Polytope of Type {8,104}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,104}*1664a
if this polytope has a name.
Group : SmallGroup(1664,3565)
Rank : 3
Schlafli Type : {8,104}
Number of vertices, edges, etc : 8, 416, 104
Order of s₀s₁s₂ : 104
Order of s₀s₁s₂s₁ : 4
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 : {4,104}*832b, {8,52}*832a
   4-fold quotients : {4,52}*416, {8,26}*416
   8-fold quotients : {2,52}*208, {4,26}*208
   13-fold quotients : {8,8}*128c
   16-fold quotients : {2,26}*104
   26-fold quotients : {8,4}*64a, {4,8}*64b
   32-fold quotients : {2,13}*52
   52-fold quotients : {4,4}*32, {8,2}*32
   104-fold quotients : {2,4}*16, {4,2}*16
   208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope