Polytope of Type {834}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {834}*1668
Also Known As : 834-gon, {834}. if this polytope has another name.
Group : SmallGroup(1668,14)
Rank : 2
Schlafli Type : {834}
Number of vertices, edges, etc : 834, 834
Order of s0s1 : 834
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
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 : {417}*834
3-fold quotients : {278}*556
6-fold quotients : {139}*278
139-fold quotients : {6}*12
278-fold quotients : {3}*6
417-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,139)( 3,138)( 4,137)( 5,136)( 6,135)( 7,134)( 8,133)( 9,132)
( 10,131)( 11,130)( 12,129)( 13,128)( 14,127)( 15,126)( 16,125)( 17,124)
( 18,123)( 19,122)( 20,121)( 21,120)( 22,119)( 23,118)( 24,117)( 25,116)
( 26,115)( 27,114)( 28,113)( 29,112)( 30,111)( 31,110)( 32,109)( 33,108)
( 34,107)( 35,106)( 36,105)( 37,104)( 38,103)( 39,102)( 40,101)( 41,100)
( 42, 99)( 43, 98)( 44, 97)( 45, 96)( 46, 95)( 47, 94)( 48, 93)( 49, 92)
( 50, 91)( 51, 90)( 52, 89)( 53, 88)( 54, 87)( 55, 86)( 56, 85)( 57, 84)
( 58, 83)( 59, 82)( 60, 81)( 61, 80)( 62, 79)( 63, 78)( 64, 77)( 65, 76)
( 66, 75)( 67, 74)( 68, 73)( 69, 72)( 70, 71)(140,279)(141,417)(142,416)
(143,415)(144,414)(145,413)(146,412)(147,411)(148,410)(149,409)(150,408)
(151,407)(152,406)(153,405)(154,404)(155,403)(156,402)(157,401)(158,400)
(159,399)(160,398)(161,397)(162,396)(163,395)(164,394)(165,393)(166,392)
(167,391)(168,390)(169,389)(170,388)(171,387)(172,386)(173,385)(174,384)
(175,383)(176,382)(177,381)(178,380)(179,379)(180,378)(181,377)(182,376)
(183,375)(184,374)(185,373)(186,372)(187,371)(188,370)(189,369)(190,368)
(191,367)(192,366)(193,365)(194,364)(195,363)(196,362)(197,361)(198,360)
(199,359)(200,358)(201,357)(202,356)(203,355)(204,354)(205,353)(206,352)
(207,351)(208,350)(209,349)(210,348)(211,347)(212,346)(213,345)(214,344)
(215,343)(216,342)(217,341)(218,340)(219,339)(220,338)(221,337)(222,336)
(223,335)(224,334)(225,333)(226,332)(227,331)(228,330)(229,329)(230,328)
(231,327)(232,326)(233,325)(234,324)(235,323)(236,322)(237,321)(238,320)
(239,319)(240,318)(241,317)(242,316)(243,315)(244,314)(245,313)(246,312)
(247,311)(248,310)(249,309)(250,308)(251,307)(252,306)(253,305)(254,304)
(255,303)(256,302)(257,301)(258,300)(259,299)(260,298)(261,297)(262,296)
(263,295)(264,294)(265,293)(266,292)(267,291)(268,290)(269,289)(270,288)
(271,287)(272,286)(273,285)(274,284)(275,283)(276,282)(277,281)(278,280)
(419,556)(420,555)(421,554)(422,553)(423,552)(424,551)(425,550)(426,549)
(427,548)(428,547)(429,546)(430,545)(431,544)(432,543)(433,542)(434,541)
(435,540)(436,539)(437,538)(438,537)(439,536)(440,535)(441,534)(442,533)
(443,532)(444,531)(445,530)(446,529)(447,528)(448,527)(449,526)(450,525)
(451,524)(452,523)(453,522)(454,521)(455,520)(456,519)(457,518)(458,517)
(459,516)(460,515)(461,514)(462,513)(463,512)(464,511)(465,510)(466,509)
(467,508)(468,507)(469,506)(470,505)(471,504)(472,503)(473,502)(474,501)
(475,500)(476,499)(477,498)(478,497)(479,496)(480,495)(481,494)(482,493)
(483,492)(484,491)(485,490)(486,489)(487,488)(557,696)(558,834)(559,833)
(560,832)(561,831)(562,830)(563,829)(564,828)(565,827)(566,826)(567,825)
