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# Polytope of Type {9,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,9}*1944c
if this polytope has a name.
Group : SmallGroup(1944,3453)
Rank : 3
Schlafli Type : {9,9}
Number of vertices, edges, etc : 108, 486, 108
Order of s0s1s2 : 4
Order of s0s1s2s1 : 9
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
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) :
3-fold quotients : {9,9}*648b
81-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)
( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)
( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)
( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)
( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)
( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)
( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)
(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)
(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)
(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)
(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)
(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)
(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)
(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)
(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)
(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)
(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)
(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)
(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)
(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(325,865)
(326,867)(327,866)(328,883)(329,885)(330,884)(331,874)(332,876)(333,875)
(334,871)(335,873)(336,872)(337,889)(338,891)(339,890)(340,880)(341,882)
(342,881)(343,868)(344,870)(345,869)(346,886)(347,888)(348,887)(349,877)
(350,879)(351,878)(352,919)(353,921)(354,920)(355,937)(356,939)(357,938)
(358,928)(359,930)(360,929)(361,925)(362,927)(363,926)(364,943)(365,945)
(366,944)(367,934)(368,936)(369,935)(370,922)(371,924)(372,923)(373,940)
(374,942)(375,941)(376,931)(377,933)(378,932)(379,892)(380,894)(381,893)
(382,910)(383,912)(384,911)(385,901)(386,903)(387,902)(388,898)(389,900)
(390,899)(391,916)(392,918)(393,917)(394,907)(395,909)(396,908)(397,895)
(398,897)(399,896)(400,913)(401,915)(402,914)(403,904)(404,906)(405,905)
(406,946)(407,948)(408,947)(409,964)(410,966)(411,965)(412,955)(413,957)
(414,956)(415,952)(416,954)(417,953)(418,970)(419,972)(420,971)(421,961)
(422,963)(423,962)(424,949)(425,951)(426,950)(427,967)(428,969)(429,968)
(430,958)(431,960)(432,959)(433,757)(434,759)(435,758)(436,775)(437,777)
(438,776)(439,766)(440,768)(441,767)(442,763)(443,765)(444,764)(445,781)
(446,783)(447,782)(448,772)(449,774)(450,773)(451,760)(452,762)(453,761)
(454,778)(455,780)(456,779)(457,769)(458,771)(459,770)(460,811)(461,813)
(462,812)(463,829)(464,831)(465,830)(466,820)(467,822)(468,821)(469,817)
(470,819)(471,818)(472,835)(473,837)(474,836)(475,826)(476,828)(477,827)
(478,814)(479,816)(480,815)(481,832)(482,834)(483,833)(484,823)(485,825)
(486,824)(487,784)(488,786)(489,785)(490,802)(491,804)(492,803)(493,793)
(494,795)(495,794)(496,790)(497,792)(498,791)(499,808)(500,810)(501,809)
(502,799)(503,801)(504,800)(505,787)(506,789)(507,788)(508,805)(509,807)
(510,806)(511,796)(512,798)(513,797)(514,838)(515,840)(516,839)(517,856)
