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# Polytope of Type {6,48}

Atlas Canonical Name : {6,48}*1728g
if this polytope has a name.
Group : SmallGroup(1728,31412)
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}*864g
3-fold quotients : {6,16}*576
4-fold quotients : {6,12}*432h
6-fold quotients : {6,8}*288
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)(  2,327)(  3,326)(  4,331)(  5,333)(  6,332)(  7,328)(  8,330)
(  9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)
( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)
( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)
( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)
( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)
( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)
( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)
( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)
( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)
( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)
(105,422)(106,418)(107,420)(108,419)(109,298)(110,300)(111,299)(112,304)
(113,306)(114,305)(115,301)(116,303)(117,302)(118,316)(119,318)(120,317)
(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,307)(128,309)
(129,308)(130,313)(131,315)(132,314)(133,310)(134,312)(135,311)(136,271)
(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)(144,275)
(145,289)(146,291)(147,290)(148,295)(149,297)(150,296)(151,292)(152,294)
(153,293)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)(160,283)
(161,285)(162,284)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)
(169,220)(170,222)(171,221)(172,235)(173,237)(174,236)(175,241)(176,243)
(177,242)(178,238)(179,240)(180,239)(181,226)(182,228)(183,227)(184,232)
(185,234)(186,233)(187,229)(188,231)(189,230)(190,244)(191,246)(192,245)
(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,262)(200,264)
(201,263)(202,268)(203,270)(204,269)(205,265)(206,267)(207,266)(208,253)
(209,255)(210,254)(211,259)(212,261)(213,260)(214,256)(215,258)(216,257)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)
(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)
(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)
(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)
(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)
(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)
(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)
(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)
(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)
(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)
(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)
(537,854)(538,850)(539,852)(540,851)(541,730)(542,732)(543,731)(544,736)
(545,738)(546,737)(547,733)(548,735)(549,734)(550,748)(551,750)(552,749)
(553,754)(554,756)(555,755)(556,751)(557,753)(558,752)(559,739)(560,741)
(561,740)(562,745)(563,747)(564,746)(565,742)(566,744)(567,743)(568,703)
(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)(576,707)
(577,721)(578,723)(579,722)(580,727)(581,729)(582,728)(583,724)(584,726)
(585,725)(586,712)(587,714)(588,713)(589,718)(590,720)(591,719)(592,715)
(593,717)(594,716)(595,649)(596,651)(597,650)(598,655)(599,657)(600,656)
(601,652)(602,654)(603,653)(604,667)(605,669)(606,668)(607,673)(608,675)
(609,674)(610,670)(611,672)(612,671)(613,658)(614,660)(615,659)(616,664)
(617,666)(618,665)(619,661)(620,663)(621,662)(622,676)(623,678)(624,677)
(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,694)(632,696)
(633,695)(634,700)(635,702)(636,701)(637,697)(638,699)(639,698)(640,685)
(641,687)(642,686)(643,691)(644,693)(645,692)(646,688)(647,690)(648,689);;
s1 := (  1,229)(  2,227)(  3,234)(  4,226)(  5,233)(  6,231)(  7,232)(  8,230)
(  9,228)( 10,220)( 11,218)( 12,225)( 13,217)( 14,224)( 15,222)( 16,223)
( 17,221)( 18,219)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)( 24,240)
