Polytope of Type {210,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {210,4}*1680c
if this polytope has a name.
Group : SmallGroup(1680,971)
Rank : 3
Schlafli Type : {210,4}
Number of vertices, edges, etc : 210, 420, 4
Order of s0s1s2 : 105
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {105,4}*840
5-fold quotients : {42,4}*336c
7-fold quotients : {30,4}*240c
10-fold quotients : {21,4}*168
14-fold quotients : {15,4}*120
35-fold quotients : {6,4}*48b
70-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 25)( 6, 26)( 7, 28)( 8, 27)( 9, 21)( 10, 22)( 11, 24)
( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29,113)( 30,114)( 31,116)
( 32,115)( 33,137)( 34,138)( 35,140)( 36,139)( 37,133)( 38,134)( 39,136)
( 40,135)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)
( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)( 53,117)( 54,118)( 55,120)
( 56,119)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,109)( 62,110)( 63,112)
( 64,111)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)
( 72,103)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(141,281)(142,282)(143,284)
(144,283)(145,305)(146,306)(147,308)(148,307)(149,301)(150,302)(151,304)
(152,303)(153,297)(154,298)(155,300)(156,299)(157,293)(158,294)(159,296)
(160,295)(161,289)(162,290)(163,292)(164,291)(165,285)(166,286)(167,288)
(168,287)(169,393)(170,394)(171,396)(172,395)(173,417)(174,418)(175,420)
(176,419)(177,413)(178,414)(179,416)(180,415)(181,409)(182,410)(183,412)
(184,411)(185,405)(186,406)(187,408)(188,407)(189,401)(190,402)(191,404)
(192,403)(193,397)(194,398)(195,400)(196,399)(197,365)(198,366)(199,368)
(200,367)(201,389)(202,390)(203,392)(204,391)(205,385)(206,386)(207,388)
(208,387)(209,381)(210,382)(211,384)(212,383)(213,377)(214,378)(215,380)
(216,379)(217,373)(218,374)(219,376)(220,375)(221,369)(222,370)(223,372)
(224,371)(225,337)(226,338)(227,340)(228,339)(229,361)(230,362)(231,364)
(232,363)(233,357)(234,358)(235,360)(236,359)(237,353)(238,354)(239,356)
(240,355)(241,349)(242,350)(243,352)(244,351)(245,345)(246,346)(247,348)
(248,347)(249,341)(250,342)(251,344)(252,343)(253,309)(254,310)(255,312)
(256,311)(257,333)(258,334)(259,336)(260,335)(261,329)(262,330)(263,332)
(264,331)(265,325)(266,326)(267,328)(268,327)(269,321)(270,322)(271,324)
(272,323)(273,317)(274,318)(275,320)(276,319)(277,313)(278,314)(279,316)
(280,315)(423,424)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)
(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(449,533)(450,534)
(451,536)(452,535)(453,557)(454,558)(455,560)(456,559)(457,553)(458,554)
(459,556)(460,555)(461,549)(462,550)(463,552)(464,551)(465,545)(466,546)
(467,548)(468,547)(469,541)(470,542)(471,544)(472,543)(473,537)(474,538)
(475,540)(476,539)(477,505)(478,506)(479,508)(480,507)(481,529)(482,530)
(483,532)(484,531)(485,525)(486,526)(487,528)(488,527)(489,521)(490,522)
(491,524)(492,523)(493,517)(494,518)(495,520)(496,519)(497,513)(498,514)
(499,516)(500,515)(501,509)(502,510)(503,512)(504,511)(561,701)(562,702)
(563,704)(564,703)(565,725)(566,726)(567,728)(568,727)(569,721)(570,722)
(571,724)(572,723)(573,717)(574,718)(575,720)(576,719)(577,713)(578,714)
(579,716)(580,715)(581,709)(582,710)(583,712)(584,711)(585,705)(586,706)
(587,708)(588,707)(589,813)(590,814)(591,816)(592,815)(593,837)(594,838)
(595,840)(596,839)(597,833)(598,834)(599,836)(600,835)(601,829)(602,830)
(603,832)(604,831)(605,825)(606,826)(607,828)(608,827)(609,821)(610,822)
(611,824)(612,823)(613,817)(614,818)(615,820)(616,819)(617,785)(618,786)
(619,788)(620,787)(621,809)(622,810)(623,812)(624,811)(625,805)(626,806)
(627,808)(628,807)(629,801)(630,802)(631,804)(632,803)(633,797)(634,798)
(635,800)(636,799)(637,793)(638,794)(639,796)(640,795)(641,789)(642,790)
(643,792)(644,791)(645,757)(646,758)(647,760)(648,759)(649,781)(650,782)
(651,784)(652,783)(653,777)(654,778)(655,780)(656,779)(657,773)(658,774)
(659,776)(660,775)(661,769)(662,770)(663,772)(664,771)(665,765)(666,766)
(667,768)(668,767)(669,761)(670,762)(671,764)(672,763)(673,729)(674,730)
(675,732)(676,731)(677,753)(678,754)(679,756)(680,755)(681,749)(682,750)
(683,752)(684,751)(685,745)(686,746)(687,748)(688,747)(689,741)(690,742)
(691,744)(692,743)(693,737)(694,738)(695,740)(696,739)(697,733)(698,734)
(699,736)(700,735);;
s1 := ( 1,593)( 2,596)( 3,595)( 4,594)( 5,589)( 6,592)( 7,591)( 8,590)
( 9,613)( 10,616)( 11,615)( 12,614)( 13,609)( 14,612)( 15,611)( 16,610)
( 17,605)( 18,608)( 19,607)( 20,606)( 21,601)( 22,604)( 23,603)( 24,602)
( 25,597)( 26,600)( 27,599)( 28,598)( 29,565)( 30,568)( 31,567)( 32,566)
( 33,561)( 34,564)( 35,563)( 36,562)( 37,585)( 38,588)( 39,587)( 40,586)
( 41,581)( 42,584)( 43,583)( 44,582)( 45,577)( 46,580)( 47,579)( 48,578)
( 49,573)( 50,576)( 51,575)( 52,574)( 53,569)( 54,572)( 55,571)( 56,570)
( 57,677)( 58,680)( 59,679)( 60,678)( 61,673)( 62,676)( 63,675)( 64,674)
( 65,697)( 66,700)( 67,699)( 68,698)( 69,693)( 70,696)( 71,695)( 72,694)
( 73,689)( 74,692)( 75,691)( 76,690)( 77,685)( 78,688)( 79,687)( 80,686)
( 81,681)( 82,684)( 83,683)( 84,682)( 85,649)( 86,652)( 87,651)( 88,650)
( 89,645)( 90,648)( 91,647)( 92,646)( 93,669)( 94,672)( 95,671)( 96,670)
( 97,665)( 98,668)( 99,667)(100,666)(101,661)(102,664)(103,663)(104,662)
(105,657)(106,660)(107,659)(108,658)(109,653)(110,656)(111,655)(112,654)
(113,621)(114,624)(115,623)(116,622)(117,617)(118,620)(119,619)(120,618)
(121,641)(122,644)(123,643)(124,642)(125,637)(126,640)(127,639)(128,638)
(129,633)(130,636)(131,635)(132,634)(133,629)(134,632)(135,631)(136,630)
(137,625)(138,628)(139,627)(140,626)(141,453)(142,456)(143,455)(144,454)
(145,449)(146,452)(147,451)(148,450)(149,473)(150,476)(151,475)(152,474)
(153,469)(154,472)(155,471)(156,470)(157,465)(158,468)(159,467)(160,466)
(161,461)(162,464)(163,463)(164,462)(165,457)(166,460)(167,459)(168,458)
(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)
(177,445)(178,448)(179,447)(180,446)(181,441)(182,444)(183,443)(184,442)
(185,437)(186,440)(187,439)(188,438)(189,433)(190,436)(191,435)(192,434)
(193,429)(194,432)(195,431)(196,430)(197,537)(198,540)(199,539)(200,538)
(201,533)(202,536)(203,535)(204,534)(205,557)(206,560)(207,559)(208,558)
(209,553)(210,556)(211,555)(212,554)(213,549)(214,552)(215,551)(216,550)
(217,545)(218,548)(219,547)(220,546)(221,541)(222,544)(223,543)(224,542)
(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)(232,506)
(233,529)(234,532)(235,531)(236,530)(237,525)(238,528)(239,527)(240,526)
(241,521)(242,524)(243,523)(244,522)(245,517)(246,520)(247,519)(248,518)
(249,513)(250,516)(251,515)(252,514)(253,481)(254,484)(255,483)(256,482)
(257,477)(258,480)(259,479)(260,478)(261,501)(262,504)(263,503)(264,502)
(265,497)(266,500)(267,499)(268,498)(269,493)(270,496)(271,495)(272,494)
(273,489)(274,492)(275,491)(276,490)(277,485)(278,488)(279,487)(280,486)
(281,733)(282,736)(283,735)(284,734)(285,729)(286,732)(287,731)(288,730)
(289,753)(290,756)(291,755)(292,754)(293,749)(294,752)(295,751)(296,750)
(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)(304,742)
(305,737)(306,740)(307,739)(308,738)(309,705)(310,708)(311,707)(312,706)
(313,701)(314,704)(315,703)(316,702)(317,725)(318,728)(319,727)(320,726)
(321,721)(322,724)(323,723)(324,722)(325,717)(326,720)(327,719)(328,718)
(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)(336,710)
(337,817)(338,820)(339,819)(340,818)(341,813)(342,816)(343,815)(344,814)
(345,837)(346,840)(347,839)(348,838)(349,833)(350,836)(351,835)(352,834)
(353,829)(354,832)(355,831)(356,830)(357,825)(358,828)(359,827)(360,826)
(361,821)(362,824)(363,823)(364,822)(365,789)(366,792)(367,791)(368,790)
(369,785)(370,788)(371,787)(372,786)(373,809)(374,812)(375,811)(376,810)
(377,805)(378,808)(379,807)(380,806)(381,801)(382,804)(383,803)(384,802)
(385,797)(386,800)(387,799)(388,798)(389,793)(390,796)(391,795)(392,794)
(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)(400,758)
(401,781)(402,784)(403,783)(404,782)(405,777)(406,780)(407,779)(408,778)
(409,773)(410,776)(411,775)(412,774)(413,769)(414,772)(415,771)(416,770)
(417,765)(418,768)(419,767)(420,766);;
s2 := ( 1,422)( 2,421)( 3,424)( 4,423)( 5,426)( 6,425)( 7,428)( 8,427)
( 9,430)( 10,429)( 11,432)( 12,431)( 13,434)( 14,433)( 15,436)( 16,435)
( 17,438)( 18,437)( 19,440)( 20,439)( 21,442)( 22,441)( 23,444)( 24,443)
( 25,446)( 26,445)( 27,448)( 28,447)( 29,450)( 30,449)( 31,452)( 32,451)
( 33,454)( 34,453)( 35,456)( 36,455)( 37,458)( 38,457)( 39,460)( 40,459)
( 41,462)( 42,461)( 43,464)( 44,463)( 45,466)( 46,465)( 47,468)( 48,467)
( 49,470)( 50,469)( 51,472)( 52,471)( 53,474)( 54,473)( 55,476)( 56,475)
( 57,478)( 58,477)( 59,480)( 60,479)( 61,482)( 62,481)( 63,484)( 64,483)
( 65,486)( 66,485)( 67,488)( 68,487)( 69,490)( 70,489)( 71,492)( 72,491)
( 73,494)( 74,493)( 75,496)( 76,495)( 77,498)( 78,497)( 79,500)( 80,499)
( 81,502)( 82,501)( 83,504)( 84,503)( 85,506)( 86,505)( 87,508)( 88,507)
( 89,510)( 90,509)( 91,512)( 92,511)( 93,514)( 94,513)( 95,516)( 96,515)
( 97,518)( 98,517)( 99,520)(100,519)(101,522)(102,521)(103,524)(104,523)
(105,526)(106,525)(107,528)(108,527)(109,530)(110,529)(111,532)(112,531)
(113,534)(114,533)(115,536)(116,535)(117,538)(118,537)(119,540)(120,539)
(121,542)(122,541)(123,544)(124,543)(125,546)(126,545)(127,548)(128,547)
(129,550)(130,549)(131,552)(132,551)(133,554)(134,553)(135,556)(136,555)
(137,558)(138,557)(139,560)(140,559)(141,562)(142,561)(143,564)(144,563)
(145,566)(146,565)(147,568)(148,567)(149,570)(150,569)(151,572)(152,571)
(153,574)(154,573)(155,576)(156,575)(157,578)(158,577)(159,580)(160,579)
(161,582)(162,581)(163,584)(164,583)(165,586)(166,585)(167,588)(168,587)
(169,590)(170,589)(171,592)(172,591)(173,594)(174,593)(175,596)(176,595)
(177,598)(178,597)(179,600)(180,599)(181,602)(182,601)(183,604)(184,603)
(185,606)(186,605)(187,608)(188,607)(189,610)(190,609)(191,612)(192,611)
(193,614)(194,613)(195,616)(196,615)(197,618)(198,617)(199,620)(200,619)
(201,622)(202,621)(203,624)(204,623)(205,626)(206,625)(207,628)(208,627)
(209,630)(210,629)(211,632)(212,631)(213,634)(214,633)(215,636)(216,635)
(217,638)(218,637)(219,640)(220,639)(221,642)(222,641)(223,644)(224,643)
(225,646)(226,645)(227,648)(228,647)(229,650)(230,649)(231,652)(232,651)
(233,654)(234,653)(235,656)(236,655)(237,658)(238,657)(239,660)(240,659)
(241,662)(242,661)(243,664)(244,663)(245,666)(246,665)(247,668)(248,667)
(249,670)(250,669)(251,672)(252,671)(253,674)(254,673)(255,676)(256,675)
(257,678)(258,677)(259,680)(260,679)(261,682)(262,681)(263,684)(264,683)
(265,686)(266,685)(267,688)(268,687)(269,690)(270,689)(271,692)(272,691)
(273,694)(274,693)(275,696)(276,695)(277,698)(278,697)(279,700)(280,699)
(281,702)(282,701)(283,704)(284,703)(285,706)(286,705)(287,708)(288,707)
(289,710)(290,709)(291,712)(292,711)(293,714)(294,713)(295,716)(296,715)
(297,718)(298,717)(299,720)(300,719)(301,722)(302,721)(303,724)(304,723)
(305,726)(306,725)(307,728)(308,727)(309,730)(310,729)(311,732)(312,731)
(313,734)(314,733)(315,736)(316,735)(317,738)(318,737)(319,740)(320,739)
(321,742)(322,741)(323,744)(324,743)(325,746)(326,745)(327,748)(328,747)
(329,750)(330,749)(331,752)(332,751)(333,754)(334,753)(335,756)(336,755)
(337,758)(338,757)(339,760)(340,759)(341,762)(342,761)(343,764)(344,763)
(345,766)(346,765)(347,768)(348,767)(349,770)(350,769)(351,772)(352,771)
(353,774)(354,773)(355,776)(356,775)(357,778)(358,777)(359,780)(360,779)
(361,782)(362,781)(363,784)(364,783)(365,786)(366,785)(367,788)(368,787)
(369,790)(370,789)(371,792)(372,791)(373,794)(374,793)(375,796)(376,795)
(377,798)(378,797)(379,800)(380,799)(381,802)(382,801)(383,804)(384,803)
(385,806)(386,805)(387,808)(388,807)(389,810)(390,809)(391,812)(392,811)
(393,814)(394,813)(395,816)(396,815)(397,818)(398,817)(399,820)(400,819)
(401,822)(402,821)(403,824)(404,823)(405,826)(406,825)(407,828)(408,827)
(409,830)(410,829)(411,832)(412,831)(413,834)(414,833)(415,836)(416,835)
(417,838)(418,837)(419,840)(420,839);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(840)!( 3, 4)( 5, 25)( 6, 26)( 7, 28)( 8, 27)( 9, 21)( 10, 22)
( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29,113)( 30,114)
( 31,116)( 32,115)( 33,137)( 34,138)( 35,140)( 36,139)( 37,133)( 38,134)
( 39,136)( 40,135)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)
( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)( 53,117)( 54,118)
( 55,120)( 56,119)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,109)( 62,110)
( 63,112)( 64,111)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)
( 71,104)( 72,103)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)( 78, 94)
( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(141,281)(142,282)
(143,284)(144,283)(145,305)(146,306)(147,308)(148,307)(149,301)(150,302)
(151,304)(152,303)(153,297)(154,298)(155,300)(156,299)(157,293)(158,294)
(159,296)(160,295)(161,289)(162,290)(163,292)(164,291)(165,285)(166,286)
(167,288)(168,287)(169,393)(170,394)(171,396)(172,395)(173,417)(174,418)
(175,420)(176,419)(177,413)(178,414)(179,416)(180,415)(181,409)(182,410)
(183,412)(184,411)(185,405)(186,406)(187,408)(188,407)(189,401)(190,402)
(191,404)(192,403)(193,397)(194,398)(195,400)(196,399)(197,365)(198,366)
(199,368)(200,367)(201,389)(202,390)(203,392)(204,391)(205,385)(206,386)
(207,388)(208,387)(209,381)(210,382)(211,384)(212,383)(213,377)(214,378)
(215,380)(216,379)(217,373)(218,374)(219,376)(220,375)(221,369)(222,370)
(223,372)(224,371)(225,337)(226,338)(227,340)(228,339)(229,361)(230,362)
(231,364)(232,363)(233,357)(234,358)(235,360)(236,359)(237,353)(238,354)
(239,356)(240,355)(241,349)(242,350)(243,352)(244,351)(245,345)(246,346)
(247,348)(248,347)(249,341)(250,342)(251,344)(252,343)(253,309)(254,310)
(255,312)(256,311)(257,333)(258,334)(259,336)(260,335)(261,329)(262,330)
(263,332)(264,331)(265,325)(266,326)(267,328)(268,327)(269,321)(270,322)
(271,324)(272,323)(273,317)(274,318)(275,320)(276,319)(277,313)(278,314)
(279,316)(280,315)(423,424)(425,445)(426,446)(427,448)(428,447)(429,441)
(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(449,533)
(450,534)(451,536)(452,535)(453,557)(454,558)(455,560)(456,559)(457,553)
(458,554)(459,556)(460,555)(461,549)(462,550)(463,552)(464,551)(465,545)
(466,546)(467,548)(468,547)(469,541)(470,542)(471,544)(472,543)(473,537)
(474,538)(475,540)(476,539)(477,505)(478,506)(479,508)(480,507)(481,529)
(482,530)(483,532)(484,531)(485,525)(486,526)(487,528)(488,527)(489,521)
(490,522)(491,524)(492,523)(493,517)(494,518)(495,520)(496,519)(497,513)
(498,514)(499,516)(500,515)(501,509)(502,510)(503,512)(504,511)(561,701)
(562,702)(563,704)(564,703)(565,725)(566,726)(567,728)(568,727)(569,721)
(570,722)(571,724)(572,723)(573,717)(574,718)(575,720)(576,719)(577,713)
(578,714)(579,716)(580,715)(581,709)(582,710)(583,712)(584,711)(585,705)
(586,706)(587,708)(588,707)(589,813)(590,814)(591,816)(592,815)(593,837)
(594,838)(595,840)(596,839)(597,833)(598,834)(599,836)(600,835)(601,829)
(602,830)(603,832)(604,831)(605,825)(606,826)(607,828)(608,827)(609,821)
(610,822)(611,824)(612,823)(613,817)(614,818)(615,820)(616,819)(617,785)
(618,786)(619,788)(620,787)(621,809)(622,810)(623,812)(624,811)(625,805)
(626,806)(627,808)(628,807)(629,801)(630,802)(631,804)(632,803)(633,797)
(634,798)(635,800)(636,799)(637,793)(638,794)(639,796)(640,795)(641,789)
(642,790)(643,792)(644,791)(645,757)(646,758)(647,760)(648,759)(649,781)
(650,782)(651,784)(652,783)(653,777)(654,778)(655,780)(656,779)(657,773)
(658,774)(659,776)(660,775)(661,769)(662,770)(663,772)(664,771)(665,765)
(666,766)(667,768)(668,767)(669,761)(670,762)(671,764)(672,763)(673,729)
(674,730)(675,732)(676,731)(677,753)(678,754)(679,756)(680,755)(681,749)
(682,750)(683,752)(684,751)(685,745)(686,746)(687,748)(688,747)(689,741)
(690,742)(691,744)(692,743)(693,737)(694,738)(695,740)(696,739)(697,733)
(698,734)(699,736)(700,735);
s1 := Sym(840)!( 1,593)( 2,596)( 3,595)( 4,594)( 5,589)( 6,592)( 7,591)
( 8,590)( 9,613)( 10,616)( 11,615)( 12,614)( 13,609)( 14,612)( 15,611)
( 16,610)( 17,605)( 18,608)( 19,607)( 20,606)( 21,601)( 22,604)( 23,603)
( 24,602)( 25,597)( 26,600)( 27,599)( 28,598)( 29,565)( 30,568)( 31,567)
( 32,566)( 33,561)( 34,564)( 35,563)( 36,562)( 37,585)( 38,588)( 39,587)
( 40,586)( 41,581)( 42,584)( 43,583)( 44,582)( 45,577)( 46,580)( 47,579)
( 48,578)( 49,573)( 50,576)( 51,575)( 52,574)( 53,569)( 54,572)( 55,571)
( 56,570)( 57,677)( 58,680)( 59,679)( 60,678)( 61,673)( 62,676)( 63,675)
( 64,674)( 65,697)( 66,700)( 67,699)( 68,698)( 69,693)( 70,696)( 71,695)
( 72,694)( 73,689)( 74,692)( 75,691)( 76,690)( 77,685)( 78,688)( 79,687)
( 80,686)( 81,681)( 82,684)( 83,683)( 84,682)( 85,649)( 86,652)( 87,651)
( 88,650)( 89,645)( 90,648)( 91,647)( 92,646)( 93,669)( 94,672)( 95,671)
( 96,670)( 97,665)( 98,668)( 99,667)(100,666)(101,661)(102,664)(103,663)
(104,662)(105,657)(106,660)(107,659)(108,658)(109,653)(110,656)(111,655)
(112,654)(113,621)(114,624)(115,623)(116,622)(117,617)(118,620)(119,619)
(120,618)(121,641)(122,644)(123,643)(124,642)(125,637)(126,640)(127,639)
(128,638)(129,633)(130,636)(131,635)(132,634)(133,629)(134,632)(135,631)
(136,630)(137,625)(138,628)(139,627)(140,626)(141,453)(142,456)(143,455)
(144,454)(145,449)(146,452)(147,451)(148,450)(149,473)(150,476)(151,475)
(152,474)(153,469)(154,472)(155,471)(156,470)(157,465)(158,468)(159,467)
(160,466)(161,461)(162,464)(163,463)(164,462)(165,457)(166,460)(167,459)
(168,458)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)
(176,422)(177,445)(178,448)(179,447)(180,446)(181,441)(182,444)(183,443)
(184,442)(185,437)(186,440)(187,439)(188,438)(189,433)(190,436)(191,435)
(192,434)(193,429)(194,432)(195,431)(196,430)(197,537)(198,540)(199,539)
(200,538)(201,533)(202,536)(203,535)(204,534)(205,557)(206,560)(207,559)
