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Polytope of Type {8,104}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,104}*1664c
Also Known As : {8,104|2}. if this polytope has another name.
Group : SmallGroup(1664,3566)
Rank : 3
Schlafli Type : {8,104}
Number of vertices, edges, etc : 8, 416, 104
Order of s0s1s2 : 104
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 : {4,104}*832a, {8,52}*832a
   4-fold quotients : {4,52}*416, {2,104}*416, {8,26}*416
   8-fold quotients : {2,52}*208, {4,26}*208
   13-fold quotients : {8,8}*128b
   16-fold quotients : {2,26}*104
   26-fold quotients : {4,8}*64a, {8,4}*64a
   32-fold quotients : {2,13}*52
   52-fold quotients : {4,4}*32, {2,8}*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 := (  1,209)(  2,210)(  3,211)(  4,212)(  5,213)(  6,214)(  7,215)(  8,216)
(  9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)( 16,224)
( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)( 24,232)
( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)( 32,240)
( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)( 40,248)
( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)( 48,256)
( 49,257)( 50,258)( 51,259)( 52,260)( 53,274)( 54,275)( 55,276)( 56,277)
( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)( 64,285)
( 65,286)( 66,261)( 67,262)( 68,263)( 69,264)( 70,265)( 71,266)( 72,267)
( 73,268)( 74,269)( 75,270)( 76,271)( 77,272)( 78,273)( 79,300)( 80,301)
( 81,302)( 82,303)( 83,304)( 84,305)( 85,306)( 86,307)( 87,308)( 88,309)
( 89,310)( 90,311)( 91,312)( 92,287)( 93,288)( 94,289)( 95,290)( 96,291)
( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)(104,299)
(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)(112,333)
(113,334)(114,335)(115,336)(116,337)(117,338)(118,313)(119,314)(120,315)
(121,316)(122,317)(123,318)(124,319)(125,320)(126,321)(127,322)(128,323)
(129,324)(130,325)(131,352)(132,353)(133,354)(134,355)(135,356)(136,357)
(137,358)(138,359)(139,360)(140,361)(141,362)(142,363)(143,364)(144,339)
(145,340)(146,341)(147,342)(148,343)(149,344)(150,345)(151,346)(152,347)
(153,348)(154,349)(155,350)(156,351)(157,365)(158,366)(159,367)(160,368)
(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)(168,376)
(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)(176,384)
(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)(184,392)
(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)(192,400)
(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)(200,408)
(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)(208,416)
(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)(424,632)
(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)(432,640)
(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)(440,648)
(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)(448,656)
(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)(456,664)
(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)(464,672)
(465,673)(466,674)(467,675)(468,676)(469,690)(470,691)(471,692)(472,693)
(473,694)(474,695)(475,696)(476,697)(477,698)(478,699)(479,700)(480,701)
(481,702)(482,677)(483,678)(484,679)(485,680)(486,681)(487,682)(488,683)
(489,684)(490,685)(491,686)(492,687)(493,688)(494,689)(495,716)(496,717)