(568,824)(569,823)(570,822)(571,821)(572,820)(573,819)(574,818)(575,817)
(576,816)(577,815)(578,814)(579,813)(580,812)(581,811)(582,810)(583,809)
(584,808)(585,807)(586,806)(587,805)(588,804)(589,803)(590,802)(591,801)
(592,800)(593,799)(594,798)(595,797)(596,796)(597,795)(598,794)(599,793)
(600,792)(601,791)(602,790)(603,789)(604,788)(605,787)(606,786)(607,785)
(608,784)(609,783)(610,782)(611,781)(612,780)(613,779)(614,778)(615,777)
(616,776)(617,775)(618,774)(619,773)(620,772)(621,771)(622,770)(623,769)
(624,768)(625,767)(626,766)(627,765)(628,764)(629,763)(630,762)(631,761)
(632,760)(633,759)(634,758)(635,757)(636,756)(637,755)(638,754)(639,753)
(640,752)(641,751)(642,750)(643,749)(644,748)(645,747)(646,746)(647,745)
(648,744)(649,743)(650,742)(651,741)(652,740)(653,739)(654,738)(655,737)
(656,736)(657,735)(658,734)(659,733)(660,732)(661,731)(662,730)(663,729)
(664,728)(665,727)(666,726)(667,725)(668,724)(669,723)(670,722)(671,721)
(672,720)(673,719)(674,718)(675,717)(676,716)(677,715)(678,714)(679,713)
(680,712)(681,711)(682,710)(683,709)(684,708)(685,707)(686,706)(687,705)
(688,704)(689,703)(690,702)(691,701)(692,700)(693,699)(694,698)(695,697);;
s1 := ( 1,558)( 2,557)( 3,695)( 4,694)( 5,693)( 6,692)( 7,691)( 8,690)
( 9,689)( 10,688)( 11,687)( 12,686)( 13,685)( 14,684)( 15,683)( 16,682)
( 17,681)( 18,680)( 19,679)( 20,678)( 21,677)( 22,676)( 23,675)( 24,674)
( 25,673)( 26,672)( 27,671)( 28,670)( 29,669)( 30,668)( 31,667)( 32,666)
( 33,665)( 34,664)( 35,663)( 36,662)( 37,661)( 38,660)( 39,659)( 40,658)
( 41,657)( 42,656)( 43,655)( 44,654)( 45,653)( 46,652)( 47,651)( 48,650)
( 49,649)( 50,648)( 51,647)( 52,646)( 53,645)( 54,644)( 55,643)( 56,642)
( 57,641)( 58,640)( 59,639)( 60,638)( 61,637)( 62,636)( 63,635)( 64,634)
( 65,633)( 66,632)( 67,631)( 68,630)( 69,629)( 70,628)( 71,627)( 72,626)
( 73,625)( 74,624)( 75,623)( 76,622)( 77,621)( 78,620)( 79,619)( 80,618)
( 81,617)( 82,616)( 83,615)( 84,614)( 85,613)( 86,612)( 87,611)( 88,610)
( 89,609)( 90,608)( 91,607)( 92,606)( 93,605)( 94,604)( 95,603)( 96,602)
( 97,601)( 98,600)( 99,599)(100,598)(101,597)(102,596)(103,595)(104,594)
(105,593)(106,592)(107,591)(108,590)(109,589)(110,588)(111,587)(112,586)
(113,585)(114,584)(115,583)(116,582)(117,581)(118,580)(119,579)(120,578)
(121,577)(122,576)(123,575)(124,574)(125,573)(126,572)(127,571)(128,570)
(129,569)(130,568)(131,567)(132,566)(133,565)(134,564)(135,563)(136,562)
(137,561)(138,560)(139,559)(140,419)(141,418)(142,556)(143,555)(144,554)
(145,553)(146,552)(147,551)(148,550)(149,549)(150,548)(151,547)(152,546)
(153,545)(154,544)(155,543)(156,542)(157,541)(158,540)(159,539)(160,538)
(161,537)(162,536)(163,535)(164,534)(165,533)(166,532)(167,531)(168,530)
(169,529)(170,528)(171,527)(172,526)(173,525)(174,524)(175,523)(176,522)
(177,521)(178,520)(179,519)(180,518)(181,517)(182,516)(183,515)(184,514)
(185,513)(186,512)(187,511)(188,510)(189,509)(190,508)(191,507)(192,506)
(193,505)(194,504)(195,503)(196,502)(197,501)(198,500)(199,499)(200,498)
(201,497)(202,496)(203,495)(204,494)(205,493)(206,492)(207,491)(208,490)
(209,489)(210,488)(211,487)(212,486)(213,485)(214,484)(215,483)(216,482)
(217,481)(218,480)(219,479)(220,478)(221,477)(222,476)(223,475)(224,474)
(225,473)(226,472)(227,471)(228,470)(229,469)(230,468)(231,467)(232,466)
(233,465)(234,464)(235,463)(236,462)(237,461)(238,460)(239,459)(240,458)
(241,457)(242,456)(243,455)(244,454)(245,453)(246,452)(247,451)(248,450)
(249,449)(250,448)(251,447)(252,446)(253,445)(254,444)(255,443)(256,442)
(257,441)(258,440)(259,439)(260,438)(261,437)(262,436)(263,435)(264,434)
(265,433)(266,432)(267,431)(268,430)(269,429)(270,428)(271,427)(272,426)
(273,425)(274,424)(275,423)(276,422)(277,421)(278,420)(279,697)(280,696)
(281,834)(282,833)(283,832)(284,831)(285,830)(286,829)(287,828)(288,827)
(289,826)(290,825)(291,824)(292,823)(293,822)(294,821)(295,820)(296,819)
(297,818)(298,817)(299,816)(300,815)(301,814)(302,813)(303,812)(304,811)
(305,810)(306,809)(307,808)(308,807)(309,806)(310,805)(311,804)(312,803)
(313,802)(314,801)(315,800)(316,799)(317,798)(318,797)(319,796)(320,795)
(321,794)(322,793)(323,792)(324,791)(325,790)(326,789)(327,788)(328,787)
(329,786)(330,785)(331,784)(332,783)(333,782)(334,781)(335,780)(336,779)
(337,778)(338,777)(339,776)(340,775)(341,774)(342,773)(343,772)(344,771)
(345,770)(346,769)(347,768)(348,767)(349,766)(350,765)(351,764)(352,763)
(353,762)(354,761)(355,760)(356,759)(357,758)(358,757)(359,756)(360,755)
(361,754)(362,753)(363,752)(364,751)(365,750)(366,749)(367,748)(368,747)
(369,746)(370,745)(371,744)(372,743)(373,742)(374,741)(375,740)(376,739)
(377,738)(378,737)(379,736)(380,735)(381,734)(382,733)(383,732)(384,731)
(385,730)(386,729)(387,728)(388,727)(389,726)(390,725)(391,724)(392,723)
(393,722)(394,721)(395,720)(396,719)(397,718)(398,717)(399,716)(400,715)
(401,714)(402,713)(403,712)(404,711)(405,710)(406,709)(407,708)(408,707)
(409,706)(410,705)(411,704)(412,703)(413,702)(414,701)(415,700)(416,699)
(417,698);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(834)!( 2,139)( 3,138)( 4,137)( 5,136)( 6,135)( 7,134)( 8,133)
( 9,132)( 10,131)( 11,130)( 12,129)( 13,128)( 14,127)( 15,126)( 16,125)
( 17,124)( 18,123)( 19,122)( 20,121)( 21,120)( 22,119)( 23,118)( 24,117)
( 25,116)( 26,115)( 27,114)( 28,113)( 29,112)( 30,111)( 31,110)( 32,109)
( 33,108)( 34,107)( 35,106)( 36,105)( 37,104)( 38,103)( 39,102)( 40,101)
( 41,100)( 42, 99)( 43, 98)( 44, 97)( 45, 96)( 46, 95)( 47, 94)( 48, 93)
( 49, 92)( 50, 91)( 51, 90)( 52, 89)( 53, 88)( 54, 87)( 55, 86)( 56, 85)
( 57, 84)( 58, 83)( 59, 82)( 60, 81)( 61, 80)( 62, 79)( 63, 78)( 64, 77)
( 65, 76)( 66, 75)( 67, 74)( 68, 73)( 69, 72)( 70, 71)(140,279)(141,417)
(142,416)(143,415)(144,414)(145,413)(146,412)(147,411)(148,410)(149,409)
(150,408)(151,407)(152,406)(153,405)(154,404)(155,403)(156,402)(157,401)
(158,400)(159,399)(160,398)(161,397)(162,396)(163,395)(164,394)(165,393)
(166,392)(167,391)(168,390)(169,389)(170,388)(171,387)(172,386)(173,385)
(174,384)(175,383)(176,382)(177,381)(178,380)(179,379)(180,378)(181,377)
(182,376)(183,375)(184,374)(185,373)(186,372)(187,371)(188,370)(189,369)
(190,368)(191,367)(192,366)(193,365)(194,364)(195,363)(196,362)(197,361)
(198,360)(199,359)(200,358)(201,357)(202,356)(203,355)(204,354)(205,353)
(206,352)(207,351)(208,350)(209,349)(210,348)(211,347)(212,346)(213,345)
(214,344)(215,343)(216,342)(217,341)(218,340)(219,339)(220,338)(221,337)