(208,558)(209,553)(210,556)(211,555)(212,554)(213,549)(214,552)(215,551)
(216,550)(217,545)(218,548)(219,547)(220,546)(221,541)(222,544)(223,543)
(224,542)(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)
(232,506)(233,529)(234,532)(235,531)(236,530)(237,525)(238,528)(239,527)
(240,526)(241,521)(242,524)(243,523)(244,522)(245,517)(246,520)(247,519)
(248,518)(249,513)(250,516)(251,515)(252,514)(253,481)(254,484)(255,483)
(256,482)(257,477)(258,480)(259,479)(260,478)(261,501)(262,504)(263,503)
(264,502)(265,497)(266,500)(267,499)(268,498)(269,493)(270,496)(271,495)
(272,494)(273,489)(274,492)(275,491)(276,490)(277,485)(278,488)(279,487)
(280,486)(281,733)(282,736)(283,735)(284,734)(285,729)(286,732)(287,731)
(288,730)(289,753)(290,756)(291,755)(292,754)(293,749)(294,752)(295,751)
(296,750)(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)
(304,742)(305,737)(306,740)(307,739)(308,738)(309,705)(310,708)(311,707)
(312,706)(313,701)(314,704)(315,703)(316,702)(317,725)(318,728)(319,727)
(320,726)(321,721)(322,724)(323,723)(324,722)(325,717)(326,720)(327,719)
(328,718)(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)
(336,710)(337,817)(338,820)(339,819)(340,818)(341,813)(342,816)(343,815)
(344,814)(345,837)(346,840)(347,839)(348,838)(349,833)(350,836)(351,835)
(352,834)(353,829)(354,832)(355,831)(356,830)(357,825)(358,828)(359,827)
(360,826)(361,821)(362,824)(363,823)(364,822)(365,789)(366,792)(367,791)
(368,790)(369,785)(370,788)(371,787)(372,786)(373,809)(374,812)(375,811)
(376,810)(377,805)(378,808)(379,807)(380,806)(381,801)(382,804)(383,803)
(384,802)(385,797)(386,800)(387,799)(388,798)(389,793)(390,796)(391,795)
(392,794)(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)
(400,758)(401,781)(402,784)(403,783)(404,782)(405,777)(406,780)(407,779)
(408,778)(409,773)(410,776)(411,775)(412,774)(413,769)(414,772)(415,771)
(416,770)(417,765)(418,768)(419,767)(420,766);
s2 := Sym(840)!( 1,422)( 2,421)( 3,424)( 4,423)( 5,426)( 6,425)( 7,428)
( 8,427)( 9,430)( 10,429)( 11,432)( 12,431)( 13,434)( 14,433)( 15,436)
( 16,435)( 17,438)( 18,437)( 19,440)( 20,439)( 21,442)( 22,441)( 23,444)
( 24,443)( 25,446)( 26,445)( 27,448)( 28,447)( 29,450)( 30,449)( 31,452)
( 32,451)( 33,454)( 34,453)( 35,456)( 36,455)( 37,458)( 38,457)( 39,460)
( 40,459)( 41,462)( 42,461)( 43,464)( 44,463)( 45,466)( 46,465)( 47,468)
( 48,467)( 49,470)( 50,469)( 51,472)( 52,471)( 53,474)( 54,473)( 55,476)
( 56,475)( 57,478)( 58,477)( 59,480)( 60,479)( 61,482)( 62,481)( 63,484)
( 64,483)( 65,486)( 66,485)( 67,488)( 68,487)( 69,490)( 70,489)( 71,492)
( 72,491)( 73,494)( 74,493)( 75,496)( 76,495)( 77,498)( 78,497)( 79,500)
( 80,499)( 81,502)( 82,501)( 83,504)( 84,503)( 85,506)( 86,505)( 87,508)
( 88,507)( 89,510)( 90,509)( 91,512)( 92,511)( 93,514)( 94,513)( 95,516)
( 96,515)( 97,518)( 98,517)( 99,520)(100,519)(101,522)(102,521)(103,524)
(104,523)(105,526)(106,525)(107,528)(108,527)(109,530)(110,529)(111,532)