( 25,241)( 26,239)( 27,237)( 28,256)( 29,254)( 30,261)( 31,253)( 32,260)
( 33,258)( 34,259)( 35,257)( 36,255)( 37,247)( 38,245)( 39,252)( 40,244)
( 41,251)( 42,249)( 43,250)( 44,248)( 45,246)( 46,265)( 47,263)( 48,270)
( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,310)( 56,308)
( 57,315)( 58,307)( 59,314)( 60,312)( 61,313)( 62,311)( 63,309)( 64,301)
( 65,299)( 66,306)( 67,298)( 68,305)( 69,303)( 70,304)( 71,302)( 72,300)
( 73,319)( 74,317)( 75,324)( 76,316)( 77,323)( 78,321)( 79,322)( 80,320)
( 81,318)( 82,283)( 83,281)( 84,288)( 85,280)( 86,287)( 87,285)( 88,286)
( 89,284)( 90,282)( 91,274)( 92,272)( 93,279)( 94,271)( 95,278)( 96,276)
( 97,277)( 98,275)( 99,273)(100,292)(101,290)(102,297)(103,289)(104,296)
(105,294)(106,295)(107,293)(108,291)(109,391)(110,389)(111,396)(112,388)
(113,395)(114,393)(115,394)(116,392)(117,390)(118,382)(119,380)(120,387)
(121,379)(122,386)(123,384)(124,385)(125,383)(126,381)(127,400)(128,398)
(129,405)(130,397)(131,404)(132,402)(133,403)(134,401)(135,399)(136,418)
(137,416)(138,423)(139,415)(140,422)(141,420)(142,421)(143,419)(144,417)
(145,409)(146,407)(147,414)(148,406)(149,413)(150,411)(151,412)(152,410)
(153,408)(154,427)(155,425)(156,432)(157,424)(158,431)(159,429)(160,430)
(161,428)(162,426)(163,337)(164,335)(165,342)(166,334)(167,341)(168,339)
(169,340)(170,338)(171,336)(172,328)(173,326)(174,333)(175,325)(176,332)
(177,330)(178,331)(179,329)(180,327)(181,346)(182,344)(183,351)(184,343)
(185,350)(186,348)(187,349)(188,347)(189,345)(190,364)(191,362)(192,369)
(193,361)(194,368)(195,366)(196,367)(197,365)(198,363)(199,355)(200,353)
(201,360)(202,352)(203,359)(204,357)(205,358)(206,356)(207,354)(208,373)
(209,371)(210,378)(211,370)(212,377)(213,375)(214,376)(215,374)(216,372)
(433,769)(434,767)(435,774)(436,766)(437,773)(438,771)(439,772)(440,770)
(441,768)(442,760)(443,758)(444,765)(445,757)(446,764)(447,762)(448,763)
(449,761)(450,759)(451,778)(452,776)(453,783)(454,775)(455,782)(456,780)
(457,781)(458,779)(459,777)(460,796)(461,794)(462,801)(463,793)(464,800)
(465,798)(466,799)(467,797)(468,795)(469,787)(470,785)(471,792)(472,784)
(473,791)(474,789)(475,790)(476,788)(477,786)(478,805)(479,803)(480,810)
(481,802)(482,809)(483,807)(484,808)(485,806)(486,804)(487,850)(488,848)
(489,855)(490,847)(491,854)(492,852)(493,853)(494,851)(495,849)(496,841)
(497,839)(498,846)(499,838)(500,845)(501,843)(502,844)(503,842)(504,840)
(505,859)(506,857)(507,864)(508,856)(509,863)(510,861)(511,862)(512,860)
(513,858)(514,823)(515,821)(516,828)(517,820)(518,827)(519,825)(520,826)
(521,824)(522,822)(523,814)(524,812)(525,819)(526,811)(527,818)(528,816)
(529,817)(530,815)(531,813)(532,832)(533,830)(534,837)(535,829)(536,836)
(537,834)(538,835)(539,833)(540,831)(541,661)(542,659)(543,666)(544,658)
(545,665)(546,663)(547,664)(548,662)(549,660)(550,652)(551,650)(552,657)
(553,649)(554,656)(555,654)(556,655)(557,653)(558,651)(559,670)(560,668)
(561,675)(562,667)(563,674)(564,672)(565,673)(566,671)(567,669)(568,688)
(569,686)(570,693)(571,685)(572,692)(573,690)(574,691)(575,689)(576,687)
(577,679)(578,677)(579,684)(580,676)(581,683)(582,681)(583,682)(584,680)
(585,678)(586,697)(587,695)(588,702)(589,694)(590,701)(591,699)(592,700)
(593,698)(594,696)(595,742)(596,740)(597,747)(598,739)(599,746)(600,744)
(601,745)(602,743)(603,741)(604,733)(605,731)(606,738)(607,730)(608,737)
(609,735)(610,736)(611,734)(612,732)(613,751)(614,749)(615,756)(616,748)
(617,755)(618,753)(619,754)(620,752)(621,750)(622,715)(623,713)(624,720)
(625,712)(626,719)(627,717)(628,718)(629,716)(630,714)(631,706)(632,704)
(633,711)(634,703)(635,710)(636,708)(637,709)(638,707)(639,705)(640,724)
(641,722)(642,729)(643,721)(644,728)(645,726)(646,727)(647,725)(648,723);;
s2 := (  1,649)(  2,650)(  3,651)(  4,657)(  5,655)(  6,656)(  7,653)(  8,654)
(  9,652)( 10,667)( 11,668)( 12,669)( 13,675)( 14,673)( 15,674)( 16,671)
