Polytope of Type {8,106}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,106}*1696
Also Known As : {8,106|2}. if this polytope has another name.
Group : SmallGroup(1696,155)
Rank : 3
Schlafli Type : {8,106}
Number of vertices, edges, etc : 8, 424, 106
Order of s₀s₁s₂ : 424
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,106}*848
   4-fold quotients : {2,106}*424
   8-fold quotients : {2,53}*212
   53-fold quotients : {8,2}*32
   106-fold quotients : {4,2}*16
   212-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (107,160)(108,161)(109,162)(110,163)(111,164)(112,165)(113,166)(114,167)
(115,168)(116,169)(117,170)(118,171)(119,172)(120,173)(121,174)(122,175)
(123,176)(124,177)(125,178)(126,179)(127,180)(128,181)(129,182)(130,183)
(131,184)(132,185)(133,186)(134,187)(135,188)(136,189)(137,190)(138,191)
(139,192)(140,193)(141,194)(142,195)(143,196)(144,197)(145,198)(146,199)
(147,200)(148,201)(149,202)(150,203)(151,204)(152,205)(153,206)(154,207)
(155,208)(156,209)(157,210)(158,211)(159,212)(319,372)(320,373)(321,374)
(322,375)(323,376)(324,377)(325,378)(326,379)(327,380)(328,381)(329,382)
(330,383)(331,384)(332,385)(333,386)(334,387)(335,388)(336,389)(337,390)
(338,391)(339,392)(340,393)(341,394)(342,395)(343,396)(344,397)(345,398)
(346,399)(347,400)(348,401)(349,402)(350,403)(351,404)(352,405)(353,406)
(354,407)(355,408)(356,409)(357,410)(358,411)(359,412)(360,413)(361,414)
(362,415)(363,416)(364,417)(365,418)(366,419)(367,420)(368,421)(369,422)
(370,423)(371,424)(425,531)(426,532)(427,533)(428,534)(429,535)(430,536)
(431,537)(432,538)(433,539)(434,540)(435,541)(436,542)(437,543)(438,544)
(439,545)(440,546)(441,547)(442,548)(443,549)(444,550)(445,551)(446,552)
(447,553)(448,554)(449,555)(450,556)(451,557)(452,558)(453,559)(454,560)
(455,561)(456,562)(457,563)(458,564)(459,565)(460,566)(461,567)(462,568)
(463,569)(464,570)(465,571)(466,572)(467,573)(468,574)(469,575)(470,576)
(471,577)(472,578)(473,579)(474,580)(475,581)(476,582)(477,583)(478,584)
(479,585)(480,586)(481,587)(482,588)(483,589)(484,590)(485,591)(486,592)
(487,593)(488,594)(489,595)(490,596)(491,597)(492,598)(493,599)(494,600)
(495,601)(496,602)(497,603)(498,604)(499,605)(500,606)(501,607)(502,608)
(503,609)(504,610)(505,611)(506,612)(507,613)(508,614)(509,615)(510,616)
(511,617)(512,618)(513,619)(514,620)(515,621)(516,622)(517,623)(518,624)
(519,625)(520,626)(521,627)(522,628)(523,629)(524,630)(525,631)(526,632)
(527,633)(528,634)(529,635)(530,636)(637,743)(638,744)(639,745)(640,746)
(641,747)(642,748)(643,749)(644,750)(645,751)(646,752)(647,753)(648,754)
(649,755)(650,756)(651,757)(652,758)(653,759)(654,760)(655,761)(656,762)
(657,763)(658,764)(659,765)(660,766)(661,767)(662,768)(663,769)(664,770)
(665,771)(666,772)(667,773)(668,774)(669,775)(670,776)(671,777)(672,778)
(673,779)(674,780)(675,781)(676,782)(677,783)(678,784)(679,785)(680,786)
(681,787)(682,788)(683,789)(684,790)(685,791)(686,792)(687,793)(688,794)
(689,795)(690,796)(691,797)(692,798)(693,799)(694,800)(695,801)(696,802)
(697,803)(698,804)(699,805)(700,806)(701,807)(702,808)(703,809)(704,810)
(705,811)(706,812)(707,813)(708,814)(709,815)(710,816)(711,817)(712,818)