(112,531)(113,534)(114,533)(115,536)(116,535)(117,538)(118,537)(119,540)
(120,539)(121,542)(122,541)(123,544)(124,543)(125,546)(126,545)(127,548)
(128,547)(129,550)(130,549)(131,552)(132,551)(133,554)(134,553)(135,556)
(136,555)(137,558)(138,557)(139,560)(140,559)(141,562)(142,561)(143,564)
(144,563)(145,566)(146,565)(147,568)(148,567)(149,570)(150,569)(151,572)
(152,571)(153,574)(154,573)(155,576)(156,575)(157,578)(158,577)(159,580)
(160,579)(161,582)(162,581)(163,584)(164,583)(165,586)(166,585)(167,588)
(168,587)(169,590)(170,589)(171,592)(172,591)(173,594)(174,593)(175,596)
(176,595)(177,598)(178,597)(179,600)(180,599)(181,602)(182,601)(183,604)
(184,603)(185,606)(186,605)(187,608)(188,607)(189,610)(190,609)(191,612)
(192,611)(193,614)(194,613)(195,616)(196,615)(197,618)(198,617)(199,620)
(200,619)(201,622)(202,621)(203,624)(204,623)(205,626)(206,625)(207,628)
(208,627)(209,630)(210,629)(211,632)(212,631)(213,634)(214,633)(215,636)
(216,635)(217,638)(218,637)(219,640)(220,639)(221,642)(222,641)(223,644)
(224,643)(225,646)(226,645)(227,648)(228,647)(229,650)(230,649)(231,652)
(232,651)(233,654)(234,653)(235,656)(236,655)(237,658)(238,657)(239,660)
(240,659)(241,662)(242,661)(243,664)(244,663)(245,666)(246,665)(247,668)
(248,667)(249,670)(250,669)(251,672)(252,671)(253,674)(254,673)(255,676)
(256,675)(257,678)(258,677)(259,680)(260,679)(261,682)(262,681)(263,684)
(264,683)(265,686)(266,685)(267,688)(268,687)(269,690)(270,689)(271,692)
(272,691)(273,694)(274,693)(275,696)(276,695)(277,698)(278,697)(279,700)
(280,699)(281,702)(282,701)(283,704)(284,703)(285,706)(286,705)(287,708)
(288,707)(289,710)(290,709)(291,712)(292,711)(293,714)(294,713)(295,716)
(296,715)(297,718)(298,717)(299,720)(300,719)(301,722)(302,721)(303,724)
(304,723)(305,726)(306,725)(307,728)(308,727)(309,730)(310,729)(311,732)
(312,731)(313,734)(314,733)(315,736)(316,735)(317,738)(318,737)(319,740)
(320,739)(321,742)(322,741)(323,744)(324,743)(325,746)(326,745)(327,748)
(328,747)(329,750)(330,749)(331,752)(332,751)(333,754)(334,753)(335,756)
(336,755)(337,758)(338,757)(339,760)(340,759)(341,762)(342,761)(343,764)
(344,763)(345,766)(346,765)(347,768)(348,767)(349,770)(350,769)(351,772)
(352,771)(353,774)(354,773)(355,776)(356,775)(357,778)(358,777)(359,780)
(360,779)(361,782)(362,781)(363,784)(364,783)(365,786)(366,785)(367,788)
(368,787)(369,790)(370,789)(371,792)(372,791)(373,794)(374,793)(375,796)
(376,795)(377,798)(378,797)(379,800)(380,799)(381,802)(382,801)(383,804)
(384,803)(385,806)(386,805)(387,808)(388,807)(389,810)(390,809)(391,812)
(392,811)(393,814)(394,813)(395,816)(396,815)(397,818)(398,817)(399,820)
(400,819)(401,822)(402,821)(403,824)(404,823)(405,826)(406,825)(407,828)
(408,827)(409,830)(410,829)(411,832)(412,831)(413,834)(414,833)(415,836)
(416,835)(417,838)(418,837)(419,840)(420,839);
poly := sub<Sym(840)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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