( 17,672)( 18,670)( 19,658)( 20,659)( 21,660)( 22,666)( 23,664)( 24,665)
( 25,662)( 26,663)( 27,661)( 28,676)( 29,677)( 30,678)( 31,684)( 32,682)
( 33,683)( 34,680)( 35,681)( 36,679)( 37,694)( 38,695)( 39,696)( 40,702)
( 41,700)( 42,701)( 43,698)( 44,699)( 45,697)( 46,685)( 47,686)( 48,687)
( 49,693)( 50,691)( 51,692)( 52,689)( 53,690)( 54,688)( 55,730)( 56,731)
( 57,732)( 58,738)( 59,736)( 60,737)( 61,734)( 62,735)( 63,733)( 64,748)
( 65,749)( 66,750)( 67,756)( 68,754)( 69,755)( 70,752)( 71,753)( 72,751)
( 73,739)( 74,740)( 75,741)( 76,747)( 77,745)( 78,746)( 79,743)( 80,744)
( 81,742)( 82,703)( 83,704)( 84,705)( 85,711)( 86,709)( 87,710)( 88,707)
( 89,708)( 90,706)( 91,721)( 92,722)( 93,723)( 94,729)( 95,727)( 96,728)
( 97,725)( 98,726)( 99,724)(100,712)(101,713)(102,714)(103,720)(104,718)
(105,719)(106,716)(107,717)(108,715)(109,811)(110,812)(111,813)(112,819)
(113,817)(114,818)(115,815)(116,816)(117,814)(118,829)(119,830)(120,831)
(121,837)(122,835)(123,836)(124,833)(125,834)(126,832)(127,820)(128,821)
(129,822)(130,828)(131,826)(132,827)(133,824)(134,825)(135,823)(136,838)
(137,839)(138,840)(139,846)(140,844)(141,845)(142,842)(143,843)(144,841)
(145,856)(146,857)(147,858)(148,864)(149,862)(150,863)(151,860)(152,861)
(153,859)(154,847)(155,848)(156,849)(157,855)(158,853)(159,854)(160,851)
(161,852)(162,850)(163,757)(164,758)(165,759)(166,765)(167,763)(168,764)
(169,761)(170,762)(171,760)(172,775)(173,776)(174,777)(175,783)(176,781)
(177,782)(178,779)(179,780)(180,778)(181,766)(182,767)(183,768)(184,774)
(185,772)(186,773)(187,770)(188,771)(189,769)(190,784)(191,785)(192,786)
(193,792)(194,790)(195,791)(196,788)(197,789)(198,787)(199,802)(200,803)
(201,804)(202,810)(203,808)(204,809)(205,806)(206,807)(207,805)(208,793)
(209,794)(210,795)(211,801)(212,799)(213,800)(214,797)(215,798)(216,796)
(217,433)(218,434)(219,435)(220,441)(221,439)(222,440)(223,437)(224,438)
(225,436)(226,451)(227,452)(228,453)(229,459)(230,457)(231,458)(232,455)
(233,456)(234,454)(235,442)(236,443)(237,444)(238,450)(239,448)(240,449)
(241,446)(242,447)(243,445)(244,460)(245,461)(246,462)(247,468)(248,466)
(249,467)(250,464)(251,465)(252,463)(253,478)(254,479)(255,480)(256,486)
(257,484)(258,485)(259,482)(260,483)(261,481)(262,469)(263,470)(264,471)
(265,477)(266,475)(267,476)(268,473)(269,474)(270,472)(271,514)(272,515)
(273,516)(274,522)(275,520)(276,521)(277,518)(278,519)(279,517)(280,532)
(281,533)(282,534)(283,540)(284,538)(285,539)(286,536)(287,537)(288,535)
(289,523)(290,524)(291,525)(292,531)(293,529)(294,530)(295,527)(296,528)
(297,526)(298,487)(299,488)(300,489)(301,495)(302,493)(303,494)(304,491)
(305,492)(306,490)(307,505)(308,506)(309,507)(310,513)(311,511)(312,512)
(313,509)(314,510)(315,508)(316,496)(317,497)(318,498)(319,504)(320,502)
(321,503)(322,500)(323,501)(324,499)(325,595)(326,596)(327,597)(328,603)
(329,601)(330,602)(331,599)(332,600)(333,598)(334,613)(335,614)(336,615)
(337,621)(338,619)(339,620)(340,617)(341,618)(342,616)(343,604)(344,605)
(345,606)(346,612)(347,610)(348,611)(349,608)(350,609)(351,607)(352,622)
(353,623)(354,624)(355,630)(356,628)(357,629)(358,626)(359,627)(360,625)
(361,640)(362,641)(363,642)(364,648)(365,646)(366,647)(367,644)(368,645)
(369,643)(370,631)(371,632)(372,633)(373,639)(374,637)(375,638)(376,635)
(377,636)(378,634)(379,541)(380,542)(381,543)(382,549)(383,547)(384,548)
(385,545)(386,546)(387,544)(388,559)(389,560)(390,561)(391,567)(392,565)
(393,566)(394,563)(395,564)(396,562)(397,550)(398,551)(399,552)(400,558)
(401,556)(402,557)(403,554)(404,555)(405,553)(406,568)(407,569)(408,570)
(409,576)(410,574)(411,575)(412,572)(413,573)(414,571)(415,586)(416,587)
(417,588)(418,594)(419,592)(420,593)(421,590)(422,591)(423,589)(424,577)
(425,578)(426,579)(427,585)(428,583)(429,584)(430,581)(431,582)(432,580);;
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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope