Polytope of Type {894}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {894}*1788
Also Known As : 894-gon, {894}. if this polytope has another name.
Group : SmallGroup(1788,11)
Rank : 2
Schlafli Type : {894}
Number of vertices, edges, etc : 894, 894
Order of s0s1 : 894
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 : {447}*894
3-fold quotients : {298}*596
6-fold quotients : {149}*298
149-fold quotients : {6}*12
298-fold quotients : {3}*6
447-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 2,149)( 3,148)( 4,147)( 5,146)( 6,145)( 7,144)( 8,143)( 9,142)( 10,141)( 11,140)( 12,139)( 13,138)( 14,137)( 15,136)( 16,135)( 17,134)( 18,133)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,126)( 26,125)( 27,124)( 28,123)( 29,122)( 30,121)( 31,120)( 32,119)( 33,118)( 34,117)( 35,116)( 36,115)( 37,114)( 38,113)( 39,112)( 40,111)( 41,110)( 42,109)( 43,108)( 44,107)( 45,106)( 46,105)( 47,104)( 48,103)( 49,102)( 50,101)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 95)( 57, 94)( 58, 93)( 59, 92)( 60, 91)( 61, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)( 73, 78)( 74, 77)( 75, 76)(150,299)(151,447)(152,446)(153,445)(154,444)(155,443)(156,442)(157,441)(158,440)(159,439)(160,438)(161,437)(162,436)(163,435)(164,434)(165,433)(166,432)(167,431)(168,430)(169,429)(170,428)(171,427)(172,426)(173,425)(174,424)(175,423)(176,422)(177,421)(178,420)(179,419)(180,418)(181,417)(182,416)(183,415)(184,414)(185,413)(186,412)(187,411)(188,410)(189,409)(190,408)(191,407)(192,406)(193,405)(194,404)(195,403)(196,402)(197,401)(198,400)(199,399)(200,398)(201,397)(202,396)(203,395)(204,394)(205,393)(206,392)(207,391)(208,390)(209,389)(210,388)(211,387)(212,386)(213,385)(214,384)(215,383)(216,382)(217,381)(218,380)(219,379)(220,378)(221,377)(222,376)(223,375)(224,374)(225,373)(226,372)(227,371)(228,370)(229,369)(230,368)(231,367)(232,366)(233,365)(234,364)(235,363)(236,362)(237,361)(238,360)(239,359)(240,358)(241,357)(242,356)(243,355)(244,354)(245,353)(246,352)(247,351)(248,350)(249,349)(250,348)(251,347)(252,346)(253,345)(254,344)(255,343)(256,342)(257,341)(258,340)(259,339)(260,338)(261,337)(262,336)(263,335)(264,334)(265,333)(266,332)(267,331)(268,330)(269,329)(270,328)(271,327)(272,326)(273,325)(274,324)(275,323)(276,322)(277,321)(278,320)(279,319)(280,318)(281,317)(282,316)(283,315)(284,314)(285,313)(286,312)(287,311)(288,310)(289,309)(290,308)(291,307)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(449,596)(450,595)(451,594)(452,593)(453,592)(454,591)(455,590)(456,589)(457,588)(458,587)(459,586)(460,585)(461,584)(462,583)(463,582)(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,575)(471,574)(472,573)(473,572)(474,571)(475,570)(476,569)(477,568)(478,567)(479,566)(480,565)(481,564)(482,563)(483,562)(484,561)(485,560)(486,559)(487,558)(488,557)(489,556)(490,555)(491,554)(492,553)(493,552)(494,551)(495,550)(496,549)(497,548)(498,547)(499,546)(500,545)(501,544)(502,543)(503,542)(504,541)(505,540)(506,539)(507,538)(508,537)(509,536)(510,535)(511,534)(512,533)(513,532)(514,531)(515,530)(516,529)(517,528)(518,527)(519,526)(520,525)(521,524)(522,523)(597,746)(598,894)(599,893)(600,892)(601,891)(602,890)(603,889)(604,888)(605,887)(606,886)(607,885)(608,884)(609,883)(610,882)(611,881)(612,880)(613,879)(614,878)(615,877)(616,876)(617,875)(618,874)(619,873)(620,872)(621,871)(622,870)(623,869)(624,868)(625,867)(626,866)(627,865)(628,864)(629,863)(630,862)(631,861)(632,860)(633,859)(634,858)(635,857)(636,856)(637,855)(638,854)(639,853)(640,852)(641,851)(642,850)(643,849)(644,848)(645,847)(646,846)(647,845)(648,844)(649,843)(650,842)(651,841)(652,840)(653,839)(654,838)(655,837)(656,836)(657,835)(658,834)(659,833)(660,832)(661,831)(662,830)(663,829)(664,828)(665,827)(666,826)(667,825)(668,824)(669,823)(670,822)(671,821)(672,820)(673,819)(674,818)(675,817)(676,816)(677,815)(678,814)(679,813)(680,812)(681,811)(682,810)(683,809)(684,808)(685,807)(686,806)(687,805)(688,804)(689,803)(690,802)(691,801)(692,800)(693,799)(694,798)(695,797)(696,796)(697,795)(698,794)(699,793)(700,792)(701,791)(702,790)(703,789)(704,788)(705,787)(706,786)(707,785)(708,784)(709,783)(710,782)(711,781)(712,780)(713,779)(714,778)(715,777)(716,776)(717,775)(718,774)(719,773)(720,772)(721,771)(722,770)(723,769)(724,768)(725,767)(726,766)(727,765)(728,764)(729,763)(730,762)(731,761)(732,760)(733,759)(734,758)(735,757)(736,756)(737,755)(738,754)(739,753)(740,752)(741,751)(742,750)(743,749)(744,748)(745,747);;
s1 := ( 1,598)( 2,597)( 3,745)( 4,744)( 5,743)( 6,742)( 7,741)( 8,740)( 9,739)( 10,738)( 11,737)( 12,736)( 13,735)( 14,734)( 15,733)( 16,732)( 17,731)( 18,730)( 19,729)( 20,728)( 21,727)( 22,726)( 23,725)( 24,724)( 25,723)( 26,722)( 27,721)( 28,720)( 29,719)( 30,718)( 31,717)( 32,716)( 33,715)( 34,714)( 35,713)( 36,712)( 37,711)( 38,710)( 39,709)( 40,708)( 41,707)( 42,706)( 43,705)( 44,704)( 45,703)( 46,702)( 47,701)( 48,700)( 49,699)( 50,698)( 51,697)( 52,696)( 53,695)( 54,694)( 55,693)( 56,692)( 57,691)( 58,690)( 59,689)( 60,688)( 61,687)( 62,686)( 63,685)( 64,684)( 65,683)( 66,682)( 67,681)( 68,680)( 69,679)( 70,678)( 71,677)( 72,676)( 73,675)( 74,674)( 75,673)( 76,672)( 77,671)( 78,670)( 79,669)( 80,668)( 81,667)( 82,666)( 83,665)( 84,664)( 85,663)( 86,662)( 87,661)( 88,660)( 89,659)( 90,658)( 91,657)( 92,656)( 93,655)( 94,654)( 95,653)( 96,652)( 97,651)( 98,650)( 99,649)(100,648)(101,647)(102,646)(103,645)(104,644)(105,643)(106,642)(107,641)(108,640)(109,639)(110,638)(111,637)(112,636)(113,635)(114,634)(115,633)(116,632)(117,631)(118,630)(119,629)(120,628)(121,627)(122,626)(123,625)(124,624)(125,623)(126,622)(127,621)(128,620)(129,619)(130,618)(131,617)(132,616)(133,615)(134,614)(135,613)(136,612)(137,611)(138,610)(139,609)(140,608)(141,607)(142,606)(143,605)(144,604)(145,603)(146,602)(147,601)(148,600)(149,599)(150,449)(151,448)(152,596)(153,595)(154,594)(155,593)(156,592)(157,591)(158,590)(159,589)(160,588)(161,587)(162,586)(163,585)(164,584)(165,583)(166,582)(167,581)(168,580)(169,579)(170,578)(171,577)(172,576)(173,575)(174,574)(175,573)(176,572)(177,571)(178,570)(179,569)(180,568)(181,567)(182,566)(183,565)(184,564)(185,563)(186,562)(187,561)(188,560)(189,559)(190,558)(191,557)(192,556)(193,555)(194,554)(195,553)(196,552)(197,551)(198,550)(199,549)(200,548)(201,547)(202,546)(203,545)(204,544)(205,543)(206,542)(207,541)(208,540)(209,539)(210,538)(211,537)(212,536)(213,535)(214,534)(215,533)(216,532)(217,531)(218,530)(219,529)(220,528)(221,527)(222,526)(223,525)(224,524)(225,523)(226,522)(227,521)(228,520)(229,519)(230,518)(231,517)(232,516)(233,515)(234,514)(235,513)(236,512)(237,511)(238,510)(239,509)(240,508)(241,507)(242,506)(243,505)(244,504)(245,503)(246,502)(247,501)(248,500)(249,499)(250,498)(251,497)(252,496)(253,495)(254,494)(255,493)(256,492)(257,491)(258,490)(259,489)(260,488)(261,487)(262,486)(263,485)(264,484)(265,483)(266,482)(267,481)(268,480)(269,479)(270,478)(271,477)(272,476)(273,475)(274,474)(275,473)(276,472)(277,471)(278,470)(279,469)(280,468)(281,467)(282,466)(283,465)(284,464)(285,463)(286,462)(287,461)(288,460)(289,459)(290,458)(291,457)(292,456)(293,455)(294,454)(295,453)(296,452)(297,451)(298,450)(299,747)(300,746)(301,894)(302,893)(303,892)(304,891)(305,890)(306,889)(307,888)(308,887)(309,886)(310,885)(311,884)(312,883)(313,882)(314,881)(315,880)(316,879)(317,878)(318,877)(319,876)(320,875)(321,874)(322,873)(323,872)(324,871)(325,870)(326,869)(327,868)(328,867)(329,866)(330,865)(331,864)(332,863)(333,862)(334,861)(335,860)(336,859)(337,858)(338,857)(339,856)(340,855)(341,854)(342,853)(343,852)(344,851)(345,850)(346,849)(347,848)(348,847)(349,846)(350,845)(351,844)(352,843)(353,842)(354,841)(355,840)(356,839)(357,838)(358,837)(359,836)(360,835)(361,834)(362,833)(363,832)(364,831)(365,830)(366,829)(367,828)(368,827)(369,826)(370,825)(371,824)(372,823)(373,822)(374,821)(375,820)(376,819)(377,818)(378,817)(379,816)(380,815)(381,814)(382,813)(383,812)(384,811)(385,810)(386,809)(387,808)(388,807)(389,806)(390,805)(391,804)(392,803)(393,802)(394,801)(395,800)(396,799)(397,798)(398,797)(399,796)(400,795)(401,794)(402,793)(403,792)(404,791)(405,790)(406,789)(407,788)(408,787)(409,786)(410,785)(411,784)(412,783)(413,782)(414,781)(415,780)(416,779)(417,778)(418,777)(419,776)(420,775)(421,774)(422,773)(423,772)(424,771)(425,770)(426,769)(427,768)(428,767)(429,766)(430,765)(431,764)(432,763)(433,762)(434,761)(435,760)(436,759)(437,758)(438,757)(439,756)(440,755)(441,754)(442,753)(443,752)(444,751)(445,750)(446,749)(447,748);;
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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];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(894)!( 2,149)( 3,148)( 4,147)( 5,146)( 6,145)( 7,144)( 8,143)( 9,142)( 10,141)( 11,140)( 12,139)( 13,138)( 14,137)( 15,136)( 16,135)( 17,134)( 18,133)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,126)( 26,125)( 27,124)( 28,123)( 29,122)( 30,121)( 31,120)( 32,119)( 33,118)( 34,117)( 35,116)( 36,115)( 37,114)( 38,113)( 39,112)( 40,111)( 41,110)( 42,109)( 43,108)( 44,107)( 45,106)( 46,105)( 47,104)( 48,103)( 49,102)( 50,101)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 95)( 57, 94)( 58, 93)( 59, 92)( 60, 91)( 61, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)( 73, 78)( 74, 77)( 75, 76)(150,299)(151,447)(152,446)(153,445)(154,444)(155,443)(156,442)(157,441)(158,440)(159,439)(160,438)(161,437)(162,436)(163,435)(164,434)(165,433)(166,432)(167,431)(168,430)(169,429)(170,428)(171,427)(172,426)(173,425)(174,424)(175,423)(176,422)(177,421)(178,420)(179,419)(180,418)(181,417)(182,416)(183,415)(184,414)(185,413)(186,412)(187,411)(188,410)(189,409)(190,408)(191,407)(192,406)(193,405)(194,404)(195,403)(196,402)(197,401)(198,400)(199,399)(200,398)(201,397)(202,396)(203,395)(204,394)(205,393)(206,392)(207,391)(208,390)(209,389)(210,388)(211,387)(212,386)(213,385)(214,384)(215,383)(216,382)(217,381)(218,380)(219,379)(220,378)(221,377)(222,376)(223,375)(224,374)(225,373)(226,372)(227,371)(228,370)(229,369)(230,368)(231,367)(232,366)(233,365)(234,364)(235,363)(236,362)(237,361)(238,360)(