(518,858)(519,857)(520,847)(521,849)(522,848)(523,844)(524,846)(525,845)
(526,862)(527,864)(528,863)(529,853)(530,855)(531,854)(532,841)(533,843)
(534,842)(535,859)(536,861)(537,860)(538,850)(539,852)(540,851)(541,649)
(542,651)(543,650)(544,667)(545,669)(546,668)(547,658)(548,660)(549,659)
(550,655)(551,657)(552,656)(553,673)(554,675)(555,674)(556,664)(557,666)
(558,665)(559,652)(560,654)(561,653)(562,670)(563,672)(564,671)(565,661)
(566,663)(567,662)(568,703)(569,705)(570,704)(571,721)(572,723)(573,722)
(574,712)(575,714)(576,713)(577,709)(578,711)(579,710)(580,727)(581,729)
(582,728)(583,718)(584,720)(585,719)(586,706)(587,708)(588,707)(589,724)
(590,726)(591,725)(592,715)(593,717)(594,716)(595,676)(596,678)(597,677)
(598,694)(599,696)(600,695)(601,685)(602,687)(603,686)(604,682)(605,684)
(606,683)(607,700)(608,702)(609,701)(610,691)(611,693)(612,692)(613,679)
(614,681)(615,680)(616,697)(617,699)(618,698)(619,688)(620,690)(621,689)
(622,730)(623,732)(624,731)(625,748)(626,750)(627,749)(628,739)(629,741)
(630,740)(631,736)(632,738)(633,737)(634,754)(635,756)(636,755)(637,745)
(638,747)(639,746)(640,733)(641,735)(642,734)(643,751)(644,753)(645,752)
(646,742)(647,744)(648,743);;
s1 := (  1,334)(  2,340)(  3,337)(  4,336)(  5,342)(  6,339)(  7,335)(  8,341)
(  9,338)( 10,325)( 11,331)( 12,328)( 13,327)( 14,333)( 15,330)( 16,326)
( 17,332)( 18,329)( 19,343)( 20,349)( 21,346)( 22,345)( 23,351)( 24,348)
( 25,344)( 26,350)( 27,347)( 28,361)( 29,367)( 30,364)( 31,363)( 32,369)
( 33,366)( 34,362)( 35,368)( 36,365)( 37,352)( 38,358)( 39,355)( 40,354)
( 41,360)( 42,357)( 43,353)( 44,359)( 45,356)( 46,370)( 47,376)( 48,373)
( 49,372)( 50,378)( 51,375)( 52,371)( 53,377)( 54,374)( 55,415)( 56,421)
( 57,418)( 58,417)( 59,423)( 60,420)( 61,416)( 62,422)( 63,419)( 64,406)
( 65,412)( 66,409)( 67,408)( 68,414)( 69,411)( 70,407)( 71,413)( 72,410)
( 73,424)( 74,430)( 75,427)( 76,426)( 77,432)( 78,429)( 79,425)( 80,431)
( 81,428)( 82,388)( 83,394)( 84,391)( 85,390)( 86,396)( 87,393)( 88,389)
( 89,395)( 90,392)( 91,379)( 92,385)( 93,382)( 94,381)( 95,387)( 96,384)
( 97,380)( 98,386)( 99,383)(100,397)(101,403)(102,400)(103,399)(104,405)
(105,402)(106,398)(107,404)(108,401)(109,550)(110,556)(111,553)(112,552)
(113,558)(114,555)(115,551)(116,557)(117,554)(118,541)(119,547)(120,544)
(121,543)(122,549)(123,546)(124,542)(125,548)(126,545)(127,559)(128,565)
(129,562)(130,561)(131,567)(132,564)(133,560)(134,566)(135,563)(136,577)
(137,583)(138,580)(139,579)(140,585)(141,582)(142,578)(143,584)(144,581)
(145,568)(146,574)(147,571)(148,570)(149,576)(150,573)(151,569)(152,575)
(153,572)(154,586)(155,592)(156,589)(157,588)(158,594)(159,591)(160,587)
(161,593)(162,590)(163,631)(164,637)(165,634)(166,633)(167,639)(168,636)
(169,632)(170,638)(171,635)(172,622)(173,628)(174,625)(175,624)(176,630)
(177,627)(178,623)(179,629)(180,626)(181,640)(182,646)(183,643)(184,642)
(185,648)(186,645)(187,641)(188,647)(189,644)(190,604)(191,610)(192,607)
(193,606)(194,612)(195,609)(196,605)(197,611)(198,608)(199,595)(200,601)
(201,598)(202,597)(203,603)(204,600)(205,596)(206,602)(207,599)(208,613)
(209,619)(210,616)(211,615)(212,621)(213,618)(214,614)(215,620)(216,617)
(217,442)(218,448)(219,445)(220,444)(221,450)(222,447)(223,443)(224,449)
