Polytope of Type {104,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {104,8}*1664a
if this polytope has a name.
Group : SmallGroup(1664,3565)
Rank : 3
Schlafli Type : {104,8}
Number of vertices, edges, etc : 104, 416, 8
Order of s₀s₁s₂ : 104
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {104,4}*832b, {52,8}*832a
   4-fold quotients : {52,4}*416, {26,8}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {8,8}*128a
   16-fold quotients : {26,2}*104
   26-fold quotients : {4,8}*64a, {8,4}*64b
   32-fold quotients : {13,2}*52
   52-fold quotients : {4,4}*32, {2,8}*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)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)(  8,215)
(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)( 16,233)
( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)( 24,225)
( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)( 32,243)
( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)( 40,248)
( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)( 48,253)
( 49,252)( 50,251)( 51,250)( 52,249)( 53,274)( 54,286)( 55,285)( 56,284)
( 57,283)( 58,282)( 59,281)( 60,280)( 61,279)( 62,278)( 63,277)( 64,276)
( 65,275)( 66,261)( 67,273)( 68,272)( 69,271)( 70,270)( 71,269)( 72,268)
( 73,267)( 74,266)( 75,265)( 76,264)( 77,263)( 78,262)( 79,300)( 80,312)
( 81,311)( 82,310)( 83,309)( 84,308)( 85,307)( 86,306)( 87,305)( 88,304)
( 89,303)( 90,302)( 91,301)( 92,287)( 93,299)( 94,298)( 95,297)( 96,296)
( 97,295)( 98,294)( 99,293)(100,292)(101,291)(102,290)(103,289)(104,288)
(105,326)(106,338)(107,337)(108,336)(109,335)(110,334)(111,333)(112,332)
(113,331)(114,330)(115,329)(116,328)(117,327)(118,313)(119,325)(120,324)
(121,323)(122,322)(123,321)(124,320)(125,319)(126,318)(127,317)(128,316)
(129,315)(130,314)(131,352)(132,364)(133,363)(134,362)(135,361)(136,360)
(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)(144,339)
(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)(152,344)
(153,343)(154,342)(155,341)(156,340)(157,365)(158,377)(159,376)(160,375)
(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)(168,367)
(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)(176,385)
(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)(184,403)
(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)
(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)(200,413)
(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)(208,405)
(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)
(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)(432,649)
(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)
(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)(448,659)
(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)(456,664)
(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)(464,669)
(465,668)(466,667)(467,666)(468,665)(469,690)(470,702)(471,701)(472,700)
(473,699)(474,698)(475,697)(476,696)(477,695)(478,694)(479,693)(480,692)
(481,691)(482,677)(483,689)(484,688)(485,687)(486,686)(487,685)(488,684)
(489,683)(490,682)(491,681)(492,680)(493,679)(494,678)(495,716)(496,728)
(497,727)(498,726)(499,725)(500,724)(501,723)(502,722)(503,721)(504,720)
(505,719)(506,718)(507,717)(508,703)(509,715)(510,714)(511,713)(512,712)
(513,711)(514,710)(515,709)(516,708)(517,707)(518,706)(519,705)(520,704)
(521,742)(522,754)(523,753)(524,752)(525,751)(526,750)(527,749)(528,748)
(529,747)(530,746)(531,745)(532,744)(533,743)(534,729)(535,741)(536,740)
(537,739)(538,738)(539,737)(540,736)(541,735)(542,734)(543,733)(544,732)
(545,731)(546,730)(547,768)(548,780)(549,779)(550,778)(551,777)(552,776)