239,359)(240,358)(241,357)(242,356)(243,355)(244,354)(245,353)(246,352)(247,351)(248,350)(249,349)(250,348)(251,347)(252,346)(253,345)(254,344)(255,343)(256,342)(257,341)(258,340)(259,339)(260,338)(261,337)(262,336)(263,335)(264,334)(265,333)(266,332)(267,331)(268,330)(269,329)(270,328)(271,327)(272,326)(273,325)(274,324)(275,323)(276,322)(277,321)(278,320)(279,319)(280,318)(281,317)(282,316)(283,315)(284,314)(285,313)(286,312)(287,311)(288,310)(289,309)(290,308)(291,307)(292,306)(293,305)(294,304)(295,303)(296,302)(297,301)(298,300)(449,596)(450,595)(451,594)(452,593)(453,592)(454,591)(455,590)(456,589)(457,588)(458,587)(459,586)(460,585)(461,584)(462,583)(463,582)(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,575)(471,574)(472,573)(473,572)(474,571)(475,570)(476,569)(477,568)(478,567)(479,566)(480,565)(481,564)(482,563)(483,562)(484,561)(485,560)(486,559)(487,558)(488,557)(489,556)(490,555)(491,554)(492,553)(493,552)(494,551)(495,550)(496,549)(497,548)(498,547)(499,546)(500,545)(501,544)(502,543)(503,542)(504,541)(505,540)(506,539)(507,538)(508,537)(509,536)(510,535)(511,534)(512,533)(513,532)(514,531)(515,530)(516,529)(517,528)(518,527)(519,526)(520,525)(521,524)(522,523)(597,746)(598,894)(599,893)(600,892)(601,891)(602,890)(603,889)(604,888)(605,887)(606,886)(607,885)(608,884)(609,883)(610,882)(611,881)(612,880)(613,879)(614,878)(615,877)(616,876)(617,875)(618,874)(619,873)(620,872)(621,871)(622,870)(623,869)(624,868)(625,867)(626,866)(627,865)(628,864)(629,863)(630,862)(631,861)(632,860)(633,859)(634,858)(635,857)(636,856)(637,855)(638,854)(639,853)(640,852)(641,851)(642,850)(643,849)(644,848)(645,847)(646,846)(647,845)(648,844)(649,843)(650,842)(651,841)(652,840)(653,839)(654,838)(655,837)(656,836)(657,835)(658,834)(659,833)(660,832)(661,831)(662,830)(663,829)(664,828)(665,827)(666,826)(667,825)(668,824)(669,823)(670,822)(671,821)(672,820)(673,819)(674,818)(675,817)(676,816)(677,815)(678,814)(679,813)(680,812)(681,811)(682,810)(683,809)(684,808)(685,807)(686,806)(687,805)(688,804)(689,803)(690,802)(691,801)(692,800)(693,799)(694,798)(695,797)(696,796)(697,795)(698,794)(699,793)(700,792)(701,791)(702,790)(703,789)(704,788)(705,787)(706,786)(707,785)(708,784)(709,783)(710,782)(711,781)(712,780)(713,779)(714,778)(715,777)(716,776)(717,775)(718,774)(719,773)(720,772)(721,771)(722,770)(723,769)(724,768)(725,767)(726,766)(727,765)(728,764)(729,763)(730,762)(731,761)(732,760)(733,759)(734,758)(735,757)(736,756)(737,755)(738,754)(739,753)(740,752)(741,751)(742,750)(743,749)(744,748)(745,747);
s1 := Sym(894)!( 1,598)( 2,597)( 3,745)( 4,744)( 5,743)( 6,742)( 7,741)( 8,740)( 9,739)( 10,738)( 11,737)( 12,736)( 13,735)( 14,734)( 15,733)( 16,732)( 17,731)( 18,730)( 19,729)( 20,728)( 21,727)( 22,726)( 23,725)( 24,724)( 25,723)( 26,722)( 27,721)( 28,720)( 29,719)( 30,718)( 31,717)( 32,716)( 33,715)( 34,714)( 35,713)( 36,712)( 37,711)( 38,710)( 39,709)( 40,708)( 41,707)( 42,706)( 43,705)( 44,704)( 45,703)( 46,702)( 47,701)( 48,700)( 49,699)( 50,698)( 51,697)( 52,696)( 53,695)( 54,694)( 55,693)( 56,692)( 57,691)( 58,690)( 59,689)( 60,688)( 61,687)( 62,686)( 63,685)( 64,684)( 65,683)( 66,682)( 67,681)( 68,680)( 69,679)( 70,678)( 71,677)( 72,676)( 73,675)( 74,674)( 75,673)( 76,672)( 77,671)( 78,670)( 79,669)( 80,668)( 81,667)( 82,666)( 83,665)( 84,664)( 85,663)( 86,662)( 87,661)( 88,660)( 89,659)( 