(713,819)(714,820)(715,821)(716,822)(717,823)(718,824)(719,825)(720,826)
(721,827)(722,828)(723,829)(724,830)(725,831)(726,832)(727,833)(728,834)
(729,835)(730,836)(731,837)(732,838)(733,839)(734,840)(735,841)(736,842)
(737,843)(738,844)(739,845)(740,846)(741,847)(742,848);;
s1 := (  1,637)(  2,689)(  3,688)(  4,687)(  5,686)(  6,685)(  7,684)(  8,683)
(  9,682)( 10,681)( 11,680)( 12,679)( 13,678)( 14,677)( 15,676)( 16,675)
( 17,674)( 18,673)( 19,672)( 20,671)( 21,670)( 22,669)( 23,668)( 24,667)
( 25,666)( 26,665)( 27,664)( 28,663)( 29,662)( 30,661)( 31,660)( 32,659)
( 33,658)( 34,657)( 35,656)( 36,655)( 37,654)( 38,653)( 39,652)( 40,651)
( 41,650)( 42,649)( 43,648)( 44,647)( 45,646)( 46,645)( 47,644)( 48,643)
( 49,642)( 50,641)( 51,640)( 52,639)( 53,638)( 54,690)( 55,742)( 56,741)
( 57,740)( 58,739)( 59,738)( 60,737)( 61,736)( 62,735)( 63,734)( 64,733)
( 65,732)( 66,731)( 67,730)( 68,729)( 69,728)( 70,727)( 71,726)( 72,725)
( 73,724)( 74,723)( 75,722)( 76,721)( 77,720)( 78,719)( 79,718)( 80,717)
( 81,716)( 82,715)( 83,714)( 84,713)( 85,712)( 86,711)( 87,710)( 88,709)
( 89,708)( 90,707)( 91,706)( 92,705)( 93,704)( 94,703)( 95,702)( 96,701)
( 97,700)( 98,699)( 99,698)(100,697)(101,696)(102,695)(103,694)(104,693)
(105,692)(106,691)(107,796)(108,848)(109,847)(110,846)(111,845)(112,844)
(113,843)(114,842)(115,841)(116,840)(117,839)(118,838)(119,837)(120,836)
(121,835)(122,834)(123,833)(124,832)(125,831)(126,830)(127,829)(128,828)
(129,827)(130,826)(131,825)(132,824)(133,823)(134,822)(135,821)(136,820)
(137,819)(138,818)(139,817)(140,816)(141,815)(142,814)(143,813)(144,812)
(145,811)(146,810)(147,809)(148,808)(149,807)(150,806)(151,805)(152,804)
(153,803)(154,802)(155,801)(156,800)(157,799)(158,798)(159,797)(160,743)
(161,795)(162,794)(163,793)(164,792)(165,791)(166,790)(167,789)(168,788)
(169,787)(170,786)(171,785)(172,784)(173,783)(174,782)(175,781)(176,780)
(177,779)(178,778)(179,777)(180,776)(181,775)(182,774)(183,773)(184,772)
(185,771)(186,770)(187,769)(188,768)(189,767)(190,766)(191,765)(192,764)
(193,763)(194,762)(195,761)(196,760)(197,759)(198,758)(199,757)(200,756)
(201,755)(202,754)(203,753)(204,752)(205,751)(206,750)(207,749)(208,748)
(209,747)(210,746)(211,745)(212,744)(213,425)(214,477)(215,476)(216,475)
(217,474)(218,473)(219,472)(220,471)(221,470)(222,469)(223,468)(224,467)
(225,466)(226,465)(227,464)(228,463)(229,462)(230,461)(231,460)(232,459)
(233,458)(234,457)(235,456)(236,455)(237,454)(238,453)(239,452)(240,451)
(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)(248,443)
(249,442)(250,441)(251,440)(252,439)(253,438)(254,437)(255,436)(256,435)
(257,434)(258,433)(259,432)(260,431)(261,430)(262,429)(263,428)(264,427)
(265,426)(266,478)(267,530)(268,529)(269,528)(270,527)(271,526)(272,525)
(273,524)(274,523)(275,522)(276,521)(277,520)(278,519)(279,518)(280,517)
(281,516)(282,515)(283,514)(284,513)(285,512)(286,511)(287,510)(288,509)
(289,508)(290,507)(291,506)(292,505)(293,504)(294,503)(295,502)(296,501)
(297,500)(298,499)(299,498)(300,497)(301,496)(302,495)(303,494)(304,493)
(305,492)(306,491)(307,490)(308,489)(309,488)(310,487)(311,486)(312,485)
(313,484)(314,483)(315,482)(316,481)(317,480)(318,479)(319,584)(320,636)
(321,635)(322,634)(323,633)(324,632)(325,631)(326,630)(327,629)(328,628)
(329,627)(330,626)(331,625)(332,624)(333,623)(334,622)(335,621)(336,620)
(337,619)(338,618)(339,617)(340,616)(341,615)(342,614)(343,613)(344,612)
(345,611)(346,610)(347,609)(348,608)(349,607)(350,606)(351,605)(352,604)
(353,603)(354,602)(355,601)(356,600)(357,599)(358,598)(359,597)(360,596)
(361,595)(362,594)(363,593)(364,592)(365,591)(366,590)(367,589)(368,588)
(369,587)(370,586)(371,585)(372,531)(373,583)(374,582)(375,581)(376,580)
(377,579)(378,578)(379,577)(380,576)(381,575)(382,574)(383,573)(384,572)
(385,571)(386,570)(387,569)(388,568)(389,567)(390,566)(391,565)(392,564)
(393,563)(394,562)(395,561)(396,560)(397,559)(398,558)(399,557)(400,556)
(401,555)(402,554)(403,553)(404,552)(405,551)(406,550)(407,549)(408,548)
(409,547)(410,546)(411,545)(412,544)(413,543)(414,542)(415,541)(416,540)
(417,539)(418,538)(419,537)(420,536)(421,535)(422,534)(423,533)(424,532);;
s2 := (  1,214)(  2,213)(  3,265)(  4,264)(  5,263)(  6,262)(  7,261)(  8,260)
(  9,259)( 10,258)( 11,257)( 12,256)( 13,255)( 14,254)( 15,253)( 16,252)
( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,246)( 23,245)( 24,244)
( 25,243)( 26,242)( 27,241)( 28,240)( 29,239)( 30,238)( 31,237)( 32,236)
( 33,235)( 34,234)( 35,233)( 36,232)( 37,231)( 38,230)( 39,229)( 40,228)
( 41,227)( 42,226)( 43,225)( 44,224)( 45,223)( 46,222)( 47,221)( 48,220)
( 49,219)( 50,218)( 51,217)( 52,216)( 53,215)( 54,267)( 55,266)( 56,318)
( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,310)
( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)( 72,302)
( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)
( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)
( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)(104,270)
(105,269)(106,268)(107,320)(108,319)(109,371)(110,370)(111,369)(112,368)
(113,367)(114,366)(115,365)(116,364)(117,363)(118,362)(119,361)(120,360)
(121,359)(122,358)(123,357)(124,356)(125,355)(126,354)(127,353)(128,352)
(129,351)(130,350)(131,349)(132,348)(133,347)(134,346)(135,345)(136,344)
(137,343)(138,342)(139,341)(140,340)(141,339)(142,338)(143,337)(144,336)
(145,335)(146,334)(147,333)(148,332)(149,331)(150,330)(151,329)(152,328)
(153,327)(154,326)(155,325)(156,324)(157,323)(158,322)(159,321)(160,373)
(161,372)(162,424)(163,423)(164,422)(165,421)(166,420)(167,419)(168,418)
(169,417)(170,416)(171,415)(172,414)(173,413)(174,412)(175,411)(176,410)
(177,409)(178,408)(179,407)(180,406)(181,405)(182,404)(183,403)(184,402)
(185,401)(186,400)(187,399)(188,398)(189,397)(190,396)(191,395)(192,394)
(193,393)(194,392)(195,391)(196,390)(197,389)(198,388)(199,387)(200,386)
(201,385)(202,384)(203,383)(204,382)(205,381)(206,380)(207,379)(208,378)
(209,377)(210,376)(211,375)(212,374)(425,638)(426,637)(427,689)(428,688)
(429,687)(430,686)(431,685)(432,684)(433,683)(434,682)(435,681)(436,680)
(437,679)(438,678)(439,677)(440,676)(441,675)(442,674)(443,673)(444,672)
(445,671)(446,670)(447,669)(448,668)(449,667)(450,666)(451,665)(452,664)
(453,663)(454,662)(455,661)(456,660)(457,659)(458,658)(459,657)(460,656)
(461,655)(462,654)(463,653)(464,652)(465,651)(466,650)(467,649)(468,648)
(469,647)(470,646)(471,645)(472,644)(473,643)(474,642)(475,641)(476,640)
(477,639)(478,691)(479,690)(480,742)(481,741)(482,740)(483,739)(484,738)
(485,737)(486,736)(487,735)(488,734)(489,733)(490,732)(491,731)(492,730)
(493,729)(494,728)(495,727)(496,726)(497,725)(498,724)(499,723)(500,722)
(501,721)(502,720)(503,719)(504,718)(505,717)(506,716)(507,715)(508,714)
(509,713)(510,712)(511,711)(512,710)(513,709)(514,708)(515,707)(516,706)
(517,705)(518,704)(519,703)(520,702)(521,701)(522,700)(523,699)(524,698)
(525,697)(526,696)(527,695)(528,694)(529,693)(530,692)(531,744)(532,743)
(533,795)(534,794)(535,793)(536,792)(537,791)(538,790)(539,789)(540,788)
(541,787)(542,786)(543,785)(544,784)(545,783)(546,782)(547,781)(548,780)
(549,779)(550,778)(551,777)(552,776)(553,775)(554,774)(555,773)(556,772)
(557,771)(558,770)(559,769)(560,768)(561,767)(562,766)(563,765)(564,764)
(565,763)(566,762)(567,761)(568,760)(569,759)(570,758)(571,757)(572,756)
(573,755)(574,754)(575,753)(576,752)(577,751)(578,750)(579,749)(580,748)
(581,747)(582,746)(583,745)(584,797)(585,796)(586,848)(587,847)(588,846)
(589,845)(590,844)(591,843)(592,842)(593,841)(594,840)(595,839)(596,838)
(597,837)(598,836)(599,835)(600,834)(601,833)(602,832)(603,831)(604,830)
(605,829)(606,828)(607,827)(608,826)(609,825)(610,824)(611,823)(612,822)
(613,821)(614,820)(615,819)(616,818)(617,817)(618,816)(619,815)(620,814)
(621,813)(622,812)(623,811)(624,810)(625,809)(626,808)(627,807)(628,806)
(629,805)(630,804)(631,803)(632,802)(633,801)(634,800)(635,799)(636,798);;
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*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(848)!(107,160)(108,161)(109,162)(110,163)(111,164)(112,165)(113,166)
(114,167)(115,168)(116,169)(117,170)(118,171)(119,172)(120,173)(121,174)
(122,175)(123,176)(124,177)(125,178)(126,179)(127,180)(128,181)(129,182)
(130,183)(131,184)(132,185)(133,186)(134,187)(135,188)(136,189)(137,190)
(138,191)(139,192)(140,193)(141,194)(142,195)(143,196)(144,197)(145,198)
(146,199)(147,200)(148,201)(149,202)(150,203)(151,204)(152,205)(153,206)
(154,207)(155,208)(156,209)(157,210)(158,211)(159,212)(319,372)(320,373)
(321,374)(322,375)(323,376)(324,377)(325,378)(326,379)(327,380)(328,381)
(329,382)(330,383)(331,384)(332,385)(333,386)(334,387)(335,388)(336,389)
(337,390)(338,391)(339,392)(340,393)(341,394)(342,395)(343,396)(344,397)
(345,398)(346,399)(347,400)(348,401)(349,402)(350,403)(351,404)(352,405)
(353,406)(354,407)(355,408)(356,409)(357,410)(358,411)(359,412)(360,413)
(361,414)(362,415)(363,416)(364,417)(365,418)(366,419)(367,420)(368,421)
(369,422)(370,423)(371,424)(425,531)(426,532)(427,533)(428,534)(429,535)
(430,536)(431,537)(432,538)(433,539)(434,540)(435,541)(436,542)(437,543)
(438,544)(439,545)(440,546)(441,547)(442,548)(443,549)(444,550)(445,551)
(446,552)(447,553)(448,554)(449,555)(450,556)(451,557)(452,558)(453,559)
(454,560)(455,561)(456,562)(457,563)(458,564)(459,565)(460,566)(461,567)
(462,568)(463,569)(464,570)(465,571)(466,572)(467,573)(468,574)(469,575)
(470,576)(471,577)(472,578)(473,579)(474,580)(475,581)(476,582)(477,583)
(478,584)(479,585)(480,586)(481,587)(482,588)(483,589)(484,590)(485,591)
(486,592)(487,593)(488,594)(489,595)(490,596)(491,597)(492,598)(493,599)
(494,600)(495,601)(496,602)(497,603)(498,604)(499,605)(500,606)(501,607)
(502,608)(503,609)(504,610)(505,611)(506,612)(507,613)(508,614)(509,615)
(510,616)(511,617)(512,618)(513,619)(514,620)(515,621)(516,622)(517,623)
(518,624)(519,625)(520,626)(521,627)(522,628)(523,629)(524,630)(525,631)
(526,632)(527,633)(528,634)(529,635)(530,636)(637,743)(638,744)(639,745)
(640,746)(641,747)(642,748)(643,749)(644,750)(645,751)(646,752)(647,753)
(648,754)(649,755)(650,756)(651,757)(652,758)(653,759)(654,760)(655,761)
(656,762)(657,763)(658,764)(659,765)(660,766)(661,767)(662,768)(663,769)
(664,770)(665,771)(666,772)(667,773)(668,774)(669,775)(670,776)(671,777)
(672,778)(673,779)(674,780)(675,781)(676,782)(677,783)(678,784)(679,785)
(680,786)(681,787)(682,788)(683,789)(684,790)(685,791)(686,792)(687,793)
(688,794)(689,795)(690,796)(691,797)(692,798)(693,799)(694,800)(695,801)
(696,802)(697,803)(698,804)(699,805)(700,806)(701,807)(702,808)(703,809)
(704,810)(705,811)(706,812)(707,813)(708,814)(709,815)(710,816)(711,817)
(712,818)(713,819)(714,820)(715,821)(716,822)(717,823)(718,824)(719,825)
(720,826)(721,827)(722,828)(723,829)(724,830)(725,831)(726,832)(727,833)
(728,834)(729,835)(730,836)(731,837)(732,838)(733,839)(734,840)(735,841)
(736,842)(737,843)(738,844)(739,845)(740,846)(741,847)(742,848);
s1 := Sym(848)!(  1,637)(  2,689)(  3,688)(  4,687)(  5,686)(  6,685)(  7,684)
(  8,683)(  9,682)( 10,681)( 11,680)( 12,679)( 13,678)( 14,677)( 15,676)
( 16,675)( 17,674)( 18,673)( 19,672)( 20,671)( 21,670)( 22,669)( 23,668)
( 24,667)( 25,666)( 26,665)( 27,664)( 28,663)( 29,662)( 30,661)( 31,660)
( 32,659)( 33,658)( 34,657)( 35,656)( 36,655)( 37,654)( 38,653)( 39,652)
( 40,651)( 41,650)( 42,649)( 43,648)( 44,647)( 45,646)( 46,645)( 47,644)
( 48,643)( 49,642)( 50,641)( 51,640)( 52,639)( 53,638)( 54,690)( 55,742)
( 56,741)( 57,740)( 58,739)( 59,738)( 60,737)( 61,736)( 62,735)( 63,734)
( 64,733)( 65,732)( 66,731)( 67,730)( 68,729)( 69,728)( 70,727)( 71,726)
( 72,725)( 73,724)( 74,723)( 75,722)( 76,721)( 77,720)( 78,719)( 79,718)
( 80,717)( 81,716)( 82,715)( 83,714)( 84,713)( 85,712)( 86,711)( 87,710)
( 88,709)( 89,708)( 90,707)( 91,706)( 92,705)( 93,704)( 94,703)( 95,702)
( 96,701)( 97,700)( 98,699)( 99,698)(100,697)(101,696)(102,695)(103,694)
(104,693)(105,692)(106,691)(107,796)(108,848)(109,847)(110,846)(111,845)
(112,844)(113,843)(114,842)(115,841)(116,840)(117,839)(118,838)(119,837)
(120,836)(121,835)(122,834)(123,833)(124,832)(125,831)(126,830)(127,829)
(128,828)(129,827)(130,826)(131,825)(132,824)(133,823)(134,822)(135,821)
(136,820)(137,819)(138,818)(139,817)(140,816)(141,815)(142,814)(143,813)
(144,812)(145,811)(146,810)(147,809)(148,808)(149,807)(150,806)(151,805)
(152,804)(153,803)(154,802)(155,801)(156,800)(157,799)(158,798)(159,797)
(160,743)(161,795)(162,794)(163,793)(164,792)(165,791)(166,790)(167,789)
(168,788)(169,787)(170,786)(171,785)(172,784)(173,783)(174,782)(175,781)
(176,780)(177,779)(178,778)(179,777)(180,776)(181,775)(182,774)(183,773)