(222,336)(223,335)(224,334)(225,333)(226,332)(227,331)(228,330)(229,329)
(230,328)(231,327)(232,326)(233,325)(234,324)(235,323)(236,322)(237,321)
(238,320)(239,319)(240,318)(241,317)(242,316)(243,315)(244,314)(245,313)
(246,312)(247,311)(248,310)(249,309)(250,308)(251,307)(252,306)(253,305)
(254,304)(255,303)(256,302)(257,301)(258,300)(259,299)(260,298)(261,297)
(262,296)(263,295)(264,294)(265,293)(266,292)(267,291)(268,290)(269,289)
(270,288)(271,287)(272,286)(273,285)(274,284)(275,283)(276,282)(277,281)
(278,280)(419,556)(420,555)(421,554)(422,553)(423,552)(424,551)(425,550)
(426,549)(427,548)(428,547)(429,546)(430,545)(431,544)(432,543)(433,542)
(434,541)(435,540)(436,539)(437,538)(438,537)(439,536)(440,535)(441,534)
(442,533)(443,532)(444,531)(445,530)(446,529)(447,528)(448,527)(449,526)
(450,525)(451,524)(452,523)(453,522)(454,521)(455,520)(456,519)(457,518)
(458,517)(459,516)(460,515)(461,514)(462,513)(463,512)(464,511)(465,510)
(466,509)(467,508)(468,507)(469,506)(470,505)(471,504)(472,503)(473,502)
(474,501)(475,500)(476,499)(477,498)(478,497)(479,496)(480,495)(481,494)
(482,493)(483,492)(484,491)(485,490)(486,489)(487,488)(557,696)(558,834)
(559,833)(560,832)(561,831)(562,830)(563,829)(564,828)(565,827)(566,826)
(567,825)(568,824)(569,823)(570,822)(571,821)(572,820)(573,819)(574,818)
(575,817)(576,816)(577,815)(578,814)(579,813)(580,812)(581,811)(582,810)
(583,809)(584,808)(585,807)(586,806)(587,805)(588,804)(589,803)(590,802)
(591,801)(592,800)(593,799)(594,798)(595,797)(596,796)(597,795)(598,794)
(599,793)(600,792)(601,791)(602,790)(603,789)(604,788)(605,787)(606,786)
(607,785)(608,784)(609,783)(610,782)(611,781)(612,780)(613,779)(614,778)
(615,777)(616,776)(617,775)(618,774)(619,773)(620,772)(621,771)(622,770)
(623,769)(624,768)(625,767)(626,766)(627,765)(628,764)(629,763)(630,762)
(631,761)(632,760)(633,759)(634,758)(635,757)(636,756)(637,755)(638,754)
(639,753)(640,752)(641,751)(642,750)(643,749)(644,748)(645,747)(646,746)
(647,745)(648,744)(649,743)(650,742)(651,741)(652,740)(653,739)(654,738)
(655,737)(656,736)(657,735)(658,734)(659,733)(660,732)(661,731)(662,730)
(663,729)(664,728)(665,727)(666,726)(667,725)(668,724)(669,723)(670,722)
(671,721)(672,720)(673,719)(674,718)(675,717)(676,716)(677,715)(678,714)
(679,713)(680,712)(681,711)(682,710)(683,709)(684,708)(685,707)(686,706)
(687,705)(688,704)(689,703)(690,702)(691,701)(692,700)(693,699)(694,698)
(695,697);
s1 := Sym(834)!( 1,558)( 2,557)( 3,695)( 4,694)( 5,693)( 6,692)( 7,691)
( 8,690)( 9,689)( 10,688)( 11,687)( 12,686)( 13,685)( 14,684)( 15,683)
( 16,682)( 17,681)( 18,680)( 19,679)( 20,678)( 21,677)( 22,676)( 23,675)
( 24,674)( 25,673)( 26,672)( 27,671)( 28,670)( 29,669)( 30,668)( 31,667)
( 32,666)( 33,665)( 34,664)( 35,663)( 36,662)( 37,661)( 38,660)( 39,659)
( 40,658)( 41,657)( 42,656)( 43,655)( 44,654)( 45,653)( 46,652)( 47,651)
( 48,650)( 49,649)( 50,648)( 51,647)( 52,646)( 53,645)( 54,644)( 55,643)
( 56,642)( 57,641)( 58,640)( 59,639)( 60,638)( 61,637)( 62,636)( 63,635)
( 64,634)( 65,633)( 66,632)( 67,631)( 68,630)( 69,629)( 70,628)( 71,627)
( 72,626)( 73,625)( 74,624)( 75,623)( 76,622)( 77,621)( 78,620)( 79,619)