90,658)( 91,657)( 92,656)( 93,655)( 94,654)( 95,653)( 96,652)( 97,651)( 98,650)( 99,649)(100,648)(101,647)(102,646)(103,645)(104,644)(105,643)(106,642)(107,641)(108,640)(109,639)(110,638)(111,637)(112,636)(113,635)(114,634)(115,633)(116,632)(117,631)(118,630)(119,629)(120,628)(121,627)(122,626)(123,625)(124,624)(125,623)(126,622)(127,621)(128,620)(129,619)(130,618)(131,617)(132,616)(133,615)(134,614)(135,613)(136,612)(137,611)(138,610)(139,609)(140,608)(141,607)(142,606)(143,605)(144,604)(145,603)(146,602)(147,601)(148,600)(149,599)(150,449)(151,448)(152,596)(153,595)(154,594)(155,593)(156,592)(157,591)(158,590)(159,589)(160,588)(161,587)(162,586)(163,585)(164,584)(165,583)(166,582)(167,581)(168,580)(169,579)(170,578)(171,577)(172,576)(173,575)(174,574)(175,573)(176,572)(177,571)(178,570)(179,569)(180,568)(181,567)(182,566)(183,565)(184,564)(185,563)(186,562)(187,561)(188,560)(189,559)(190,558)(191,557)(192,556)(193,555)(194,554)(195,553)(196,552)(197,551)(198,550)(199,549)(200,548)(201,547)(202,546)(203,545)(204,544)(205,543)(206,542)(207,541)(208,540)(209,539)(210,538)(211,537)(212,536)(213,535)(214,534)(215,533)(216,532)(217,531)(218,530)(219,529)(220,528)(221,527)(222,526)(223,525)(224,524)(225,523)(226,522)(227,521)(228,520)(229,519)(230,518)(231,517)(232,516)(233,515)(234,514)(235,513)(236,512)(237,511)(238,510)(239,509)(240,508)(241,507)(242,506)(243,505)(244,504)(245,503)(246,502)(247,501)(248,500)(249,499)(250,498)(251,497)(252,496)(253,495)(254,494)(255,493)(256,492)(257,491)(258,490)(259,489)(260,488)(261,487)(262,486)(263,485)(264,484)(265,483)(266,482)(267,481)(268,480)(269,479)(270,478)(271,477)(272,476)(273,475)(274,474)(275,473)(276,472)(277,471)(278,470)(279,469)(280,468)(281,467)(282,466)(283,465)(284,464)(285,463)(286,462)(287,461)(288,460)(289,459)(290,458)(291,457)(292,456)(293,455)(294,454)(295,453)(296,452)(297,451)(298,450)(299,747)(300,746)(301,894)(302,893)(303,892)(304,891)(305,890)(306,889)(307,888)(308,887)(309,886)(310,885)(311,884)(312,883)(313,882)(314,881)(315,880)(316,879)(317,878)(318,877)(319,876)(320,875)(321,874)(322,873)(323,872)(324,871)(325,870)(326,869)(327,868)(328,867)(329,866)(330,865)(331,864)(332,863)(333,862)(334,861)(335,860)(336,859)(337,858)(338,857)(339,856)(340,855)(341,854)(342,853)(343,852)(344,851)(345,850)(346,849)(347,848)(348,847)(349,846)(350,845)(351,844)(352,843)(353,842)(354,841)(355,840)(356,839)(357,838)(358,837)(359,836)(360,835)(361,834)(362,833)(363,832)(364,831)(365,830)(366,829)(367,828)(368,827)(369,826)(370,825)(371,824)(372,823)(373,822)(374,821)(375,820)(376,819)(377,818)(378,817)(379,816)(380,815)(381,814)(382,813)(383,812)(384,811)(385,810)(386,809)(387,808)(388,807)(389,806)(390,805)(391,804)(392,803)(393,802)(394,801)(395,800)(396,799)(397,798)(398,797)(399,796)(400,795)(401,794)(402,793)(403,792)(404,791)(405,790)(406,789)(407,788)(408,787)(409,786)(410,785)(411,784)(412,783)(413,782)(414,781)(415,780)(416,779)(417,778)(418,777)(419,776)(420,775)(421,774)(422,773)(423,772)(424,771)(425,770)(426,769)(427,768)(428,767)(429,766)(430,765)(431,764)(432,763)(433,762)(434,761)(435,760)(436,759)(437,758)(438,757)(439,756)(440,755)(441,754)(442,753)(443,752)(444,751)(445,750)(446,749)(447,748);
poly := sub<Sym(894)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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