Polytope of Type {122,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {122,8}*1952
Also Known As : {122,8|2}. if this polytope has another name.
Group : SmallGroup(1952,155)
Rank : 3
Schlafli Type : {122,8}
Number of vertices, edges, etc : 122, 488, 8
Order of s0s1s2 : 488
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {122,4}*976
4-fold quotients : {122,2}*488
8-fold quotients : {61,2}*244
61-fold quotients : {2,8}*32
122-fold quotients : {2,4}*16
244-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,245)( 2,305)( 3,304)( 4,303)( 5,302)( 6,301)( 7,300)( 8,299)
( 9,298)( 10,297)( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)( 16,291)
( 17,290)( 18,289)( 19,288)( 20,287)( 21,286)( 22,285)( 23,284)( 24,283)
( 25,282)( 26,281)( 27,280)( 28,279)( 29,278)( 30,277)( 31,276)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,271)( 37,270)( 38,269)( 39,268)( 40,267)
( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)( 48,259)
( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)( 56,251)
( 57,250)( 58,249)( 59,248)( 60,247)( 61,246)( 62,306)( 63,366)( 64,365)
( 65,364)( 66,363)( 67,362)( 68,361)( 69,360)( 70,359)( 71,358)( 72,357)
( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,351)( 79,350)( 80,349)
( 81,348)( 82,347)( 83,346)( 84,345)( 85,344)( 86,343)( 87,342)( 88,341)
( 89,340)( 90,339)( 91,338)( 92,337)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,332)( 98,331)( 99,330)(100,329)(101,328)(102,327)(103,326)(104,325)
(105,324)(106,323)(107,322)(108,321)(109,320)(110,319)(111,318)(112,317)
(113,316)(114,315)(115,314)(116,313)(117,312)(118,311)(119,310)(120,309)
(121,308)(122,307)(123,367)(124,427)(125,426)(126,425)(127,424)(128,423)
(129,422)(130,421)(131,420)(132,419)(133,418)(134,417)(135,416)(136,415)
(137,414)(138,413)(139,412)(140,411)(141,410)(142,409)(143,408)(144,407)
(145,406)(146,405)(147,404)(148,403)(149,402)(150,401)(151,400)(152,399)
(153,398)(154,397)(155,396)(156,395)(157,394)(158,393)(159,392)(160,391)
(161,390)(162,389)(163,388)(164,387)(165,386)(166,385)(167,384)(168,383)
(169,382)(170,381)(171,380)(172,379)(173,378)(174,377)(175,376)(176,375)
(177,374)(178,373)(179,372)(180,371)(181,370)(182,369)(183,368)(184,428)
(185,488)(186,487)(187,486)(188,485)(189,484)(190,483)(191,482)(192,481)
(193,480)(194,479)(195,478)(196,477)(197,476)(198,475)(199,474)(200,473)
(201,472)(202,471)(203,470)(204,469)(205,468)(206,467)(207,466)(208,465)
(209,464)(210,463)(211,462)(212,461)(213,460)(214,459)(215,458)(216,457)
(217,456)(218,455)(219,454)(220,453)(221,452)(222,451)(223,450)(224,449)
(225,448)(226,447)(227,446)(228,445)(229,444)(230,443)(231,442)(232,441)
(233,440)(234,439)(235,438)(236,437)(237,436)(238,435)(239,434)(240,433)
(241,432)(242,431)(243,430)(244,429)(489,733)(490,793)(491,792)(492,791)
(493,790)(494,789)(495,788)(496,787)(497,786)(498,785)(499,784)(500,783)
(501,782)(502,781)(503,780)(504,779)(505,778)(506,777)(507,776)(508,775)
(509,774)(510,773)(511,772)(512,771)(513,770)(514,769)(515,768)(516,767)
(517,766)(518,765)(519,764)(520,763)(521,762)(522,761)(523,760)(524,759)
(525,758)(526,757)(527,756)(528,755)(529,754)(530,753)(531,752)(532,751)
(533,750)(534,749)(535,748)(536,747)(537,746)(538,745)(539,744)(540,743)
(541,742)(542,741)(543,740)(544,739)(545,738)(546,737)(547,736)(548,735)
(549,734)(550,794)(551,854)(552,853)(553,852)(554,851)(555,850)(556,849)
(557,848)(558,847)(559,846)(560,845)(561,844)(562,843)(563,842)(564,841)
(565,840)(566,839)(567,838)(568,837)(569,836)(570,835)(571,834)(572,833)
(573,832)(574,831)(575,830)(576,829)(577,828)(578,827)(579,826)(580,825)
(581,824)(582,823)(583,822)(584,821)(585,820)(586,819)(587,818)(588,817)
(589,816)(590,815)(591,814)(592,813)(593,812)(594,811)(595,810)(596,809)
(597,808)(598,807)(599,806)(600,805)(601,804)(602,803)(603,802)(604,801)
(605,800)(606,799)(607,798)(608,797)(609,796)(610,795)(611,855)(612,915)
(613,914)(614,913)(615,912)(616,911)(617,910)(618,909)(619,908)(620,907)
(621,906)(622,905)(623,904)(624,903)(625,902)(626,901)(627,900)(628,899)
(629,898)(630,897)(631,896)(632,895)(633,894)(634,893)(635,892)(636,891)
(637,890)(638,889)(639,888)(640,887)(641,886)(642,885)(643,884)(644,883)
(645,882)(646,881)(647,880)(648,879)(649,878)(650,877)(651,876)(652,875)
(653,874)(654,873)(655,872)(656,871)(657,870)(658,869)(659,868)(660,867)
(661,866)(662,865)(663,864)(664,863)(665,862)(666,861)(667,860)(668,859)
(669,858)(670,857)(671,856)(672,916)(673,976)(674,975)(675,974)(676,973)
(677,972)(678,971)(679,970)(680,969)(681,968)(682,967)(683,966)(684,965)
(685,964)(686,963)(687,962)(688,961)(689,960)(690,959)(691,958)(692,957)
(693,956)(694,955)(695,954)(696,953)(697,952)(698,951)(699,950)(700,949)
(701,948)(702,947)(703,946)(704,945)(705,944)(706,943)(707,942)(708,941)
(709,940)(710,939)(711,938)(712,937)(713,936)(714,935)(715,934)(716,933)
(717,932)(718,931)(719,930)(720,929)(721,928)(722,927)(723,926)(724,925)
(725,924)(726,923)(727,922)(728,921)(729,920)(730,919)(731,918)(732,917);;
s1 := ( 1,246)( 2,245)( 3,305)( 4,304)( 5,303)( 6,302)( 7,301)( 8,300)
( 9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)( 16,292)
( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)( 24,284)
( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)( 32,276)
( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)( 40,268)
( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)( 48,260)
( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)( 56,252)
( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,307)( 63,306)( 64,366)
( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)( 72,358)
( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)( 80,350)
( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)( 88,342)
( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)( 96,334)
( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)(112,318)
(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)(120,310)
(121,309)(122,308)(123,429)(124,428)(125,488)(126,487)(127,486)(128,485)
(129,484)(130,483)(131,482)(132,481)(133,480)(134,479)(135,478)(136,477)
(137,476)(138,475)(139,474)(140,473)(141,472)(142,471)(143,470)(144,469)
(145,468)(146,467)(147,466)(148,465)(149,464)(150,463)(151,462)(152,461)
(153,460)(154,459)(155,458)(156,457)(157,456)(158,455)(159,454)(160,453)
(161,452)(162,451)(163,450)(164,449)(165,448)(166,447)(167,446)(168,445)
(169,444)(170,443)(171,442)(172,441)(173,440)(174,439)(175,438)(176,437)
(177,436)(178,435)(179,434)(180,433)(181,432)(182,431)(183,430)(184,368)
(185,367)(186,427)(187,426)(188,425)(189,424)(190,423)(191,422)(192,421)
(193,420)(194,419)(195,418)(196,417)(197,416)(198,415)(199,414)(200,413)
(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)(208,405)
(209,404)(210,403)(211,402)(212,401)(213,400)(214,399)(215,398)(216,397)
(217,396)(218,395)(219,394)(220,393)(221,392)(222,391)(223,390)(224,389)
(225,388)(226,387)(227,386)(228,385)(229,384)(230,383)(231,382)(232,381)
(233,380)(234,379)(235,378)(236,377)(237,376)(238,375)(239,374)(240,373)
(241,372)(242,371)(243,370)(244,369)(489,856)(490,855)(491,915)(492,914)
(493,913)(494,912)(495,911)(496,910)(497,909)(498,908)(499,907)(500,906)
(501,905)(502,904)(503,903)(504,902)(505,901)(506,900)(507,899)(508,898)
(509,897)(510,896)(511,895)(512,894)(513,893)(514,892)(515,891)(516,890)
(517,889)(518,888)(519,887)(520,886)(521,885)(522,884)(523,883)(524,882)
(525,881)(526,880)(527,879)(528,878)(529,877)(530,876)(531,875)(532,874)
(533,873)(534,872)(535,871)(536,870)(537,869)(538,868)(539,867)(540,866)
(541,865)(542,864)(543,863)(544,862)(545,861)(546,860)(547,859)(548,858)
(549,857)(550,917)(551,916)(552,976)(553,975)(554,974)(555,973)(556,972)
(557,971)(558,970)(559,969)(560,968)(561,967)(562,966)(563,965)(564,964)
(565,963)(566,962)(567,961)(568,960)(569,959)(570,958)(571,957)(572,956)
(573,955)(574,954)(575,953)(576,952)(577,951)(578,950)(579,949)(580,948)
(581,947)(582,946)(583,945)(584,944)(585,943)(586,942)(587,941)(588,940)
(589,939)(590,938)(591,937)(592,936)(593,935)(594,934)(595,933)(596,932)
(597,931)(598,930)(599,929)(600,928)(601,927)(602,926)(603,925)(604,924)
(605,923)(606,922)(607,921)(608,920)(609,919)(610,918)(611,734)(612,733)
(613,793)(614,792)(615,791)(616,790)(617,789)(618,788)(619,787)(620,786)
(621,785)(622,784)(623,783)(624,782)(625,781)(626,780)(627,779)(628,778)
(629,777)(630,776)(631,775)(632,774)(633,773)(634,772)(635,771)(636,770)
(637,769)(638,768)(639,767)(640,766)(641,765)(642,764)(643,763)(644,762)
(645,761)(646,760)(647,759)(648,758)(649,757)(650,756)(651,755)(652,754)
(653,753)(654,752)(655,751)(656,750)(657,749)(658,748)(659,747)(660,746)
(661,745)(662,744)(663,743)(664,742)(665,741)(666,740)(667,739)(668,738)
(669,737)(670,736)(671,735)(672,795)(673,794)(674,854)(675,853)(676,852)
(677,851)(678,850)(679,849)(680,848)(681,847)(682,846)(683,845)(684,844)
(685,843)(686,842)(687,841)(688,840)(689,839)(690,838)(691,837)(692,836)
(693,835)(694,834)(695,833)(696,832)(697,831)(698,830)(699,829)(700,828)
(701,827)(702,826)(703,825)(704,824)(705,823)(706,822)(707,821)(708,820)
(709,819)(710,818)(711,817)(712,816)(713,815)(714,814)(715,813)(716,812)
(717,811)(718,810)(719,809)(720,808)(721,807)(722,806)(723,805)(724,804)
(725,803)(726,802)(727,801)(728,800)(729,799)(730,798)(731,797)(732,796);;
s2 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)
( 9,497)( 10,498)( 11,499)( 12,500)( 13,501)( 14,502)( 15,503)( 16,504)
( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)( 24,512)
( 25,513)( 26,514)( 27,515)( 28,516)( 29,517)( 30,518)( 31,519)( 32,520)
( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)
( 41,529)( 42,530)( 43,531)( 44,532)( 45,533)( 46,534)( 47,535)( 48,536)
( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)( 56,544)
( 57,545)( 58,546)( 59,547)( 60,548)( 61,549)( 62,550)( 63,551)( 64,552)
( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)
( 73,561)( 74,562)( 75,563)( 76,564)( 77,565)( 78,566)( 79,567)( 80,568)
( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)( 88,576)
( 89,577)( 90,578)( 91,579)( 92,580)( 93,581)( 94,582)( 95,583)( 96,584)
( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)
(105,593)(106,594)(107,595)(108,596)(109,597)(110,598)(111,599)(112,600)
(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)(120,608)
(121,609)(122,610)(123,672)(124,673)(125,674)(126,675)(127,676)(128,677)
(129,678)(130,679)(131,680)(132,681)(133,682)(134,683)(135,684)(136,685)
(137,686)(138,687)(139,688)(140,689)(141,690)(142,691)(143,692)(144,693)
(145,694)(146,695)(147,696)(148,697)(149,698)(150,699)(151,700)(152,701)
(153,702)(154,703)(155,704)(156,705)(157,706)(158,707)(159,708)(160,709)
(161,710)(162,711)(163,712)(164,713)(165,714)(166,715)(167,716)(168,717)
(169,718)(170,719)(171,720)(172,721)(173,722)(174,723)(175,724)(176,725)
(177,726)(178,727)(179,728)(180,729)(181,730)(182,731)(183,732)(184,611)
(185,612)(186,613)(187,614)(188,615)(189,616)(190,617)(191,618)(192,619)
(193,620)(194,621)(195,622)(196,623)(197,624)(198,625)(199,626)(200,627)
(201,628)(202,629)(203,630)(204,631)(205,632)(206,633)(207,634)(208,635)
(209,636)(210,637)(211,638)(212,639)(213,640)(214,641)(215,642)(216,643)
(217,644)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)
(225,652)(226,653)(227,654)(228,655)(229,656)(230,657)(231,658)(232,659)
(233,660)(234,661)(235,662)(236,663)(237,664)(238,665)(239,666)(240,667)
(241,668)(242,669)(243,670)(244,671)(245,733)(246,734)(247,735)(248,736)
(249,737)(250,738)(251,739)(252,740)(253,741)(254,742)(255,743)(256,744)
(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)
(265,753)(266,754)(267,755)(268,756)(269,757)(270,758)(271,759)(272,760)
(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)(280,768)
(281,769)(282,770)(283,771)(284,772)(285,773)(286,774)(287,775)(288,776)
(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)
(297,785)(298,786)(299,787)(300,788)(301,789)(302,790)(303,791)(304,792)
(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)(312,800)
(313,801)(314,802)(315,803)(316,804)(317,805)(318,806)(319,807)(320,808)
(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)
(329,817)(330,818)(331,819)(332,820)(333,821)(334,822)(335,823)(336,824)
(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)(344,832)
(345,833)(346,834)(347,835)(348,836)(349,837)(350,838)(351,839)(352,840)
(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)
(361,849)(362,850)(363,851)(364,852)(365,853)(366,854)(367,916)(368,917)
(369,918)(370,919)(371,920)(372,921)(373,922)(374,923)(375,924)(376,925)
(377,926)(378,927)(379,928)(380,929)(381,930)(382,931)(383,932)(384,933)
(385,934)(386,935)(387,936)(388,937)(389,938)(390,939)(391,940)(392,941)
(393,942)(394,943)(395,944)(396,945)(397,946)(398,947)(399,948)(400,949)
(401,950)(402,951)(403,952)(404,953)(405,954)(406,955)(407,956)(408,957)
(409,958)(410,959)(411,960)(412,961)(413,962)(414,963)(415,964)(416,965)
(417,966)(418,967)(419,968)(420,969)(421,970)(422,971)(423,972)(424,973)
(425,974)(426,975)(427,976)(428,855)(429,856)(430,857)(431,858)(432,859)
(433,860)(434,861)(435,862)(436,863)(437,864)(438,865)(439,866)(440,867)
(441,868)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875)
(449,876)(450,877)(451,878)(452,879)(453,880)(454,881)(455,882)(456,883)
(457,884)(458,885)(459,886)(460,887)(461,888)(462,889)(463,890)(464,891)
(465,892)(466,893)(467,894)(468,895)(469,896)(470,897)(471,898)(472,899)
(473,900)(474,901)(475,902)(476,903)(477,904)(478,905)(479,906)(480,907)
(481,908)(482,909)(483,910)(484,911)(485,912)(486,913)(487,914)(488,915);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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(976)!( 1,245)( 2,305)( 3,304)( 4,303)( 5,302)( 6,301)( 7,300)
( 8,299)( 9,298)( 10,297)( 11,296)( 12,295)( 13,294)( 14,293)( 15,292)
( 16,291)( 17,290)( 18,289)( 19,288)( 20,287)( 21,286)( 22,285)( 23,284)
( 24,283)( 25,282)( 26,281)( 27,280)( 28,279)( 29,278)( 30,277)( 31,276)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,271)( 37,270)( 38,269)( 39,268)
( 40,267)( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)
( 48,259)( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,251)( 57,250)( 58,249)( 59,248)( 60,247)( 61,246)( 62,306)( 63,366)
( 64,365)( 65,364)( 66,363)( 67,362)( 68,361)( 69,360)( 70,359)( 71,358)
( 72,357)( 73,356)( 74,355)( 75,354)( 76,353)( 77,352)( 78,351)( 79,350)
( 80,349)( 81,348)( 82,347)( 83,346)( 84,345)( 85,344)( 86,343)( 87,342)
( 88,341)( 89,340)( 90,339)( 91,338)( 92,337)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,332)( 98,331)( 99,330)(100,329)(101,328)(102,327)(103,326)
(104,325)(105,324)(106,323)(107,322)(108,321)(109,320)(110,319)(111,318)
(112,317)(113,316)(114,315)(115,314)(116,313)(117,312)(118,311)(119,310)
(120,309)(121,308)(122,307)(123,367)(124,427)(125,426)(126,425)(127,424)
(128,423)(129,422)(130,421)(131,420)(132,419)(133,418)(134,417)(135,416)
(136,415)(137,414)(138,413)(139,412)(140,411)(141,410)(142,409)(143,408)
(144,407)(145,406)(146,405)(147,404)(148,403)(149,402)(150,401)(151,400)
(152,399)(153,398)(154,397)(155,396)(156,395)(157,394)(158,393)(159,392)
(160,391)(161,390)(162,389)(163,388)(164,387)(165,386)(166,385)(167,384)
(168,383)(169,382)(170,381)(171,380)(172,379)(173,378)(174,377)(175,376)
(176,375)(177,374)(178,373)(179,372)(180,371)(181,370)(182,369)(183,368)
(184,428)(185,488)(186,487)(187,486)(188,485)(189,484)(190,483)(191,482)
(192,481)(193,480)(194,479)(195,478)(196,477)(197,476)(198,475)(199,474)
(200,473)(201,472)(202,471)(203,470)(204,469)(205,468)(206,467)(207,466)
(208,465)(209,464)(210,463)(211,462)(212,461)(213,460)(214,459)(215,458)
(216,457)(217,456)(218,455)(219,454)(220,453)(221,452)(222,451)(223,450)
(224,449)(225,448)(226,447)(227,446)(228,445)(229,444)(230,443)(231,442)
(232,441)(233,440)(234,439)(235,438)(236,437)(237,436)(238,435)(239,434)
(240,433)(241,432)(242,431)(243,430)(244,429)(489,733)(490,793)(491,792)
(492,791)(493,790)(494,789)(495,788)(496,787)(497,786)(498,785)(499,784)
(500,783)(501,782)(502,781)(503,780)(504,779)(505,778)(506,777)(507,776)
(508,775)(509,774)(510,773)(511,772)(512,771)(513,770)(514,769)(515,768)
(516,767)(517,766)(518,765)(519,764)(520,763)(521,762)(522,761)(523,760)
(524,759)(525,758)(526,757)(527,756)(528,755)(529,754)(530,753)(531,752)
(532,751)(533,750)(534,749)(535,748)(536,747)(537,746)(538,745)(539,744)
(540,743)(541,742)(542,741)(543,740)(544,739)(545,738)(546,737)(547,736)
(548,735)(549,734)(550,794)(551,854)(552,853)(553,852)(554,851)(555,850)
(556,849)(557,848)(558,847)(559,846)(560,845)(561,844)(562,843)(563,842)
(564,841)(565,840)(566,839)(567,838)(568,837)(569,836)(570,835)(571,834)
(572,833)(573,832)(574,831)(575,830)(576,829)(577,828)(578,827)(579,826)
(580,825)(581,824)(582,823)(583,822)(584,821)(585,820)(586,819)(587,818)
(588,817)(589,816)(590,815)(591,814)(592,813)(593,812)(594,811)(595,810)
(596,809)(597,808)(598,807)(599,806)(600,805)(601,804)(602,803)(603,802)