(184,772)(185,771)(186,770)(187,769)(188,768)(189,767)(190,766)(191,765)
(192,764)(193,763)(194,762)(195,761)(196,760)(197,759)(198,758)(199,757)
(200,756)(201,755)(202,754)(203,753)(204,752)(205,751)(206,750)(207,749)
(208,748)(209,747)(210,746)(211,745)(212,744)(213,425)(214,477)(215,476)
(216,475)(217,474)(218,473)(219,472)(220,471)(221,470)(222,469)(223,468)
(224,467)(225,466)(226,465)(227,464)(228,463)(229,462)(230,461)(231,460)
(232,459)(233,458)(234,457)(235,456)(236,455)(237,454)(238,453)(239,452)
(240,451)(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)
(248,443)(249,442)(250,441)(251,440)(252,439)(253,438)(254,437)(255,436)
(256,435)(257,434)(258,433)(259,432)(260,431)(261,430)(262,429)(263,428)
(264,427)(265,426)(266,478)(267,530)(268,529)(269,528)(270,527)(271,526)
(272,525)(273,524)(274,523)(275,522)(276,521)(277,520)(278,519)(279,518)
(280,517)(281,516)(282,515)(283,514)(284,513)(285,512)(286,511)(287,510)
(288,509)(289,508)(290,507)(291,506)(292,505)(293,504)(294,503)(295,502)
(296,501)(297,500)(298,499)(299,498)(300,497)(301,496)(302,495)(303,494)
(304,493)(305,492)(306,491)(307,490)(308,489)(309,488)(310,487)(311,486)
(312,485)(313,484)(314,483)(315,482)(316,481)(317,480)(318,479)(319,584)
(320,636)(321,635)(322,634)(323,633)(324,632)(325,631)(326,630)(327,629)
(328,628)(329,627)(330,626)(331,625)(332,624)(333,623)(334,622)(335,621)
(336,620)(337,619)(338,618)(339,617)(340,616)(341,615)(342,614)(343,613)
(344,612)(345,611)(346,610)(347,609)(348,608)(349,607)(350,606)(351,605)
(352,604)(353,603)(354,602)(355,601)(356,600)(357,599)(358,598)(359,597)
(360,596)(361,595)(362,594)(363,593)(364,592)(365,591)(366,590)(367,589)
(368,588)(369,587)(370,586)(371,585)(372,531)(373,583)(374,582)(375,581)
(376,580)(377,579)(378,578)(379,577)(380,576)(381,575)(382,574)(383,573)
(384,572)(385,571)(386,570)(387,569)(388,568)(389,567)(390,566)(391,565)
(392,564)(393,563)(394,562)(395,561)(396,560)(397,559)(398,558)(399,557)
(400,556)(401,555)(402,554)(403,553)(404,552)(405,551)(406,550)(407,549)
(408,548)(409,547)(410,546)(411,545)(412,544)(413,543)(414,542)(415,541)
(416,540)(417,539)(418,538)(419,537)(420,536)(421,535)(422,534)(423,533)
(424,532);
s2 := Sym(848)!(  1,214)(  2,213)(  3,265)(  4,264)(  5,263)(  6,262)(  7,261)
(  8,260)(  9,259)( 10,258)( 11,257)( 12,256)( 13,255)( 14,254)( 15,253)
( 16,252)( 17,251)( 18,250)( 19,249)( 20,248)( 21,247)( 22,246)( 23,245)
( 24,244)( 25,243)( 26,242)( 27,241)( 28,240)( 29,239)( 30,238)( 31,237)
( 32,236)( 33,235)( 34,234)( 35,233)( 36,232)( 37,231)( 38,230)( 39,229)
( 40,228)( 41,227)( 42,226)( 43,225)( 44,224)( 45,223)( 46,222)( 47,221)
( 48,220)( 49,219)( 50,218)( 51,217)( 52,216)( 53,215)( 54,267)( 55,266)
( 56,318)( 57,317)( 58,316)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)
( 64,310)( 65,309)( 66,308)( 67,307)( 68,306)( 69,305)( 70,304)( 71,303)
( 72,302)( 73,301)( 74,300)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)
( 80,294)( 81,293)( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)
( 88,286)( 89,285)( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)
