Polytope of Type {32,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,26}*1664
Also Known As : {32,26|2}. if this polytope has another name.
Group : SmallGroup(1664,6806)
Rank : 3
Schlafli Type : {32,26}
Number of vertices, edges, etc : 32, 416, 26
Order of s₀s₁s₂ : 416
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 : {16,26}*832
   4-fold quotients : {8,26}*416
   8-fold quotients : {4,26}*208
   13-fold quotients : {32,2}*128
   16-fold quotients : {2,26}*104
   26-fold quotients : {16,2}*64
   32-fold quotients : {2,13}*52
   52-fold quotients : {8,2}*32
   104-fold quotients : {4,2}*16
   208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope