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Polytope of Type {4,105}

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