( 96,278)( 97,277)( 98,276)( 99,275)(100,274)(101,273)(102,272)(103,271)
(104,270)(105,269)(106,268)(107,320)(108,319)(109,371)(110,370)(111,369)
(112,368)(113,367)(114,366)(115,365)(116,364)(117,363)(118,362)(119,361)
(120,360)(121,359)(122,358)(123,357)(124,356)(125,355)(126,354)(127,353)
(128,352)(129,351)(130,350)(131,349)(132,348)(133,347)(134,346)(135,345)
(136,344)(137,343)(138,342)(139,341)(140,340)(141,339)(142,338)(143,337)
(144,336)(145,335)(146,334)(147,333)(148,332)(149,331)(150,330)(151,329)
(152,328)(153,327)(154,326)(155,325)(156,324)(157,323)(158,322)(159,321)
(160,373)(161,372)(162,424)(163,423)(164,422)(165,421)(166,420)(167,419)
(168,418)(169,417)(170,416)(171,415)(172,414)(173,413)(174,412)(175,411)
(176,410)(177,409)(178,408)(179,407)(180,406)(181,405)(182,404)(183,403)
(184,402)(185,401)(186,400)(187,399)(188,398)(189,397)(190,396)(191,395)
(192,394)(193,393)(194,392)(195,391)(196,390)(197,389)(198,388)(199,387)
(200,386)(201,385)(202,384)(203,383)(204,382)(205,381)(206,380)(207,379)
(208,378)(209,377)(210,376)(211,375)(212,374)(425,638)(426,637)(427,689)
(428,688)(429,687)(430,686)(431,685)(432,684)(433,683)(434,682)(435,681)
(436,680)(437,679)(438,678)(439,677)(440,676)(441,675)(442,674)(443,673)
(444,672)(445,671)(446,670)(447,669)(448,668)(449,667)(450,666)(451,665)
(452,664)(453,663)(454,662)(455,661)(456,660)(457,659)(458,658)(459,657)
(460,656)(461,655)(462,654)(463,653)(464,652)(465,651)(466,650)(467,649)
(468,648)(469,647)(470,646)(471,645)(472,644)(473,643)(474,642)(475,641)
(476,640)(477,639)(478,691)(479,690)(480,742)(481,741)(482,740)(483,739)
(484,738)(485,737)(486,736)(487,735)(488,734)(489,733)(490,732)(491,731)
(492,730)(493,729)(494,728)(495,727)(496,726)(497,725)(498,724)(499,723)
(500,722)(501,721)(502,720)(503,719)(504,718)(505,717)(506,716)(507,715)
(508,714)(509,713)(510,712)(511,711)(512,710)(513,709)(514,708)(515,707)
(516,706)(517,705)(518,704)(519,703)(520,702)(521,701)(522,700)(523,699)
(524,698)(525,697)(526,696)(527,695)(528,694)(529,693)(530,692)(531,744)
(532,743)(533,795)(534,794)(535,793)(536,792)(537,791)(538,790)(539,789)
(540,788)(541,787)(542,786)(543,785)(544,784)(545,783)(546,782)(547,781)
(548,780)(549,779)(550,778)(551,777)(552,776)(553,775)(554,774)(555,773)
(556,772)(557,771)(558,770)(559,769)(560,768)(561,767)(562,766)(563,765)
(564,764)(565,763)(566,762)(567,761)(568,760)(569,759)(570,758)(571,757)
(572,756)(573,755)(574,754)(575,753)(576,752)(577,751)(578,750)(579,749)
(580,748)(581,747)(582,746)(583,745)(584,797)(585,796)(586,848)(587,847)
(588,846)(589,845)(590,844)(591,843)(592,842)(593,841)(594,840)(595,839)
(596,838)(597,837)(598,836)(599,835)(600,834)(601,833)(602,832)(603,831)
(604,830)(605,829)(606,828)(607,827)(608,826)(609,825)(610,824)(611,823)
(612,822)(613,821)(614,820)(615,819)(616,818)(617,817)(618,816)(619,815)
(620,814)(621,813)(622,812)(623,811)(624,810)(625,809)(626,808)(627,807)
(628,806)(629,805)(630,804)(631,803)(632,802)(633,801)(634,800)(635,799)
(636,798);
poly := sub<Sym(848)|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*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2 >;

References : None.
to this polytope