Polytope of Type {870}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {870}*1740
Also Known As : 870-gon, {870}. if this polytope has another name.
Group : SmallGroup(1740,36)
Rank : 2
Schlafli Type : {870}
Number of vertices, edges, etc : 870, 870
Order of s0s1 : 870
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 : {435}*870
3-fold quotients : {290}*580
5-fold quotients : {174}*348
6-fold quotients : {145}*290
10-fold quotients : {87}*174
15-fold quotients : {58}*116
29-fold quotients : {30}*60
30-fold quotients : {29}*58
58-fold quotients : {15}*30
87-fold quotients : {10}*20
145-fold quotients : {6}*12
174-fold quotients : {5}*10
290-fold quotients : {3}*6
435-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 29)( 3, 28)( 4, 27)( 5, 26)( 6, 25)( 7, 24)( 8, 23)( 9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30,117)( 31,145)
( 32,144)( 33,143)( 34,142)( 35,141)( 36,140)( 37,139)( 38,138)( 39,137)
( 40,136)( 41,135)( 42,134)( 43,133)( 44,132)( 45,131)( 46,130)( 47,129)
( 48,128)( 49,127)( 50,126)( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)
( 56,120)( 57,119)( 58,118)( 59, 88)( 60,116)( 61,115)( 62,114)( 63,113)
( 64,112)( 65,111)( 66,110)( 67,109)( 68,108)( 69,107)( 70,106)( 71,105)
( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)( 78, 98)( 79, 97)
( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)( 85, 91)( 86, 90)( 87, 89)
(146,291)(147,319)(148,318)(149,317)(150,316)(151,315)(152,314)(153,313)
(154,312)(155,311)(156,310)(157,309)(158,308)(159,307)(160,306)(161,305)
(162,304)(163,303)(164,302)(165,301)(166,300)(167,299)(168,298)(169,297)
(170,296)(171,295)(172,294)(173,293)(174,292)(175,407)(176,435)(177,434)
(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)(184,427)(185,426)
(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)(192,419)(193,418)
(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)(200,411)(201,410)
(202,409)(203,408)(204,378)(205,406)(206,405)(207,404)(208,403)(209,402)
(210,401)(211,400)(212,399)(213,398)(214,397)(215,396)(216,395)(217,394)
(218,393)(219,392)(220,391)(221,390)(222,389)(223,388)(224,387)(225,386)
(226,385)(227,384)(228,383)(229,382)(230,381)(231,380)(232,379)(233,349)
(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)
(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,363)(249,362)
(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)
(258,353)(259,352)(260,351)(261,350)(262,320)(263,348)(264,347)(265,346)
(266,345)(267,344)(268,343)(269,342)(270,341)(271,340)(272,339)(273,338)
(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)(281,330)
(282,329)(283,328)(284,327)(285,326)(286,325)(287,324)(288,323)(289,322)
(290,321)(437,464)(438,463)(439,462)(440,461)(441,460)(442,459)(443,458)
(444,457)(445,456)(446,455)(447,454)(448,453)(449,452)(450,451)(465,552)
(466,580)(467,579)(468,578)(469,577)(470,576)(471,575)(472,574)(473,573)
(474,572)(475,571)(476,570)(477,569)(478,568)(479,567)(480,566)(481,565)
(482,564)(483,563)(484,562)(485,561)(486,560)(487,559)(488,558)(489,557)
(490,556)(491,555)(492,554)(493,553)(494,523)(495,551)(496,550)(497,549)
(498,548)(499,547)(500,546)(501,545)(502,544)(503,543)(504,542)(505,541)
(506,540)(507,539)(508,538)(509,537)(510,536)(511,535)(512,534)(513,533)
(514,532)(515,531)(516,530)(517,529)(518,528)(519,527)(520,526)(521,525)
(522,524)(581,726)(582,754)(583,753)(584,752)(585,751)(586,750)(587,749)
(588,748)(589,747)(590,746)(591,745)(592,744)(593,743)(594,742)(595,741)
(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)(602,734)(603,733)
(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)(610,842)(611,870)
(612,869)(613,868)(614,867)(615,866)(616,865)(617,864)(618,863)(619,862)
(620,861)(621,860)(622,859)(623,858)(624,857)(625,856)(626,855)(627,854)
(628,853)(629,852)(630,851)(631,850)(632,849)(633,848)(634,847)(635,846)
(636,845)(637,844)(638,843)(639,813)(640,841)(641,840)(642,839)(643,838)
(644,837)(645,836)(646,835)(647,834)(648,833)(649,832)(650,831)(651,830)
(652,829)(653,828)(654,827)(655,826)(656,825)(657,824)(658,823)(659,822)
(660,821)(661,820)(662,819)(663,818)(664,817)(665,816)(666,815)(667,814)
(668,784)(669,812)(670,811)(671,810)(672,809)(673,808)(674,807)(675,806)
(676,805)(677,804)(678,803)(679,802)(680,801)(681,800)(682,799)(683,798)
(684,797)(685,796)(686,795)(687,794)(688,793)(689,792)(690,791)(691,790)
(692,789)(693,788)(694,787)(695,786)(696,785)(697,755)(698,783)(699,782)
(700,781)(701,780)(702,779)(703,778)(704,777)(705,776)(706,775)(707,774)
(708,773)(709,772)(710,771)(711,770)(712,769)(713,768)(714,767)(715,766)
(716,765)(717,764)(718,763)(719,762)(720,761)(721,760)(722,759)(723,758)
(724,757)(725,756);;
s1 := ( 1,611)( 2,610)( 3,638)( 4,637)( 5,636)( 6,635)( 7,634)( 8,633)
( 9,632)( 10,631)( 11,630)( 12,629)( 13,628)( 14,627)( 15,626)( 16,625)
( 17,624)( 18,623)( 19,622)( 20,621)( 21,620)( 22,619)( 23,618)( 24,617)
( 25,616)( 26,615)( 27,614)( 28,613)( 29,612)( 30,582)( 31,581)( 32,609)
( 33,608)( 34,607)( 35,606)( 36,605)( 37,604)( 38,603)( 39,602)( 40,601)
( 41,600)( 42,599)( 43,598)( 44,597)( 45,596)( 46,595)( 47,594)( 48,593)
( 49,592)( 50,591)( 51,590)( 52,589)( 53,588)( 54,587)( 55,586)( 56,585)
( 57,584)( 58,583)( 59,698)( 60,697)( 61,725)( 62,724)( 63,723)( 64,722)
( 65,721)( 66,720)( 67,719)( 68,718)( 69,717)( 70,716)( 71,715)( 72,714)
( 73,713)( 74,712)( 75,711)( 76,710)( 77,709)( 78,708)( 79,707)( 80,706)
( 81,705)( 82,704)( 83,703)( 84,702)( 85,701)( 86,700)( 87,699)( 88,669)
( 89,668)( 90,696)( 91,695)( 92,694)( 93,693)( 94,692)( 95,691)( 96,690)
( 97,689)( 98,688)( 99,687)(100,686)(101,685)(102,684)(103,683)(104,682)
(105,681)(106,680)(107,679)(108,678)(109,677)(110,676)(111,675)(112,674)
(113,673)(114,672)(115,671)(116,670)(117,640)(118,639)(119,667)(120,666)
(121,665)(122,664)(123,663)(124,662)(125,661)(126,660)(127,659)(128,658)
(129,657)(130,656)(131,655)(132,654)(133,653)(134,652)(135,651)(136,650)
(137,649)(138,648)(139,647)(140,646)(141,645)(142,644)(143,643)(144,642)
(145,641)(146,466)(147,465)(148,493)(149,492)(150,491)(151,490)(152,489)
(153,488)(154,487)(155,486)(156,485)(157,484)(158,483)(159,482)(160,481)
(161,480)(162,479)(163,478)(164,477)(165,476)(166,475)(167,474)(168,473)
(169,472)(170,471)(171,470)(172,469)(173,468)(174,467)(175,437)(176,436)
(177,464)(178,463)(179,462)(180,461)(181,460)(182,459)(183,458)(184,457)
(185,456)(186,455)(187,454)(188,453)(189,452)(190,451)(191,450)(192,449)
(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,442)(200,441)
(201,440)(202,439)(203,438)(204,553)(205,552)(206,580)(207,579)(208,578)
(209,577)(210,576)(211,575)(212,574)(213,573)(214,572)(215,571)(216,570)
(217,569)(218,568)(219,567)(220,566)(221,565)(222,564)(223,563)(224,562)
(225,561)(226,560)(227,559)(228,558)(229,557)(230,556)(231,555)(232,554)
(233,524)(234,523)(235,551)(236,550)(237,549)(238,548)(239,547)(240,546)
(241,545)(242,544)(243,543)(244,542)(245,541)(246,540)(247,539)(248,538)
(249,537)(250,536)(251,535)(252,534)(253,533)(254,532)(255,531)(256,530)
(257,529)(258,528)(259,527)(260,526)(261,525)(262,495)(263,494)(264,522)
(265,521)(266,520)(267,519)(268,518)(269,517)(270,516)(271,515)(272,514)
(273,513)(274,512)(275,511)(276,510)(277,509)(278,508)(279,507)(280,506)
(281,505)(282,504)(283,503)(284,502)(285,501)(286,500)(287,499)(288,498)
(289,497)(290,496)(291,756)(292,755)(293,783)(294,782)(295,781)(296,780)
(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)(304,772)
(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)(312,764)
(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)(320,727)
(321,726)(322,754)(323,753)(324,752)(325,751)(326,750)(327,749)(328,748)
(329,747)(330,746)(331,745)(332,744)(333,743)(334,742)(335,741)(336,740)
(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)(344,732)
(345,731)(346,730)(347,729)(348,728)(349,843)(350,842)(351,870)(352,869)
(353,868)(354,867)(355,866)(356,865)(357,864)(358,863)(359,862)(360,861)
(361,860)(362,859)(363,858)(364,857)(365,856)(366,855)(367,854)(368,853)
(369,852)(370,851)(371,850)(372,849)(373,848)(374,847)(375,846)(376,845)
(377,844)(378,814)(379,813)(380,841)(381,840)(382,839)(383,838)(384,837)
(385,836)(386,835)(387,834)(388,833)(389,832)(390,831)(391,830)(392,829)
(393,828)(394,827)(395,826)(396,825)(397,824)(398,823)(399,822)(400,821)
(401,820)(402,819)(403,818)(404,817)(405,816)(406,815)(407,785)(408,784)
(409,812)(410,811)(411,810)(412,809)(413,808)(414,807)(415,806)(416,805)
(417,804)(418,803)(419,802)(420,801)(421,800)(422,799)(423,798)(424,797)
(425,796)(426,795)(427,794)(428,793)(429,792)(430,791)(431,790)(432,789)
(433,788)(434,787)(435,786);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(870)!( 2, 29)( 3, 28)( 4, 27)( 5, 26)( 6, 25)( 7, 24)( 8, 23)
( 9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30,117)
( 31,145)( 32,144)( 33,143)( 34,142)( 35,141)( 36,140)( 37,139)( 38,138)
( 39,137)( 40,136)( 41,135)( 42,134)( 43,133)( 44,132)( 45,131)( 46,130)
( 47,129)( 48,128)( 49,127)( 50,126)( 51,125)( 52,124)( 53,123)( 54,122)
( 55,121)( 56,120)( 57,119)( 58,118)( 59, 88)( 60,116)( 61,115)( 62,114)
( 63,113)( 64,112)( 65,111)( 66,110)( 67,109)( 68,108)( 69,107)( 70,106)
( 71,105)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)( 78, 98)
( 79, 97)( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)( 85, 91)( 86, 90)
( 87, 89)(146,291)(147,319)(148,318)(149,317)(150,316)(151,315)(152,314)
(153,313)(154,312)(155,311)(156,310)(157,309)(158,308)(159,307)(160,306)
(161,305)(162,304)(163,303)(164,302)(165,301)(166,300)(167,299)(168,298)
(169,297)(170,296)(171,295)(172,294)(173,293)(174,292)(175,407)(176,435)
(177,434)(178,433)(179,432)(180,431)(181,430)(182,429)(183,428)(184,427)
(185,426)(186,425)(187,424)(188,423)(189,422)(190,421)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,414)(198,413)(199,412)(200,411)
(201,410)(202,409)(203,408)(204,378)(205,406)(206,405)(207,404)(208,403)
(209,402)(210,401)(211,400)(212,399)(213,398)(214,397)(215,396)(216,395)
(217,394)(218,393)(219,392)(220,391)(221,390)(222,389)(223,388)(224,387)
(225,386)(226,385)(227,384)(228,383)(229,382)(230,381)(231,380)(232,379)
(233,349)(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)
(241,370)(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,363)
(249,362)(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)
(257,354)(258,353)(259,352)(260,351)(261,350)(262,320)(263,348)(264,347)
(265,346)(266,345)(267,344)(268,343)(269,342)(270,341)(271,340)(272,339)
(273,338)(274,337)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)
(281,330)(282,329)(283,328)(284,327)(285,326)(286,325)(287,324)(288,323)
(289,322)(290,321)(437,464)(438,463)(439,462)(440,461)(441,460)(442,459)
(443,458)(444,457)(445,456)(446,455)(447,454)(448,453)(449,452)(450,451)
(465,552)(466,580)(467,579)(468,578)(469,577)(470,576)(471,575)(472,574)
(473,573)(474,572)(475,571)(476,570)(477,569)(478,568)(479,567)(480,566)
(481,565)(482,564)(483,563)(484,562)(485,561)(486,560)(487,559)(488,558)
(489,557)(490,556)(491,555)(492,554)(493,553)(494,523)(495,551)(496,550)
(497,549)(498,548)(499,547)(500,546)(501,545)(502,544)(503,543)(504,542)
(505,541)(506,540)(507,539)(508,538)(509,537)(510,536)(511,535)(512,534)
(513,533)(514,532)(515,531)(516,530)(517,529)(518,528)(519,527)(520,526)
(521,525)(522,524)(581,726)(582,754)(583,753)(584,752)(585,751)(586,750)
(587,749)(588,748)(589,747)(590,746)(591,745)(592,744)(593,743)(594,742)
(595,741)(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)(602,734)
(603,733)(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)(610,842)
(611,870)(612,869)(613,868)(614,867)(615,866)(616,865)(617,864)(618,863)
(619,862)(620,861)(621,860)(622,859)(623,858)(624,857)(625,856)(626,855)
(627,854)(628,853)(629,852)(630,851)(631,850)(632,849)(633,848)(634,847)
(635,846)(636,845)(637,844)(638,843)(639,813)(640,841)(641,840)(642,839)
(643,838)(644,837)(645,836)(646,835)(647,834)(648,833)(649,832)(650,831)
(651,830)(652,829)(653,828)(654,827)(655,826)(656,825)(657,824)(658,823)
(659,822)(660,821)(661,820)(662,819)(663,818)(664,817)(665,816)(666,815)
(667,814)(668,784)(669,812)(670,811)(671,810)(672,809)(673,808)(674,807)
(675,806)(676,805)(677,804)(678,803)(679,802)(680,801)(681,800)(682,799)
(683,798)(684,797)(685,796)(686,795)(687,794)(688,793)(689,792)(690,791)
(691,790)(692,789)(693,788)(694,787)(695,786)(696,785)(697,755)(698,783)
(699,782)(700,781)(701,780)(702,779)(703,778)(704,777)(705,776)(706,775)
(707,774)(708,773)(709,772)(710,771)(711,770)(712,769)(713,768)(714,767)
(715,766)(716,765)(717,764)(718,763)(719,762)(720,761)(721,760)(722,759)
(723,758)(724,757)(725,756);
s1 := Sym(870)!( 1,611)( 2,610)( 3,638)( 4,637)( 5,636)( 6,635)( 7,634)
( 8,633)( 9,632)( 10,631)( 11,630)( 12,629)( 13,628)( 14,627)( 15,626)
( 16,625)( 17,624)( 18,623)( 19,622)( 20,621)( 21,620)( 22,619)( 23,618)
( 24,617)( 25,616)( 26,615)( 27,614)( 28,613)( 29,612)( 30,582)( 31,581)
( 32,609)( 33,608)( 34,607)( 35,606)( 36,605)( 37,604)( 38,603)( 39,602)
( 40,601)( 41,600)( 42,599)( 43,598)( 44,597)( 45,596)( 46,595)( 47,594)
( 48,593)( 49,592)( 50,591)( 51,590)( 52,589)( 53,588)( 54,587)( 55,586)
( 56,585)( 57,584)( 58,583)( 59,698)( 60,697)( 61,725)( 62,724)( 63,723)
( 64,722)( 65,721)( 66,720)( 67,719)( 68,718)( 69,717)( 70,716)( 71,715)
( 72,714)( 73,713)( 74,712)( 75,711)( 76,710)( 77,709)( 78,708)( 79,707)
( 80,706)( 81,705)( 82,704)( 83,703)( 84,702)( 85,701)( 86,700)( 87,699)
( 88,669)( 89,668)( 90,696)( 91,695)( 92,694)( 93,693)( 94,692)( 95,691)
( 96,690)( 97,689)( 98,688)( 99,687)(100,686)(101,685)(102,684)(103,683)
(104,682)(105,681)(106,680)(107,679)(108,678)(109,677)(110,676)(111,675)
(112,674)(113,673)(114,672)(115,671)(116,670)(117,640)(118,639)(119,667)
(120,666)(121,665)(122,664)(123,663)(124,662)(125,661)(126,660)(127,659)
(128,658)(129,657)(130,656)(131,655)(132,654)(133,653)(134,652)(135,651)
(136,650)(137,649)(138,648)(139,647)(140,646)(141,645)(142,644)(143,643)
(144,642)(145,641)(146,466)(147,465)(148,493)(149,492)(150,491)(151,490)
(152,489)(153,488)(154,487)(155,486)(156,485)(157,484)(158,483)(159,482)
(160,481)(161,480)(162,479)(163,478)(164,477)(165,476)(166,475)(167,474)
(168,473)(169,472)(170,471)(171,470)(172,469)(173,468)(174,467)(175,437)
(176,436)(177,464)(178,463)(179,462)(180,461)(181,460)(182,459)(183,458)
(184,457)(185,456)(186,455)(187,454)(188,453)(189,452)(190,451)(191,450)
(192,449)(193,448)(194,447)(195,446)(196,445)(197,444)(198,443)(199,442)
(200,441)(201,440)(202,439)(203,438)(204,553)(205,552)(206,580)(207,579)
(208,578)(209,577)(210,576)(211,575)(212,574)(213,573)(214,572)(215,571)
(216,570)(217,569)(218,568)(219,567)(220,566)(221,565)(222,564)(223,563)
(224,562)(225,561)(226,560)(227,559)(228,558)(229,557)(230,556)(231,555)
(232,554)(233,524)(234,523)(235,551)(236,550)(237,549)(238,548)(239,547)
(240,546)(241,545)(242,544)(243,543)(244,542)(245,541)(246,540)(247,539)
(248,538)(249,537)(250,536)(251,535)(252,534)(253,533)(254,532)(255,531)
(256,530)(257,529)(258,528)(259,527)(260,526)(261,525)(262,495)(263,494)
(264,522)(265,521)(266,520)(267,519)(268,518)(269,517)(270,516)(271,515)
(272,514)(273,513)(274,512)(275,511)(276,510)(277,509)(278,508)(279,507)
(280,506)(281,505)(282,504)(283,503)(284,502)(285,501)(286,500)(287,499)
(288,498)(289,497)(290,496)(291,756)(292,755)(293,783)(294,782)(295,781)
(296,780)(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)
(304,772)(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)
(312,764)(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)
(320,727)(321,726)(322,754)(323,753)(324,752)(325,751)(326,750)(327,749)
(328,748)(329,747)(330,746)(331,745)(332,744)(333,743)(334,742)(335,741)
(336,740)(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)
(344,732)(345,731)(346,730)(347,729)(348,728)(349,843)(350,842)(351,870)
(352,869)(353,868)(354,867)(355,866)(356,865)(357,864)(358,863)(359,862)
(360,861)(361,860)(362,859)(363,858)(364,857)(365,856)(366,855)(367,854)
(368,853)(369,852)(370,851)(371,850)(372,849)(373,848)(374,847)(375,846)
(376,845)(377,844)(378,814)(379,813)(380,841)(381,840)(382,839)(383,838)
(384,837)(385,836)(386,835)(387,834)(388,833)(389,832)(390,831)(391,830)
(392,829)(393,828)(394,827)(395,826)(396,825)(397,824)(398,823)(399,822)
(400,821)(401,820)(402,819)(403,818)(404,817)(405,816)(406,815)(407,785)
(408,784)(409,812)(410,811)(411,810)(412,809)(413,808)(414,807)(415,806)
(416,805)(417,804)(418,803)(419,802)(420,801)(421,800)(422,799)(423,798)
(424,797)(425,796)(426,795)(427,794)(428,793)(429,792)(430,791)(431,790)
(432,789)(433,788)(434,787)(435,786);
poly := sub<Sym(870)|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 >;
References : None.
to this polytope