(225,446)(226,433)(227,439)(228,436)(229,435)(230,441)(231,438)(232,434)
(233,440)(234,437)(235,451)(236,457)(237,454)(238,453)(239,459)(240,456)
(241,452)(242,458)(243,455)(244,469)(245,475)(246,472)(247,471)(248,477)
(249,474)(250,470)(251,476)(252,473)(253,460)(254,466)(255,463)(256,462)
(257,468)(258,465)(259,461)(260,467)(261,464)(262,478)(263,484)(264,481)
(265,480)(266,486)(267,483)(268,479)(269,485)(270,482)(271,523)(272,529)
(273,526)(274,525)(275,531)(276,528)(277,524)(278,530)(279,527)(280,514)
(281,520)(282,517)(283,516)(284,522)(285,519)(286,515)(287,521)(288,518)
(289,532)(290,538)(291,535)(292,534)(293,540)(294,537)(295,533)(296,539)
(297,536)(298,496)(299,502)(300,499)(301,498)(302,504)(303,501)(304,497)
(305,503)(306,500)(307,487)(308,493)(309,490)(310,489)(311,495)(312,492)
(313,488)(314,494)(315,491)(316,505)(317,511)(318,508)(319,507)(320,513)
(321,510)(322,506)(323,512)(324,509)(649,874)(650,880)(651,877)(652,876)
(653,882)(654,879)(655,875)(656,881)(657,878)(658,865)(659,871)(660,868)
(661,867)(662,873)(663,870)(664,866)(665,872)(666,869)(667,883)(668,889)
(669,886)(670,885)(671,891)(672,888)(673,884)(674,890)(675,887)(676,901)
(677,907)(678,904)(679,903)(680,909)(681,906)(682,902)(683,908)(684,905)
(685,892)(686,898)(687,895)(688,894)(689,900)(690,897)(691,893)(692,899)
(693,896)(694,910)(695,916)(696,913)(697,912)(698,918)(699,915)(700,911)
(701,917)(702,914)(703,955)(704,961)(705,958)(706,957)(707,963)(708,960)
(709,956)(710,962)(711,959)(712,946)(713,952)(714,949)(715,948)(716,954)
(717,951)(718,947)(719,953)(720,950)(721,964)(722,970)(723,967)(724,966)
(725,972)(726,969)(727,965)(728,971)(729,968)(730,928)(731,934)(732,931)
(733,930)(734,936)(735,933)(736,929)(737,935)(738,932)(739,919)(740,925)
(741,922)(742,921)(743,927)(744,924)(745,920)(746,926)(747,923)(748,937)
(749,943)(750,940)(751,939)(752,945)(753,942)(754,938)(755,944)(756,941)
(757,766)(758,772)(759,769)(760,768)(761,774)(762,771)(763,767)(764,773)
(765,770)(776,781)(777,778)(779,783)(784,793)(785,799)(786,796)(787,795)
(788,801)(789,798)(790,794)(791,800)(792,797)(803,808)(804,805)(806,810)
(811,847)(812,853)(813,850)(814,849)(815,855)(816,852)(817,848)(818,854)
(819,851)(820,838)(821,844)(822,841)(823,840)(824,846)(825,843)(826,839)
(827,845)(828,842)(829,856)(830,862)(831,859)(832,858)(833,864)(834,861)
(835,857)(836,863)(837,860);;
s2 := (  1, 97)(  2, 99)(  3, 98)(  4,106)(  5,108)(  6,107)(  7, 88)(  8, 90)
(  9, 89)( 10, 91)( 11, 93)( 12, 92)( 13,100)( 14,102)( 15,101)( 16, 82)
( 17, 84)( 18, 83)( 19, 94)( 20, 96)( 21, 95)( 22,103)( 23,105)( 24,104)
( 25, 85)( 26, 87)( 27, 86)( 28, 43)( 29, 45)( 30, 44)( 31, 52)( 32, 54)
( 33, 53)( 35, 36)( 38, 39)( 40, 46)( 41, 48)( 42, 47)( 50, 51)( 55, 70)
( 56, 72)( 57, 71)( 58, 79)( 59, 81)( 60, 80)( 62, 63)( 65, 66)( 67, 73)
( 68, 75)( 69, 74)( 77, 78)(109,313)(110,315)(111,314)(112,322)(113,324)
(114,323)(115,304)(116,306)(117,305)(118,307)(119,309)(120,308)(121,316)
(122,318)(123,317)(124,298)(125,300)(126,299)(127,310)(128,312)(129,311)
(130,319)(131,321)(132,320)(133,301)(134,303)(135,302)(136,259)(137,261)
(138,260)(139,268)(140,270)(141,269)(142,250)(143,252)(144,251)(145,253)
(146,255)(147,254)(148,262)(149,264)(150,263)(151,244)(152,246)(153,245)
(154,256)(155,258)(156,257)(157,265)(158,267)(159,266)(160,247)(161,249)