(497,718)(498,719)(499,720)(500,721)(501,722)(502,723)(503,724)(504,725)
(505,726)(506,727)(507,728)(508,703)(509,704)(510,705)(511,706)(512,707)
(513,708)(514,709)(515,710)(516,711)(517,712)(518,713)(519,714)(520,715)
(521,742)(522,743)(523,744)(524,745)(525,746)(526,747)(527,748)(528,749)
(529,750)(530,751)(531,752)(532,753)(533,754)(534,729)(535,730)(536,731)
(537,732)(538,733)(539,734)(540,735)(541,736)(542,737)(543,738)(544,739)
(545,740)(546,741)(547,768)(548,769)(549,770)(550,771)(551,772)(552,773)
(553,774)(554,775)(555,776)(556,777)(557,778)(558,779)(559,780)(560,755)
(561,756)(562,757)(563,758)(564,759)(565,760)(566,761)(567,762)(568,763)
(569,764)(570,765)(571,766)(572,767)(573,781)(574,782)(575,783)(576,784)
(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)(584,792)
(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)(592,800)
(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)(600,808)
(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)(608,816)
(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)(616,824)
(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)(624,832);;
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 := (  1,626)(  2,625)(  3,637)(  4,636)(  5,635)(  6,634)(  7,633)(  8,632)
(  9,631)( 10,630)( 11,629)( 12,628)( 13,627)( 14,639)( 15,638)( 16,650)
( 17,649)( 18,648)( 19,647)( 20,646)( 21,645)( 22,644)( 23,643)( 24,642)
( 25,641)( 26,640)( 27,652)( 28,651)( 29,663)( 30,662)( 31,661)( 32,660)
( 33,659)( 34,658)( 35,657)( 36,656)( 37,655)( 38,654)( 39,653)( 40,665)
( 41,664)( 42,676)( 43,675)( 44,674)( 45,673)( 46,672)( 47,671)( 48,670)
( 49,669)( 50,668)( 51,667)( 52,666)( 53,678)( 54,677)( 55,689)( 56,688)
( 57,687)( 58,686)( 59,685)( 60,684)( 61,683)( 62,682)( 63,681)( 64,680)
( 65,679)( 66,691)( 67,690)( 68,702)( 69,701)( 70,700)( 71,699)( 72,698)
( 73,697)( 74,696)( 75,695)( 76,694)( 77,693)( 78,692)( 79,704)( 80,703)
( 81,715)( 82,714)( 83,713)( 84,712)( 85,711)( 86,710)( 87,709)( 88,708)
( 89,707)( 90,706)( 91,705)( 92,717)( 93,716)( 94,728)( 95,727)( 96,726)
( 97,725)( 98,724)( 99,723)(100,722)(101,721)(102,720)(103,719)(104,718)
(105,769)(106,768)(107,780)(108,779)(109,778)(110,777)(111,776)(112,775)
(113,774)(114,773)(115,772)(116,771)(117,770)(118,756)(119,755)(120,767)
(121,766)(122,765)(123,764)(124,763)(125,762)(126,761)(127,760)(128,759)
(129,758)(130,757)(131,743)(132,742)(133,754)(134,753)(135,752)(136,751)
(137,750)(138,749)(139,748)(140,747)(141,746)(142,745)(143,744)(144,730)
(145,729)(146,741)(147,740)(148,739)(149,738)(150,737)(151,736)(152,735)
(153,734)(154,733)(155,732)(156,731)(157,821)(158,820)(159,832)(160,831)
(161,830)(162,829)(163,828)(164,827)(165,826)(166,825)(167,824)(168,823)
(169,822)(170,808)(171,807)(172,819)(173,818)(174,817)(175,816)(176,815)
(177,814)(178,813)(179,812)(180,811)(181,810)(182,809)(183,795)(184,794)
(185,806)(186,805)(187,804)(188,803)(189,802)(190,801)(191,800)(192,799)
(193,798)(194,797)(195,796)(196,782)(197,781)(198,793)(199,792)(200,791)
(201,790)(202,789)(203,788)(204,787)(205,786)(206,785)(207,784)(208,783)
(209,418)(210,417)(211,429)(212,428)(213,427)(214,426)(215,425)(216,424)
(217,423)(218,422)(219,421)(220,420)(221,419)(222,431)(223,430)(224,442)
(225,441)(226,440)(227,439)(228,438)(229,437)(230,436)(231,435)(232,434)
(233,433)(234,432)(235,444)(236,443)(237,455)(238,454)(239,453)(240,452)
(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)(248,457)
(249,456)(250,468)(251,467)(252,466)(253,465)(254,464)(255,463)(256,462)
(257,461)(258,460)(259,459)(260,458)(261,470)(262,469)(263,481)(264,480)
(265,479)(266,478)(267,477)(268,476)(269,475)(270,474)(271,473)(272,472)
(273,471)(274,483)(275,482)(276,494)(277,493)(278,492)(279,491)(280,490)
(281,489)(282,488)(283,487)(284,486)(285,485)(286,484)(287,496)(288,495)
(289,507)(290,506)(291,505)(292,504)(293,503)(294,502)(295,501)(296,500)
(297,499)(298,498)(299,497)(300,509)(301,508)(302,520)(303,519)(304,518)
(305,517)(306,516)(307,515)(308,514)(309,513)(310,512)(311,511)(312,510)
(313,561)(314,560)(315,572)(316,571)(317,570)(318,569)(319,568)(320,567)
(321,566)(322,565)(323,564)(324,563)(325,562)(326,548)(327,547)(328,559)
(329,558)(330,557)(331,556)(332,555)(333,554)(334,553)(335,552)(336,551)
(337,550)(338,549)(339,535)(340,534)(341,546)(342,545)(343,544)(344,543)
(345,542)(346,541)(347,540)(348,539)(349,538)(350,537)(351,536)(352,522)
(353,521)(354,533)(355,532)(356,531)(357,530)(358,529)(359,528)(360,527)
(361,526)(362,525)(363,524)(364,523)(365,613)(366,612)(367,624)(368,623)
(369,622)(370,621)(371,620)(372,619)(373,618)(374,617)(375,616)(376,615)
(377,614)(378,600)(379,599)(380,611)(381,610)(382,609)(383,608)(384,607)
(385,606)(386,605)(387,604)(388,603)(389,602)(390,601)(391,587)(392,586)
(393,598)(394,597)(395,596)(396,595)(397,594)(398,593)(399,592)(400,591)
(401,590)(402,589)(403,588)(404,574)(405,573)(406,585)(407,584)(408,583)
(409,582)(410,581)(411,580)(412,579)(413,578)(414,577)(415,576)(416,575);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(832)!(  1,209)(  2,210)(  3,211)(  4,212)(  5,213)(  6,214)(  7,215)
(  8,216)(  9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,222)( 15,223)
( 16,224)( 17,225)( 18,226)( 19,227)( 20,228)( 21,229)( 22,230)( 23,231)
( 24,232)( 25,233)( 26,234)( 27,235)( 28,236)( 29,237)( 30,238)( 31,239)
( 32,240)( 33,241)( 34,242)( 35,243)( 36,244)( 37,245)( 38,246)( 39,247)
( 40,248)( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)
( 48,256)( 49,257)( 50,258)( 51,259)( 52,260)( 53,274)( 54,275)( 55,276)
( 56,277)( 57,278)( 58,279)( 59,280)( 60,281)( 61,282)( 62,283)( 63,284)
( 64,285)( 65,286)( 66,261)( 67,262)( 68,263)( 69,264)( 70,265)( 71,266)
( 72,267)( 73,268)( 74,269)( 75,270)( 76,271)( 77,272)( 78,273)( 79,300)
( 80,301)( 81,302)( 82,303)( 83,304)( 84,305)( 85,306)( 86,307)( 87,308)
( 88,309)( 89,310)( 90,311)( 91,312)( 92,287)( 93,288)( 94,289)( 95,290)
( 96,291)( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)
(104,299)(105,326)(106,327)(107,328)(108,329)(109,330)(110,331)(111,332)
(112,333)(113,334)(114,335)(115,336)(116,337)(117,338)(118,313)(119,314)
(120,315)(121,316)(122,317)(123,318)(124,319)(125,320)(126,321)(127,322)
(128,323)(129,324)(130,325)(131,352)(132,353)(133,354)(134,355)(135,356)
(136,357)(137,358)(138,359)(139,360)(140,361)(141,362)(142,363)(143,364)
(144,339)(145,340)(146,341)(147,342)(148,343)(149,344)(150,345)(151,346)
(152,347)(153,348)(154,349)(155,350)(156,351)(157,365)(158,366)(159,367)
(160,368)(161,369)(162,370)(163,371)(164,372)(165,373)(166,374)(167,375)
(168,376)(169,377)(170,378)(171,379)(172,380)(173,381)(174,382)(175,383)
(176,384)(177,385)(178,386)(179,387)(180,388)(181,389)(182,390)(183,391)
(184,392)(185,393)(186,394)(187,395)(188,396)(189,397)(190,398)(191,399)
(192,400)(193,401)(194,402)(195,403)(196,404)(197,405)(198,406)(199,407)
(200,408)(201,409)(202,410)(203,411)(204,412)(205,413)(206,414)(207,415)
(208,416)(417,625)(418,626)(419,627)(420,628)(421,629)(422,630)(423,631)
(424,632)(425,633)(426,634)(427,635)(428,636)(429,637)(430,638)(431,639)
(432,640)(433,641)(434,642)(435,643)(436,644)(437,645)(438,646)(439,647)
(440,648)(441,649)(442,650)(443,651)(444,652)(445,653)(446,654)(447,655)
(448,656)(449,657)(450,658)(451,659)(452,660)(453,661)(454,662)(455,663)
(456,664)(457,665)(458,666)(459,667)(460,668)(461,669)(462,670)(463,671)
(464,672)(465,673)(466,674)(467,675)(468,676)(469,690)(470,691)(471,692)
(472,693)(473,694)(474,695)(475,696)(476,697)(477,698)(478,699)(479,700)
(480,701)(481,702)(482,677)(483,678)(484,679)(485,680)(486,681)(487,682)
(488,683)(489,684)(490,685)(491,686)(492,687)(493,688)(494,689)(495,716)
(496,717)(497,718)(498,719)(499,720)(500,721)(501,722)(502,723)(503,724)
(504,725)(505,726)(506,727)(507,728)(508,703)(509,704)(510,705)(511,706)
(512,707)(513,708)(514,709)(515,710)(516,711)(517,712)(518,713)(519,714)
(520,715)(521,742)(522,743)(523,744)(524,745)(525,746)(526,747)(527,748)
(528,749)(529,750)(530,751)(531,752)(532,753)(533,754)(534,729)(535,730)
(536,731)(537,732)(538,733)(539,734)(540,735)(541,736)(542,737)(543,738)
(544,739)(545,740)(546,741)(547,768)(548,769)(549,770)(550,771)(551,772)
(552,773)(553,774)(554,775)(555,776)(556,777)(557,778)(558,779)(559,780)
(560,755)(561,756)(562,757)(563,758)(564,759)(565,760)(566,761)(567,762)
(568,763)(569,764)(570,765)(571,766)(572,767)(573,781)(574,782)(575,783)
(576,784)(577,785)(578,786)(579,787)(580,788)(581,789)(582,790)(583,791)
(584,792)(585,793)(586,794)(587,795)(588,796)(589,797)(590,798)(591,799)
(592,800)(593,801)(594,802)(595,803)(596,804)(597,805)(598,806)(599,807)
(600,808)(601,809)(602,810)(603,811)(604,812)(605,813)(606,814)(607,815)
(608,816)(609,817)(610,818)(611,819)(612,820)(613,821)(614,822)(615,823)
(616,824)(617,825)(618,826)(619,827)(620,828)(621,829)(622,830)(623,831)
(624,832);
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)!(  1,626)(  2,625)(  3,637)(  4,636)(  5,635)(  6,634)(  7,633)
(  8,632)(  9,631)( 10,630)( 11,629)( 12,628)( 13,627)( 14,639)( 15,638)
( 16,650)( 17,649)( 18,648)( 19,647)( 20,646)( 21,645)( 22,644)( 23,643)
( 24,642)( 25,641)( 26,640)( 27,652)( 28,651)( 29,663)( 30,662)( 31,661)
( 32,660)( 33,659)( 34,658)( 35,657)( 36,656)( 37,655)( 38,654)( 39,653)
( 40,665)( 41,664)( 42,676)( 43,675)( 44,674)( 45,673)( 46,672)( 47,671)
( 48,670)( 49,669)( 50,668)( 51,667)( 52,666)( 53,678)( 54,677)( 55,689)
( 56,688)( 57,687)( 58,686)( 59,685)( 60,684)( 61,683)( 62,682)( 63,681)
( 64,680)( 65,679)( 66,691)( 67,690)( 68,702)( 69,701)( 70,700)( 71,699)
( 72,698)( 73,697)( 74,696)( 75,695)( 76,694)( 77,693)( 78,692)( 79,704)
( 80,703)( 81,715)( 82,714)( 83,713)( 84,712)( 85,711)( 86,710)( 87,709)
( 88,708)( 89,707)( 90,706)( 91,705)( 92,717)( 93,716)( 94,728)( 95,727)
( 96,726)( 97,725)( 98,724)( 99,723)(100,722)(101,721)(102,720)(103,719)
(104,718)(105,769)(106,768)(107,780)(108,779)(109,778)(110,777)(111,776)
(112,775)(113,774)(114,773)(115,772)(116,771)(117,770)(118,756)(119,755)
(120,767)(121,766)(122,765)(123,764)(124,763)(125,762)(126,761)(127,760)
(128,759)(129,758)(130,757)(131,743)(132,742)(133,754)(134,753)(135,752)
(136,751)(137,750)(138,749)(139,748)(140,747)(141,746)(142,745)(143,744)
(144,730)(145,729)(146,741)(147,740)(148,739)(149,738)(150,737)(151,736)
(152,735)(153,734)(154,733)(155,732)(156,731)(157,821)(158,820)(159,832)
(160,831)(161,830)(162,829)(163,828)(164,827)(165,826)(166,825)(167,824)
(168,823)(169,822)(170,808)(171,807)(172,819)(173,818)(174,817)(175,816)
(176,815)(177,814)(178,813)(179,812)(180,811)(181,810)(182,809)(183,795)
(184,794)(185,806)(186,805)(187,804)(188,803)(189,802)(190,801)(191,800)
(192,799)(193,798)(194,797)(195,796)(196,782)(197,781)(198,793)(199,792)
(200,791)(201,790)(202,789)(203,788)(204,787)(205,786)(206,785)(207,784)
(208,783)(209,418)(210,417)(211,429)(212,428)(213,427)(214,426)(215,425)
(216,424)(217,423)(218,422)(219,421)(220,420)(221,419)(222,431)(223,430)
(224,442)(225,441)(226,440)(227,439)(228,438)(229,437)(230,436)(231,435)
(232,434)(233,433)(234,432)(235,444)(236,443)(237,455)(238,454)(239,453)
(240,452)(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)
(248,457)(249,456)(250,468)(251,467)(252,466)(253,465)(254,464)(255,463)
(256,462)(257,461)(258,460)(259,459)(260,458)(261,470)(262,469)(263,481)
(264,480)(265,479)(266,478)(267,477)(268,476)(269,475)(270,474)(271,473)
(272,472)(273,471)(274,483)(275,482)(276,494)(277,493)(278,492)(279,491)
(280,490)(281,489)(282,488)(283,487)(284,486)(285,485)(286,484)(287,496)
(288,495)(289,507)(290,506)(291,505)(292,504)(293,503)(294,502)(295,501)
(296,500)(297,499)(298,498)(299,497)(300,509)(301,508)(302,520)(303,519)
(304,518)(305,517)(306,516)(307,515)(308,514)(309,513)(310,512)(311,511)
(312,510)(313,561)(314,560)(315,572)(316,571)(317,570)(318,569)(319,568)
(320,567)(321,566)(322,565)(323,564)(324,563)(325,562)(326,548)(327,547)
(328,559)(329,558)(330,557)(331,556)(332,555)(333,554)(334,553)(335,552)
(336,551)(337,550)(338,549)(339,535)(340,534)(341,546)(342,545)(343,544)
(344,543)(345,542)(346,541)(347,540)(348,539)(349,538)(350,537)(351,536)
(352,522)(353,521)(354,533)(355,532)(356,531)(357,530)(358,529)(359,528)
(360,527)(361,526)(362,525)(363,524)(364,523)(365,613)(366,612)(367,624)
(368,623)(369,622)(370,621)(371,620)(372,619)(373,618)(374,617)(375,616)
(376,615)(377,614)(378,600)(379,599)(380,611)(381,610)(382,609)(383,608)
(384,607)(385,606)(386,605)(387,604)(388,603)(389,602)(390,601)(391,587)
(392,586)(393,598)(394,597)(395,596)(396,595)(397,594)(398,593)(399,592)
(400,591)(401,590)(402,589)(403,588)(404,574)(405,573)(406,585)(407,584)
(408,583)(409,582)(410,581)(411,580)(412,579)(413,578)(414,577)(415,576)
(416,575);
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, 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 >; 
 
References : None.
to this polytope