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