(162,248)(163,286)(164,288)(165,287)(166,295)(167,297)(168,296)(169,277)
(170,279)(171,278)(172,280)(173,282)(174,281)(175,289)(176,291)(177,290)
(178,271)(179,273)(180,272)(181,283)(182,285)(183,284)(184,292)(185,294)
(186,293)(187,274)(188,276)(189,275)(190,232)(191,234)(192,233)(193,241)
(194,243)(195,242)(196,223)(197,225)(198,224)(199,226)(200,228)(201,227)
(202,235)(203,237)(204,236)(205,217)(206,219)(207,218)(208,229)(209,231)
(210,230)(211,238)(212,240)(213,239)(214,220)(215,222)(216,221)(325,961)
(326,963)(327,962)(328,970)(329,972)(330,971)(331,952)(332,954)(333,953)
(334,955)(335,957)(336,956)(337,964)(338,966)(339,965)(340,946)(341,948)
(342,947)(343,958)(344,960)(345,959)(346,967)(347,969)(348,968)(349,949)
(350,951)(351,950)(352,907)(353,909)(354,908)(355,916)(356,918)(357,917)
(358,898)(359,900)(360,899)(361,901)(362,903)(363,902)(364,910)(365,912)
(366,911)(367,892)(368,894)(369,893)(370,904)(371,906)(372,905)(373,913)
(374,915)(375,914)(376,895)(377,897)(378,896)(379,934)(380,936)(381,935)
(382,943)(383,945)(384,944)(385,925)(386,927)(387,926)(388,928)(389,930)
(390,929)(391,937)(392,939)(393,938)(394,919)(395,921)(396,920)(397,931)
(398,933)(399,932)(400,940)(401,942)(402,941)(403,922)(404,924)(405,923)
(406,880)(407,882)(408,881)(409,889)(410,891)(411,890)(412,871)(413,873)
(414,872)(415,874)(416,876)(417,875)(418,883)(419,885)(420,884)(421,865)
(422,867)(423,866)(424,877)(425,879)(426,878)(427,886)(428,888)(429,887)
(430,868)(431,870)(432,869)(433,853)(434,855)(435,854)(436,862)(437,864)
(438,863)(439,844)(440,846)(441,845)(442,847)(443,849)(444,848)(445,856)
(446,858)(447,857)(448,838)(449,840)(450,839)(451,850)(452,852)(453,851)
(454,859)(455,861)(456,860)(457,841)(458,843)(459,842)(460,799)(461,801)
(462,800)(463,808)(464,810)(465,809)(466,790)(467,792)(468,791)(469,793)
(470,795)(471,794)(472,802)(473,804)(474,803)(475,784)(476,786)(477,785)
(478,796)(479,798)(480,797)(481,805)(482,807)(483,806)(484,787)(485,789)
(486,788)(487,826)(488,828)(489,827)(490,835)(491,837)(492,836)(493,817)
(494,819)(495,818)(496,820)(497,822)(498,821)(499,829)(500,831)(501,830)
(502,811)(503,813)(504,812)(505,823)(506,825)(507,824)(508,832)(509,834)
(510,833)(511,814)(512,816)(513,815)(514,772)(515,774)(516,773)(517,781)
(518,783)(519,782)(520,763)(521,765)(522,764)(523,766)(524,768)(525,767)
(526,775)(527,777)(528,776)(529,757)(530,759)(531,758)(532,769)(533,771)
(534,770)(535,778)(536,780)(537,779)(538,760)(539,762)(540,761)(541,745)
(542,747)(543,746)(544,754)(545,756)(546,755)(547,736)(548,738)(549,737)
(550,739)(551,741)(552,740)(553,748)(554,750)(555,749)(556,730)(557,732)
(558,731)(559,742)(560,744)(561,743)(562,751)(563,753)(564,752)(565,733)
(566,735)(567,734)(568,691)(569,693)(570,692)(571,700)(572,702)(573,701)
(574,682)(575,684)(576,683)(577,685)(578,687)(579,686)(580,694)(581,696)
(582,695)(583,676)(584,678)(585,677)(586,688)(587,690)(588,689)(589,697)
(590,699)(591,698)(592,679)(593,681)(594,680)(595,718)(596,720)(597,719)
(598,727)(599,729)(600,728)(601,709)(602,711)(603,710)(604,712)(605,714)
(606,713)(607,721)(608,723)(609,722)(610,703)(611,705)(612,704)(613,715)
(614,717)(615,716)(616,724)(617,726)(618,725)(619,706)(620,708)(621,707)
(622,664)(623,666)(624,665)(625,673)(626,675)(627,674)(628,655)(629,657)
(630,656)(631,658)(632,660)(633,659)(634,667)(635,669)(636,668)(637,649)
(638,651)(639,650)(640,661)(641,663)(642,662)(643,670)(644,672)(645,671)
(646,652)(647,654)(648,653);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(972)!(  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)
( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)
( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)
( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)
( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)
( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)
( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)
(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)
(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)
(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)
(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)
(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)
(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)
(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)
(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)
(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)
(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)
(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)
(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)
(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)
(325,865)(326,867)(327,866)(328,883)(329,885)(330,884)(331,874)(332,876)
(333,875)(334,871)(335,873)(336,872)(337,889)(338,891)(339,890)(340,880)
(341,882)(342,881)(343,868)(344,870)(345,869)(346,886)(347,888)(348,887)
(349,877)(350,879)(351,878)(352,919)(353,921)(354,920)(355,937)(356,939)
(357,938)(358,928)(359,930)(360,929)(361,925)(362,927)(363,926)(364,943)
(365,945)(366,944)(367,934)(368,936)(369,935)(370,922)(371,924)(372,923)
(373,940)(374,942)(375,941)(376,931)(377,933)(378,932)(379,892)(380,894)
(381,893)(382,910)(383,912)(384,911)(385,901)(386,903)(387,902)(388,898)
(389,900)(390,899)(391,916)(392,918)(393,917)(394,907)(395,909)(396,908)
(397,895)(398,897)(399,896)(400,913)(401,915)(402,914)(403,904)(404,906)
(405,905)(406,946)(407,948)(408,947)(409,964)(410,966)(411,965)(412,955)
(413,957)(414,956)(415,952)(416,954)(417,953)(418,970)(419,972)(420,971)
(421,961)(422,963)(423,962)(424,949)(425,951)(426,950)(427,967)(428,969)
(429,968)(430,958)(431,960)(432,959)(433,757)(434,759)(435,758)(436,775)
(437,777)(438,776)(439,766)(440,768)(441,767)(442,763)(443,765)(444,764)
(445,781)(446,783)(447,782)(448,772)(449,774)(450,773)(451,760)(452,762)
(453,761)(454,778)(455,780)(456,779)(457,769)(458,771)(459,770)(460,811)
(461,813)(462,812)(463,829)(464,831)(465,830)(466,820)(467,822)(468,821)
(469,817)(470,819)(471,818)(472,835)(473,837)(474,836)(475,826)(476,828)
(477,827)(478,814)(479,816)(480,815)(481,832)(482,834)(483,833)(484,823)
(485,825)(486,824)(487,784)(488,786)(489,785)(490,802)(491,804)(492,803)
(493,793)(494,795)(495,794)(496,790)(497,792)(498,791)(499,808)(500,810)
(501,809)(502,799)(503,801)(504,800)(505,787)(506,789)(507,788)(508,805)
(509,807)(510,806)(511,796)(512,798)(513,797)(514,838)(515,840)(516,839)
(517,856)(518,858)(519,857)(520,847)(521,849)(522,848)(523,844)(524,846)
(525,845)(526,862)(527,864)(528,863)(529,853)(530,855)(531,854)(532,841)
(533,843)(534,842)(535,859)(536,861)(537,860)(538,850)(539,852)(540,851)