( 80,618)( 81,617)( 82,616)( 83,615)( 84,614)( 85,613)( 86,612)( 87,611)
( 88,610)( 89,609)( 90,608)( 91,607)( 92,606)( 93,605)( 94,604)( 95,603)
( 96,602)( 97,601)( 98,600)( 99,599)(100,598)(101,597)(102,596)(103,595)
(104,594)(105,593)(106,592)(107,591)(108,590)(109,589)(110,588)(111,587)
(112,586)(113,585)(114,584)(115,583)(116,582)(117,581)(118,580)(119,579)
(120,578)(121,577)(122,576)(123,575)(124,574)(125,573)(126,572)(127,571)
(128,570)(129,569)(130,568)(131,567)(132,566)(133,565)(134,564)(135,563)
(136,562)(137,561)(138,560)(139,559)(140,419)(141,418)(142,556)(143,555)
(144,554)(145,553)(146,552)(147,551)(148,550)(149,549)(150,548)(151,547)
(152,546)(153,545)(154,544)(155,543)(156,542)(157,541)(158,540)(159,539)
(160,538)(161,537)(162,536)(163,535)(164,534)(165,533)(166,532)(167,531)
(168,530)(169,529)(170,528)(171,527)(172,526)(173,525)(174,524)(175,523)
(176,522)(177,521)(178,520)(179,519)(180,518)(181,517)(182,516)(183,515)
(184,514)(185,513)(186,512)(187,511)(188,510)(189,509)(190,508)(191,507)
(192,506)(193,505)(194,504)(195,503)(196,502)(197,501)(198,500)(199,499)
(200,498)(201,497)(202,496)(203,495)(204,494)(205,493)(206,492)(207,491)
(208,490)(209,489)(210,488)(211,487)(212,486)(213,485)(214,484)(215,483)
(216,482)(217,481)(218,480)(219,479)(220,478)(221,477)(222,476)(223,475)
(224,474)(225,473)(226,472)(227,471)(228,470)(229,469)(230,468)(231,467)
(232,466)(233,465)(234,464)(235,463)(236,462)(237,461)(238,460)(239,459)
(240,458)(241,457)(242,456)(243,455)(244,454)(245,453)(246,452)(247,451)
(248,450)(249,449)(250,448)(251,447)(252,446)(253,445)(254,444)(255,443)
(256,442)(257,441)(258,440)(259,439)(260,438)(261,437)(262,436)(263,435)
(264,434)(265,433)(266,432)(267,431)(268,430)(269,429)(270,428)(271,427)
(272,426)(273,425)(274,424)(275,423)(276,422)(277,421)(278,420)(279,697)
(280,696)(281,834)(282,833)(283,832)(284,831)(285,830)(286,829)(287,828)
(288,827)(289,826)(290,825)(291,824)(292,823)(293,822)(294,821)(295,820)
(296,819)(297,818)(298,817)(299,816)(300,815)(301,814)(302,813)(303,812)
(304,811)(305,810)(306,809)(307,808)(308,807)(309,806)(310,805)(311,804)
(312,803)(313,802)(314,801)(315,800)(316,799)(317,798)(318,797)(319,796)
(320,795)(321,794)(322,793)(323,792)(324,791)(325,790)(326,789)(327,788)
(328,787)(329,786)(330,785)(331,784)(332,783)(333,782)(334,781)(335,780)
(336,779)(337,778)(338,777)(339,776)(340,775)(341,774)(342,773)(343,772)
(344,771)(345,770)(346,769)(347,768)(348,767)(349,766)(350,765)(351,764)
(352,763)(353,762)(354,761)(355,760)(356,759)(357,758)(358,757)(359,756)
(360,755)(361,754)(362,753)(363,752)(364,751)(365,750)(366,749)(367,748)
(368,747)(369,746)(370,745)(371,744)(372,743)(373,742)(374,741)(375,740)
(376,739)(377,738)(378,737)(379,736)(380,735)(381,734)(382,733)(383,732)
(384,731)(385,730)(386,729)(387,728)(388,727)(389,726)(390,725)(391,724)
(392,723)(393,722)(394,721)(395,720)(396,719)(397,718)(398,717)(399,716)
(400,715)(401,714)(402,713)(403,712)(404,711)(405,710)(406,709)(407,708)
(408,707)(409,706)(410,705)(411,704)(412,703)(413,702)(414,701)(415,700)
(416,699)(417,698);
poly := sub<Sym(834)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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