(604,801)(605,800)(606,799)(607,798)(608,797)(609,796)(610,795)(611,855)
(612,915)(613,914)(614,913)(615,912)(616,911)(617,910)(618,909)(619,908)
(620,907)(621,906)(622,905)(623,904)(624,903)(625,902)(626,901)(627,900)
(628,899)(629,898)(630,897)(631,896)(632,895)(633,894)(634,893)(635,892)
(636,891)(637,890)(638,889)(639,888)(640,887)(641,886)(642,885)(643,884)
(644,883)(645,882)(646,881)(647,880)(648,879)(649,878)(650,877)(651,876)
(652,875)(653,874)(654,873)(655,872)(656,871)(657,870)(658,869)(659,868)
(660,867)(661,866)(662,865)(663,864)(664,863)(665,862)(666,861)(667,860)
(668,859)(669,858)(670,857)(671,856)(672,916)(673,976)(674,975)(675,974)
(676,973)(677,972)(678,971)(679,970)(680,969)(681,968)(682,967)(683,966)
(684,965)(685,964)(686,963)(687,962)(688,961)(689,960)(690,959)(691,958)
(692,957)(693,956)(694,955)(695,954)(696,953)(697,952)(698,951)(699,950)
(700,949)(701,948)(702,947)(703,946)(704,945)(705,944)(706,943)(707,942)
(708,941)(709,940)(710,939)(711,938)(712,937)(713,936)(714,935)(715,934)
(716,933)(717,932)(718,931)(719,930)(720,929)(721,928)(722,927)(723,926)
(724,925)(725,924)(726,923)(727,922)(728,921)(729,920)(730,919)(731,918)
(732,917);
s1 := Sym(976)!( 1,246)( 2,245)( 3,305)( 4,304)( 5,303)( 6,302)( 7,301)
( 8,300)( 9,299)( 10,298)( 11,297)( 12,296)( 13,295)( 14,294)( 15,293)
( 16,292)( 17,291)( 18,290)( 19,289)( 20,288)( 21,287)( 22,286)( 23,285)
( 24,284)( 25,283)( 26,282)( 27,281)( 28,280)( 29,279)( 30,278)( 31,277)
( 32,276)( 33,275)( 34,274)( 35,273)( 36,272)( 37,271)( 38,270)( 39,269)
( 40,268)( 41,267)( 42,266)( 43,265)( 44,264)( 45,263)( 46,262)( 47,261)
( 48,260)( 49,259)( 50,258)( 51,257)( 52,256)( 53,255)( 54,254)( 55,253)
( 56,252)( 57,251)( 58,250)( 59,249)( 60,248)( 61,247)( 62,307)( 63,306)
( 64,366)( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)
( 72,358)( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)
( 80,350)( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)
( 88,342)( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)
( 96,334)( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)
(112,318)(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)
(120,310)(121,309)(122,308)(123,429)(124,428)(125,488)(126,487)(127,486)
(128,485)(129,484)(130,483)(131,482)(132,481)(133,480)(134,479)(135,478)
(136,477)(137,476)(138,475)(139,474)(140,473)(141,472)(142,471)(143,470)
(144,469)(145,468)(146,467)(147,466)(148,465)(149,464)(150,463)(151,462)
(152,461)(153,460)(154,459)(155,458)(156,457)(157,456)(158,455)(159,454)
(160,453)(161,452)(162,451)(163,450)(164,449)(165,448)(166,447)(167,446)
(168,445)(169,444)(170,443)(171,442)(172,441)(173,440)(174,439)(175,438)
(176,437)(177,436)(178,435)(179,434)(180,433)(181,432)(182,431)(183,430)
(184,368)(185,367)(186,427)(187,426)(188,425)(189,424)(190,423)(191,422)
(192,421)(193,420)(194,419)(195,418)(196,417)(197,416)(198,415)(199,414)
(200,413)(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)
(208,405)(209,404)(210,403)(211,402)(212,401)(213,400)(214,399)(215,398)
(216,397)(217,396)(218,395)(219,394)(220,393)(221,392)(222,391)(223,390)
(224,389)(225,388)(226,387)(227,386)(228,385)(229,384)(230,383)(231,382)
(232,381)(233,380)(234,379)(235,378)(236,377)(237,376)(238,375)(239,374)
(240,373)(241,372)(242,371)(243,370)(244,369)(489,856)(490,855)(491,915)
(492,914)(493,913)(494,912)(495,911)(496,910)(497,909)(498,908)(499,907)
(500,906)(501,905)(502,904)(503,903)(504,902)(505,901)(506,900)(507,899)
(508,898)(509,897)(510,896)(511,895)(512,894)(513,893)(514,892)(515,891)
(516,890)(517,889)(518,888)(519,887)(520,886)(521,885)(522,884)(523,883)
(524,882)(525,881)(526,880)(527,879)(528,878)(529,877)(530,876)(531,875)
(532,874)(533,873)(534,872)(535,871)(536,870)(537,869)(538,868)(539,867)
(540,866)(541,865)(542,864)(543,863)(544,862)(545,861)(546,860)(547,859)
(548,858)(549,857)(550,917)(551,916)(552,976)(553,975)(554,974)(555,973)
(556,972)(557,971)(558,970)(559,969)(560,968)(561,967)(562,966)(563,965)
(564,964)(565,963)(566,962)(567,961)(568,960)(569,959)(570,958)(571,957)
(572,956)(573,955)(574,954)(575,953)(576,952)(577,951)(578,950)(579,949)
(580,948)(581,947)(582,946)(583,945)(584,944)(585,943)(586,942)(587,941)
(588,940)(589,939)(590,938)(591,937)(592,936)(593,935)(594,934)(595,933)
(596,932)(597,931)(598,930)(599,929)(600,928)(601,927)(602,926)(603,925)
(604,924)(605,923)(606,922)(607,921)(608,920)(609,919)(610,918)(611,734)
(612,733)(613,793)(614,792)(615,791)(616,790)(617,789)(618,788)(619,787)
(620,786)(621,785)(622,784)(623,783)(624,782)(625,781)(626,780)(627,779)
(628,778)(629,777)(630,776)(631,775)(632,774)(633,773)(634,772)(635,771)
(636,770)(637,769)(638,768)(639,767)(640,766)(641,765)(642,764)(643,763)
(644,762)(645,761)(646,760)(647,759)(648,758)(649,757)(650,756)(651,755)
(652,754)(653,753)(654,752)(655,751)(656,750)(657,749)(658,748)(659,747)
(660,746)(661,745)(662,744)(663,743)(664,742)(665,741)(666,740)(667,739)
(668,738)(669,737)(670,736)(671,735)(672,795)(673,794)(674,854)(675,853)
(676,852)(677,851)(678,850)(679,849)(680,848)(681,847)(682,846)(683,845)
(684,844)(685,843)(686,842)(687,841)(688,840)(689,839)(690,838)(691,837)
(692,836)(693,835)(694,834)(695,833)(696,832)(697,831)(698,830)(699,829)
(700,828)(701,827)(702,826)(703,825)(704,824)(705,823)(706,822)(707,821)
(708,820)(709,819)(710,818)(711,817)(712,816)(713,815)(714,814)(715,813)
(716,812)(717,811)(718,810)(719,809)(720,808)(721,807)(722,806)(723,805)
(724,804)(725,803)(726,802)(727,801)(728,800)(729,799)(730,798)(731,797)
(732,796);
s2 := Sym(976)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)
( 8,496)( 9,497)( 10,498)( 11,499)( 12,500)( 13,501)( 14,502)( 15,503)
( 16,504)( 17,505)( 18,506)( 19,507)( 20,508)( 21,509)( 22,510)( 23,511)
( 24,512)( 25,513)( 26,514)( 27,515)( 28,516)( 29,517)( 30,518)( 31,519)
( 32,520)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)
( 40,528)( 41,529)( 42,530)( 43,531)( 44,532)( 45,533)( 46,534)( 47,535)
( 48,536)( 49,537)( 50,538)( 51,539)( 52,540)( 53,541)( 54,542)( 55,543)
( 56,544)( 57,545)( 58,546)( 59,547)( 60,548)( 61,549)( 62,550)( 63,551)
( 64,552)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)
( 72,560)( 73,561)( 74,562)( 75,563)( 76,564)( 77,565)( 78,566)( 79,567)
( 80,568)( 81,569)( 82,570)( 83,571)( 84,572)( 85,573)( 86,574)( 87,575)
( 88,576)( 89,577)( 90,578)( 91,579)( 92,580)( 93,581)( 94,582)( 95,583)
( 96,584)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)
(104,592)(105,593)(106,594)(107,595)(108,596)(109,597)(110,598)(111,599)
(112,600)(113,601)(114,602)(115,603)(116,604)(117,605)(118,606)(119,607)
(120,608)(121,609)(122,610)(123,672)(124,673)(125,674)(126,675)(127,676)
(128,677)(129,678)(130,679)(131,680)(132,681)(133,682)(134,683)(135,684)
(136,685)(137,686)(138,687)(139,688)(140,689)(141,690)(142,691)(143,692)
(144,693)(145,694)(146,695)(147,696)(148,697)(149,698)(150,699)(151,700)
(152,701)(153,702)(154,703)(155,704)(156,705)(157,706)(158,707)(159,708)
(160,709)(161,710)(162,711)(163,712)(164,713)(165,714)(166,715)(167,716)
(168,717)(169,718)(170,719)(171,720)(172,721)(173,722)(174,723)(175,724)
(176,725)(177,726)(178,727)(179,728)(180,729)(181,730)(182,731)(183,732)
(184,611)(185,612)(186,613)(187,614)(188,615)(189,616)(190,617)(191,618)
(192,619)(193,620)(194,621)(195,622)(196,623)(197,624)(198,625)(199,626)
(200,627)(201,628)(202,629)(203,630)(204,631)(205,632)(206,633)(207,634)
(208,635)(209,636)(210,637)(211,638)(212,639)(213,640)(214,641)(215,642)
(216,643)(217,644)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)
(224,651)(225,652)(226,653)(227,654)(228,655)(229,656)(230,657)(231,658)
(232,659)(233,660)(234,661)(235,662)(236,663)(237,664)(238,665)(239,666)
(240,667)(241,668)(242,669)(243,670)(244,671)(245,733)(246,734)(247,735)
(248,736)(249,737)(250,738)(251,739)(252,740)(253,741)(254,742)(255,743)
(256,744)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)
(264,752)(265,753)(266,754)(267,755)(268,756)(269,757)(270,758)(271,759)
(272,760)(273,761)(274,762)(275,763)(276,764)(277,765)(278,766)(279,767)
(280,768)(281,769)(282,770)(283,771)(284,772)(285,773)(286,774)(287,775)
(288,776)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)
(296,784)(297,785)(298,786)(299,787)(300,788)(301,789)(302,790)(303,791)
(304,792)(305,793)(306,794)(307,795)(308,796)(309,797)(310,798)(311,799)
(312,800)(313,801)(314,802)(315,803)(316,804)(317,805)(318,806)(319,807)
(320,808)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)
(328,816)(329,817)(330,818)(331,819)(332,820)(333,821)(334,822)(335,823)
(336,824)(337,825)(338,826)(339,827)(340,828)(341,829)(342,830)(343,831)
(344,832)(345,833)(346,834)(347,835)(348,836)(349,837)(350,838)(351,839)
(352,840)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)
(360,848)(361,849)(362,850)(363,851)(364,852)(365,853)(366,854)(367,916)
(368,917)(369,918)(370,919)(371,920)(372,921)(373,922)(374,923)(375,924)
(376,925)(377,926)(378,927)(379,928)(380,929)(381,930)(382,931)(383,932)
(384,933)(385,934)(386,935)(387,936)(388,937)(389,938)(390,939)(391,940)
(392,941)(393,942)(394,943)(395,944)(396,945)(397,946)(398,947)(399,948)
(400,949)(401,950)(402,951)(403,952)(404,953)(405,954)(406,955)(407,956)
(408,957)(409,958)(410,959)(411,960)(412,961)(413,962)(414,963)(415,964)
(416,965)(417,966)(418,967)(419,968)(420,969)(421,970)(422,971)(423,972)
(424,973)(425,974)(426,975)(427,976)(428,855)(429,856)(430,857)(431,858)
(432,859)(433,860)(434,861)(435,862)(436,863)(437,864)(438,865)(439,866)
(440,867)(441,868)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)
(448,875)(449,876)(450,877)(451,878)(452,879)(453,880)(454,881)(455,882)
(456,883)(457,884)(458,885)(459,886)(460,887)(461,888)(462,889)(463,890)
(464,891)(465,892)(466,893)(467,894)(468,895)(469,896)(470,897)(471,898)
(472,899)(473,900)(474,901)(475,902)(476,903)(477,904)(478,905)(479,906)
(480,907)(481,908)(482,909)(483,910)(484,911)(485,912)(486,913)(487,914)
(488,915);
poly := sub<Sym(976)|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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*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*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*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