(541,649)(542,651)(543,650)(544,667)(545,669)(546,668)(547,658)(548,660)
(549,659)(550,655)(551,657)(552,656)(553,673)(554,675)(555,674)(556,664)
(557,666)(558,665)(559,652)(560,654)(561,653)(562,670)(563,672)(564,671)
(565,661)(566,663)(567,662)(568,703)(569,705)(570,704)(571,721)(572,723)
(573,722)(574,712)(575,714)(576,713)(577,709)(578,711)(579,710)(580,727)
(581,729)(582,728)(583,718)(584,720)(585,719)(586,706)(587,708)(588,707)
(589,724)(590,726)(591,725)(592,715)(593,717)(594,716)(595,676)(596,678)
(597,677)(598,694)(599,696)(600,695)(601,685)(602,687)(603,686)(604,682)
(605,684)(606,683)(607,700)(608,702)(609,701)(610,691)(611,693)(612,692)
(613,679)(614,681)(615,680)(616,697)(617,699)(618,698)(619,688)(620,690)
(621,689)(622,730)(623,732)(624,731)(625,748)(626,750)(627,749)(628,739)
(629,741)(630,740)(631,736)(632,738)(633,737)(634,754)(635,756)(636,755)
(637,745)(638,747)(639,746)(640,733)(641,735)(642,734)(643,751)(644,753)
(645,752)(646,742)(647,744)(648,743);
s1 := Sym(972)!(  1,334)(  2,340)(  3,337)(  4,336)(  5,342)(  6,339)(  7,335)
(  8,341)(  9,338)( 10,325)( 11,331)( 12,328)( 13,327)( 14,333)( 15,330)
( 16,326)( 17,332)( 18,329)( 19,343)( 20,349)( 21,346)( 22,345)( 23,351)
( 24,348)( 25,344)( 26,350)( 27,347)( 28,361)( 29,367)( 30,364)( 31,363)
( 32,369)( 33,366)( 34,362)( 35,368)( 36,365)( 37,352)( 38,358)( 39,355)
( 40,354)( 41,360)( 42,357)( 43,353)( 44,359)( 45,356)( 46,370)( 47,376)
( 48,373)( 49,372)( 50,378)( 51,375)( 52,371)( 53,377)( 54,374)( 55,415)
( 56,421)( 57,418)( 58,417)( 59,423)( 60,420)( 61,416)( 62,422)( 63,419)
( 64,406)( 65,412)( 66,409)( 67,408)( 68,414)( 69,411)( 70,407)( 71,413)
( 72,410)( 73,424)( 74,430)( 75,427)( 76,426)( 77,432)( 78,429)( 79,425)
( 80,431)( 81,428)( 82,388)( 83,394)( 84,391)( 85,390)( 86,396)( 87,393)
( 88,389)( 89,395)( 90,392)( 91,379)( 92,385)( 93,382)( 94,381)( 95,387)
( 96,384)( 97,380)( 98,386)( 99,383)(100,397)(101,403)(102,400)(103,399)
(104,405)(105,402)(106,398)(107,404)(108,401)(109,550)(110,556)(111,553)
(112,552)(113,558)(114,555)(115,551)(116,557)(117,554)(118,541)(119,547)
(120,544)(121,543)(122,549)(123,546)(124,542)(125,548)(126,545)(127,559)
(128,565)(129,562)(130,561)(131,567)(132,564)(133,560)(134,566)(135,563)
(136,577)(137,583)(138,580)(139,579)(140,585)(141,582)(142,578)(143,584)
(144,581)(145,568)(146,574)(147,571)(148,570)(149,576)(150,573)(151,569)
(152,575)(153,572)(154,586)(155,592)(156,589)(157,588)(158,594)(159,591)
(160,587)(161,593)(162,590)(163,631)(164,637)(165,634)(166,633)(167,639)
(168,636)(169,632)(170,638)(171,635)(172,622)(173,628)(174,625)(175,624)
(176,630)(177,627)(178,623)(179,629)(180,626)(181,640)(182,646)(183,643)
(184,642)(185,648)(186,645)(187,641)(188,647)(189,644)(190,604)(191,610)
(192,607)(193,606)(194,612)(195,609)(196,605)(197,611)(198,608)(199,595)
(200,601)(201,598)(202,597)(203,603)(204,600)(205,596)(206,602)(207,599)
(208,613)(209,619)(210,616)(211,615)(212,621)(213,618)(214,614)(215,620)
(216,617)(217,442)(218,448)(219,445)(220,444)(221,450)(222,447)(223,443)
(224,449)(225,446)(226,433)(227,439)(228,436)(229,435)(230,441)(231,438)
(232,434)(233,440)(234,437)(235,451)(236,457)(237,454)(238,453)(239,459)
(240,456)(241,452)(242,458)(243,455)(244,469)(245,475)(246,472)(247,471)
(248,477)(249,474)(250,470)(251,476)(252,473)(253,460)(254,466)(255,463)
