,850)
(674,848)(675,855)(676,811)(677,818)(678,816)(679,817)(680,815)(681,813)
(682,814)(683,812)(684,819)(685,829)(686,836)(687,834)(688,835)(689,833)
(690,831)(691,832)(692,830)(693,837)(694,820)(695,827)(696,825)(697,826)
(698,824)(699,822)(700,823)(701,821)(702,828)(703,784)(704,791)(705,789)
(706,790)(707,788)(708,786)(709,787)(710,785)(711,792)(712,802)(713,809)
(714,807)(715,808)(716,806)(717,804)(718,805)(719,803)(720,810)(721,793)
(722,800)(723,798)(724,799)(725,797)(726,795)(727,796)(728,794)(729,801)
(730,757)(731,764)(732,762)(733,763)(734,761)(735,759)(736,760)(737,758)
(738,765)(739,775)(740,782)(741,780)(742,781)(743,779)(744,777)(745,778)
(746,776)(747,783)(748,766)(749,773)(750,771)(751,772)(752,770)(753,768)
(754,769)(755,767)(756,774);
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)( 55,523)
( 56,524)( 57,525)( 58,531)( 59,529)( 60,530)( 61,527)( 62,528)( 63,526)
( 64,514)( 65,515)( 66,516)( 67,522)( 68,520)( 69,521)( 70,518)( 71,519)
( 72,517)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,496)( 83,497)( 84,498)( 85,504)( 86,502)( 87,503)
( 88,500)( 89,501)( 90,499)( 91,487)( 92,488)( 93,489)( 94,495)( 95,493)
( 96,494)( 97,491)( 98,492)( 99,490)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,604)(110,605)(111,606)
(112,612)(113,610)(114,611)(115,608)(116,609)(117,607)(118,595)(119,596)
(120,597)(121,603)(122,601)(123,602)(124,599)(125,600)(126,598)(127,613)
(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)
(136,631)(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)
(144,634)(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)
(152,627)(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)
(160,644)(161,645)(162,643)(163,550)(164,551)(165,552)(166,558)(167,556)
(168,557)(169,554)(170,555)(171,553)(172,541)(173,542)(174,543)(175,549)
(176,547)(177,548)(178,545)(179,546)(180,544)(181,559)(182,560)(183,561)
(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,577)(191,578)
(192,579)(193,585)(194,583)(195,584)(196,581)(197,582)(198,580)(199,568)
(200,569)(201,570)(202,576)(203,574)(204,575)(205,572)(206,573)(207,571)
(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)
(216,589)(217,739)(218,740)(219,741)(220,747)(221,745)(222,746)(223,743)
(224,744)(225,742)(226,730)(227,731)(228,732)(229,738)(230,736)(231,737)
(232,734)(233,735)(234,733)(235,748)(236,749)(237,750)(238,756)(239,754)
(240,755)(241,752)(242,753)(243,751)(244,712)(245,713)(246,714)(247,720)
(248,718)(249,719)(250,716)(251,717)(252,715)(253,703)(254,704)(255,705)
(256,711)(257,709)(258,710)(259,707)(260,708)(261,706)(262,721)(263,722)
(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,685)
(272,686)(273,687)(274,693)(275,691)(276,692)(277,689)(278,690)(279,688)
(280,676)(281,677)(282,678)(283,684)(284,682)(285,683)(286,680)(287,681)
(288,679)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)
(296,699)(297,697)(298,658)(299,659)(300,660)(301,666)(302,664)(303,665)
(304,662)(305,663)(306,661)(307,649)(308,650)(309,651)(310,657)(311,655)
(312,656)(313,653)(314,654)(315,652)(316,667)(317,668)(318,669)(319,675)
(320,673)(321,674)(322,671)(323,672)(324,670)(325,766)(326,767)(327,768)
(328,774)(329,772)(330,773)(331,770)(332,771)(333,769)(334,757)(335,758)
(336,759)(337,765)(338,763)(339,764)(340,761)(341,762)(342,760)(343,775)
(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)
(352,793)(353,794)(354,795)(355,801)(356,799)(357,800)(358,797)(359,798)
(360,796)(361,784)(362,785)(363,786)(364,792)(365,790)(366,791)(367,788)
(368,789)(369,787)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)
(376,806)(377,807)(378,805)(379,847)(380,848)(381,849)(382,855)(383,853)
(384,854)(385,851)(386,852)(387,850)(388,838)(389,839)(390,840)(391,846)
(392,844)(393,845)(394,842)(395,843)(396,841)(397,856)(398,857)(399,858)
(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,820)(407,821)
(408,822)(409,828)(410,826)(411,827)(412,824)(413,825)(414,823)(415,811)
(416,812)(417,813)(418,819)(419,817)(420,818)(421,815)(422,816)(423,814)
(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)
(432,832);
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)(109,302)(110,301)(111,303)
(112,299)(113,298)(114,300)(115,305)(116,304)(117,306)(118,311)(119,310)
(120,312)(121,308)(122,307)(123,309)(124,314)(125,313)(126,315)(127,320)
(128,319)(129,321)(130,317)(131,316)(132,318)(133,323)(134,322)(135,324)
(136,275)(137,274)(138,276)(139,272)(140,271)(141,273)(142,278)(143,277)
(144,279)(145,284)(146,283)(147,285)(148,281)(149,280)(150,282)(151,287)
(152,286)(153,288)(154,293)(155,292)(156,294)(157,290)(158,289)(159,291)
(160,296)(161,295)(162,297)(163,221)(164,220)(165,222)(166,218)(167,217)
(168,219)(169,224)(170,223)(171,225)(172,230)(173,229)(174,231)(175,227)
(176,226)(177,228)(178,233)(179,232)(180,234)(181,239)(182,238)(183,240)
(184,236)(185,235)(186,237)(187,242)(188,241)(189,243)(190,248)(191,247)
(192,249)(193,245)(194,244)(195,246)(196,251)(197,250)(198,252)(199,257)
(200,256)(201,258)(202,254)(203,253)(204,255)(205,260)(206,259)(207,261)
(208,266)(209,265)(210,267)(211,263)(212,262)(213,264)(214,269)(215,268)
(216,270)(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)(541,734)(542,733)(543,735)
(544,731)(545,730)(546,732)(547,737)(548,736)(549,738)(550,743)(551,742)
(552,744)(553,740)(554,739)(555,741)(556,746)(557,745)(558,747)(559,752)
(560,751)(561,753)(562,749)(563,748)(564,750)(565,755)(566,754)(567,756)
(568,707)(569,706)(570,708)(571,704)(572,703)(573,705)(574,710)(575,709)
(576,711)(577,716)(578,715)(579,717)(580,713)(581,712)(582,714)(583,719)
(584,718)(585,720)(586,725)(587,724)(588,726)(589,722)(590,721)(591,723)
(592,728)(593,727)(594,729)(595,653)(596,652)(597,654)(598,650)(599,649)
(600,651)(601,656)(602,655)(603,657)(604,662)(605,661)(606,663)(607,659)
(608,658)(609,660)(610,665)(611,664)(612,666)(613,671)(614,670)(615,672)
(616,668)(617,667)(618,669)(619,674)(620,673)(621,675)(622,680)(623,679)
(624,681)(625,677)(626,676)(627,678)(628,683)(629,682)(630,684)(631,689)
(632,688)(633,690)(634,686)(635,685)(636,687)(637,692)(638,691)(639,693)
(640,698)(641,697)(642,699)(643,695)(644,694)(645,696)(646,701)(647,700)
(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*s2*s0*s1*s2*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*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*s0*s1 >;

References : None.
to this polytope