(256,462)(257,468)(258,465)(259,461)(260,467)(261,464)(262,478)(263,484)
(264,481)(265,480)(266,486)(267,483)(268,479)(269,485)(270,482)(271,523)
(272,529)(273,526)(274,525)(275,531)(276,528)(277,524)(278,530)(279,527)
(280,514)(281,520)(282,517)(283,516)(284,522)(285,519)(286,515)(287,521)
(288,518)(289,532)(290,538)(291,535)(292,534)(293,540)(294,537)(295,533)
(296,539)(297,536)(298,496)(299,502)(300,499)(301,498)(302,504)(303,501)
(304,497)(305,503)(306,500)(307,487)(308,493)(309,490)(310,489)(311,495)
(312,492)(313,488)(314,494)(315,491)(316,505)(317,511)(318,508)(319,507)
(320,513)(321,510)(322,506)(323,512)(324,509)(649,874)(650,880)(651,877)
(652,876)(653,882)(654,879)(655,875)(656,881)(657,878)(658,865)(659,871)
(660,868)(661,867)(662,873)(663,870)(664,866)(665,872)(666,869)(667,883)
(668,889)(669,886)(670,885)(671,891)(672,888)(673,884)(674,890)(675,887)
(676,901)(677,907)(678,904)(679,903)(680,909)(681,906)(682,902)(683,908)
(684,905)(685,892)(686,898)(687,895)(688,894)(689,900)(690,897)(691,893)
(692,899)(693,896)(694,910)(695,916)(696,913)(697,912)(698,918)(699,915)
(700,911)(701,917)(702,914)(703,955)(704,961)(705,958)(706,957)(707,963)
(708,960)(709,956)(710,962)(711,959)(712,946)(713,952)(714,949)(715,948)
(716,954)(717,951)(718,947)(719,953)(720,950)(721,964)(722,970)(723,967)
(724,966)(725,972)(726,969)(727,965)(728,971)(729,968)(730,928)(731,934)
(732,931)(733,930)(734,936)(735,933)(736,929)(737,935)(738,932)(739,919)
(740,925)(741,922)(742,921)(743,927)(744,924)(745,920)(746,926)(747,923)
(748,937)(749,943)(750,940)(751,939)(752,945)(753,942)(754,938)(755,944)
(756,941)(757,766)(758,772)(759,769)(760,768)(761,774)(762,771)(763,767)
(764,773)(765,770)(776,781)(777,778)(779,783)(784,793)(785,799)(786,796)
(787,795)(788,801)(789,798)(790,794)(791,800)(792,797)(803,808)(804,805)
(806,810)(811,847)(812,853)(813,850)(814,849)(815,855)(816,852)(817,848)
(818,854)(819,851)(820,838)(821,844)(822,841)(823,840)(824,846)(825,843)
(826,839)(827,845)(828,842)(829,856)(830,862)(831,859)(832,858)(833,864)
(834,861)(835,857)(836,863)(837,860);
s2 := Sym(972)!(  1, 97)(  2, 99)(  3, 98)(  4,106)(  5,108)(  6,107)(  7, 88)
(  8, 90)(  9, 89)( 10, 91)( 11, 93)( 12, 92)( 13,100)( 14,102)( 15,101)
( 16, 82)( 17, 84)( 18, 83)( 19, 94)( 20, 96)( 21, 95)( 22,103)( 23,105)
( 24,104)( 25, 85)( 26, 87)( 27, 86)( 28, 43)( 29, 45)( 30, 44)( 31, 52)
( 32, 54)( 33, 53)( 35, 36)( 38, 39)( 40, 46)( 41, 48)( 42, 47)( 50, 51)
( 55, 70)( 56, 72)( 57, 71)( 58, 79)( 59, 81)( 60, 80)( 62, 63)( 65, 66)
( 67, 73)( 68, 75)( 69, 74)( 77, 78)(109,313)(110,315)(111,314)(112,322)
(113,324)(114,323)(115,304)(116,306)(117,305)(118,307)(119,309)(120,308)
(121,316)(122,318)(123,317)(124,298)(125,300)(126,299)(127,310)(128,312)
(129,311)(130,319)(131,321)(132,320)(133,301)(134,303)(135,302)(136,259)
(137,261)(138,260)(139,268)(140,270)(141,269)(142,250)(143,252)(144,251)
(145,253)(146,255)(147,254)(148,262)(149,264)(150,263)(151,244)(152,246)
(153,245)(154,256)(155,258)(156,257)(157,265)(158,267)(159,266)(160,247)
(161,249)(162,248)(163,286)(164,288)(165,287)(166,295)(167,297)(168,296)
(169,277)(170,279)(171,278)(172,280)(173,282)(174,281)(175,289)(176,291)
(177,290)(178,271)(179,273)(180,272)(181,283)(182,285)(183,284)(184,292)
(185,294)(186,293)(187,274)(188,276)(189,275)(190,232)(191,234)(192,233)
(193,241)(194,243)(195,242)(196,223)(197,225)(198,224)(199,226)(200,228)
(201,227)(202,235)(203,237)(204,236)(205,217)(206,219)(207,218)(208,229)
(209,231)(210,230)(211,238)(212,240)(213,239)(214,220)(215,222)(216,221)
(325,961)(326,963)(327,962)(328,970)(329,972)(330,971)(331,952)(332,954)
(333,953)(334,955)(335,957)(336,956)(337,964)(338,966)(339,965)(340,946)
(341,948)(342,947)(343,958)(344,960)(345,959)(346,967)(347,969)(348,968)
(349,949)(350,951)(351,950)(352,907)(353,909)(354,908)(355,916)(356,918)
(357,917)(358,898)(359,900)(360,899)(361,901)(362,903)(363,902)(364,910)
(365,912)(366,911)(367,892)(368,894)(369,893)(370,904)(371,906)(372,905)
(373,913)(374,915)(375,914)(376,895)(377,897)(378,896)(379,934)(380,936)
(381,935)(382,943)(383,945)(384,944)(385,925)(386,927)(387,926)(388,928)
(389,930)(390,929)(391,937)(392,939)(393,938)(394,919)(395,921)(396,920)
(397,931)(398,933)(399,932)(400,940)(401,942)(402,941)(403,922)(404,924)
(405,923)(406,880)(407,882)(408,881)(409,889)(410,891)(411,890)(412,871)
(413,873)(414,872)(415,874)(416,876)(417,875)(418,883)(419,885)(420,884)
(421,865)(422,867)(423,866)(424,877)(425,879)(426,878)(427,886)(428,888)
(429,887)(430,868)(431,870)(432,869)(433,853)(434,855)(435,854)(436,862)
(437,864)(438,863)(439,844)(440,846)(441,845)(442,847)(443,849)(444,848)
(445,856)(446,858)(447,857)(448,838)(449,840)(450,839)(451,850)(452,852)
(453,851)(454,859)(455,861)(456,860)(457,841)(458,843)(459,842)(460,799)
(461,801)(462,800)(463,808)(464,810)(465,809)(466,790)(467,792)(468,791)
(469,793)(470,795)(471,794)(472,802)(473,804)(474,803)(475,784)(476,786)
(477,785)(478,796)(479,798)(480,797)(481,805)(482,807)(483,806)(484,787)
(485,789)(486,788)(487,826)(488,828)(489,827)(490,835)(491,837)(492,836)
(493,817)(494,819)(495,818)(496,820)(497,822)(498,821)(499,829)(500,831)
(501,830)(502,811)(503,813)(504,812)(505,823)(506,825)(507,824)(508,832)
(509,834)(510,833)(511,814)(512,816)(513,815)(514,772)(515,774)(516,773)
(517,781)(518,783)(519,782)(520,763)(521,765)(522,764)(523,766)(524,768)
(525,767)(526,775)(527,777)(528,776)(529,757)(530,759)(531,758)(532,769)
(533,771)(534,770)(535,778)(536,780)(537,779)(538,760)(539,762)(540,761)
(541,745)(542,747)(543,746)(544,754)(545,756)(546,755)(547,736)(548,738)
(549,737)(550,739)(551,741)(552,740)(553,748)(554,750)(555,749)(556,730)
(557,732)(558,731)(559,742)(560,744)(561,743)(562,751)(563,753)(564,752)
(565,733)(566,735)(567,734)(568,691)(569,693)(570,692)(571,700)(572,702)
(573,701)(574,682)(575,684)(576,683)(577,685)(578,687)(579,686)(580,694)
(581,696)(582,695)(583,676)(584,678)(585,677)(586,688)(587,690)(588,689)
(589,697)(590,699)(591,698)(592,679)(593,681)(594,680)(595,718)(596,720)
(597,719)(598,727)(599,729)(600,728)(601,709)(602,711)(603,710)(604,712)
(605,714)(606,713)(607,721)(608,723)(609,722)(610,703)(611,705)(612,704)
(613,715)(614,717)(615,716)(616,724)(617,726)(618,725)(619,706)(620,708)
(621,707)(622,664)(623,666)(624,665)(625,673)(626,675)(627,674)(628,655)
(629,657)(630,656)(631,658)(632,660)(633,659)(634,667)(635,669)(636,668)
(637,649)(638,651)(639,650)(640,661)(641,663)(642,662)(643,670)(644,672)
(645,671)(646,652)(647,654)(648,653);
poly := sub<Sym(972)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 >;

```
References : None.
to this polytope