(553,775)(554,774)(555,773)(556,772)(557,771)(558,770)(559,769)(560,755)
(561,767)(562,766)(563,765)(564,764)(565,763)(566,762)(567,761)(568,760)
(569,759)(570,758)(571,757)(572,756)(573,781)(574,793)(575,792)(576,791)
(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)(584,783)
(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)(592,801)
(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)(600,819)
(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)(608,811)
(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)(616,829)
(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)(624,821);;
s1 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 15)( 16, 26)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)
( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)
( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)( 60, 73)
( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79, 93)( 80, 92)( 81,104)
( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)
( 90, 95)( 91, 94)(105,132)(106,131)(107,143)(108,142)(109,141)(110,140)
(111,139)(112,138)(113,137)(114,136)(115,135)(116,134)(117,133)(118,145)
(119,144)(120,156)(121,155)(122,154)(123,153)(124,152)(125,151)(126,150)
(127,149)(128,148)(129,147)(130,146)(157,197)(158,196)(159,208)(160,207)
(161,206)(162,205)(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)
(169,198)(170,184)(171,183)(172,195)(173,194)(174,193)(175,192)(176,191)
(177,190)(178,189)(179,188)(180,187)(181,186)(182,185)(209,262)(210,261)
(211,273)(212,272)(213,271)(214,270)(215,269)(216,268)(217,267)(218,266)
(219,265)(220,264)(221,263)(222,275)(223,274)(224,286)(225,285)(226,284)
(227,283)(228,282)(229,281)(230,280)(231,279)(232,278)(233,277)(234,276)
(235,288)(236,287)(237,299)(238,298)(239,297)(240,296)(241,295)(242,294)
(243,293)(244,292)(245,291)(246,290)(247,289)(248,301)(249,300)(250,312)
(251,311)(252,310)(253,309)(254,308)(255,307)(256,306)(257,305)(258,304)
(259,303)(260,302)(313,392)(314,391)(315,403)(316,402)(317,401)(318,400)
(319,399)(320,398)(321,397)(322,396)(323,395)(324,394)(325,393)(326,405)
(327,404)(328,416)(329,415)(330,414)(331,413)(332,412)(333,411)(334,410)
(335,409)(336,408)(337,407)(338,406)(339,366)(340,365)(341,377)(342,376)
(343,375)(344,374)(345,373)(346,372)(347,371)(348,370)(349,369)(350,368)
(351,367)(352,379)(353,378)(354,390)(355,389)(356,388)(357,387)(358,386)
(359,385)(360,384)(361,383)(362,382)(363,381)(364,380)(417,522)(418,521)
(419,533)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)(426,526)
(427,525)(428,524)(429,523)(430,535)(431,534)(432,546)(433,545)(434,544)
(435,543)(436,542)(437,541)(438,540)(439,539)(440,538)(441,537)(442,536)
(443,548)(444,547)(445,559)(446,558)(447,557)(448,556)(449,555)(450,554)
(451,553)(452,552)(453,551)(454,550)(455,549)(456,561)(457,560)(458,572)
(459,571)(460,570)(461,569)(462,568)(463,567)(464,566)(465,565)(466,564)
(467,563)(468,562)(469,587)(470,586)(471,598)(472,597)(473,596)(474,595)
(475,594)(476,593)(477,592)(478,591)(479,590)(480,589)(481,588)(482,574)
(483,573)(484,585)(485,584)(486,583)(487,582)(488,581)(489,580)(490,579)
(491,578)(492,577)(493,576)(494,575)(495,613)(496,612)(497,624)(498,623)
(499,622)(500,621)(501,620)(502,619)(503,618)(504,617)(505,616)(506,615)
(507,614)(508,600)(509,599)(510,611)(511,610)(512,609)(513,608)(514,607)
(515,606)(516,605)(517,604)(518,603)(519,602)(520,601)(625,795)(626,794)
(627,806)(628,805)(629,804)(630,803)(631,802)(632,801)(633,800)(634,799)
(635,798)(636,797)(637,796)(638,782)(639,781)(640,793)(641,792)(642,791)
(643,790)(644,789)(645,788)(646,787)(647,786)(648,785)(649,784)(650,783)
(651,821)(652,820)(653,832)(654,831)(655,830)(656,829)(657,828)(658,827)
(659,826)(660,825)(661,824)(662,823)(663,822)(664,808)(665,807)(666,819)
(667,818)(668,817)(669,816)(670,815)(671,814)(672,813)(673,812)(674,811)
(675,810)(676,809)(677,743)(678,742)(679,754)(680,753)(681,752)(682,751)
(683,750)(684,749)(685,748)(686,747)(687,746)(688,745)(689,744)(690,730)
(691,729)(692,741)(693,740)(694,739)(695,738)(696,737)(697,736)(698,735)
(699,734)(700,733)(701,732)(702,731)(703,769)(704,768)(705,780)(706,779)
(707,778)(708,777)(709,776)(710,775)(711,774)(712,773)(713,772)(714,771)
(715,770)(716,756)(717,755)(718,767)(719,766)(720,765)(721,764)(722,763)
(723,762)(724,761)(725,760)(726,759)(727,758)(728,757);;
s2 := (  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);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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*s2*s1*s0*s1*s0*s2*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)!(  1,209)(  2,221)(  3,220)(  4,219)(  5,218)(  6,217)(  7,216)
(  8,215)(  9,214)( 10,213)( 11,212)( 12,211)( 13,210)( 14,222)( 15,234)
( 16,233)( 17,232)( 18,231)( 19,230)( 20,229)( 21,228)( 22,227)( 23,226)
( 24,225)( 25,224)( 26,223)( 27,235)( 28,247)( 29,246)( 30,245)( 31,244)
( 32,243)( 33,242)( 34,241)( 35,240)( 36,239)( 37,238)( 38,237)( 39,236)
( 40,248)( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,255)( 47,254)
( 48,253)( 49,252)( 50,251)( 51,250)( 52,249)( 53,274)( 54,286)( 55,285)
( 56,284)( 57,283)( 58,282)( 59,281)( 60,280)( 61,279)( 62,278)( 63,277)
( 64,276)( 65,275)( 66,261)( 67,273)( 68,272)( 69,271)( 70,270)( 71,269)
( 72,268)( 73,267)( 74,266)( 75,265)( 76,264)( 77,263)( 78,262)( 79,300)
( 80,312)( 81,311)( 82,310)( 83,309)( 84,308)( 85,307)( 86,306)( 87,305)
( 88,304)( 89,303)( 90,302)( 91,301)( 92,287)( 93,299)( 94,298)( 95,297)
( 96,296)( 97,295)( 98,294)( 99,293)(100,292)(101,291)(102,290)(103,289)
(104,288)(105,326)(106,338)(107,337)(108,336)(109,335)(110,334)(111,333)
(112,332)(113,331)(114,330)(115,329)(116,328)(117,327)(118,313)(119,325)
(120,324)(121,323)(122,322)(123,321)(124,320)(125,319)(126,318)(127,317)
(128,316)(129,315)(130,314)(131,352)(132,364)(133,363)(134,362)(135,361)
(136,360)(137,359)(138,358)(139,357)(140,356)(141,355)(142,354)(143,353)
(144,339)(145,351)(146,350)(147,349)(148,348)(149,347)(150,346)(151,345)
(152,344)(153,343)(154,342)(155,341)(156,340)(157,365)(158,377)(159,376)
(160,375)(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)
(168,367)(169,366)(170,378)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,385)(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,391)
(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)
(192,395)(193,394)(194,393)(195,392)(196,404)(197,416)(198,415)(199,414)
(200,413)(201,412)(202,411)(203,410)(204,409)(205,408)(206,407)(207,406)
(208,405)(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)
(424,631)(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)
(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)
(440,641)(441,640)(442,639)(443,651)(444,663)(445,662)(446,661)(447,660)
(448,659)(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)
(456,664)(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)
(464,669)(465,668)(466,667)(467,666)(468,665)(469,690)(470,702)(471,701)
(472,700)(473,699)(474,698)(475,697)(476,696)(477,695)(478,694)(479,693)
(480,692)(481,691)(482,677)(483,689)(484,688)(485,687)(486,686)(487,685)
(488,684)(489,683)(490,682)(491,681)(492,680)(493,679)(494,678)(495,716)
(496,728)(497,727)(498,726)(499,725)(500,724)(501,723)(502,722)(503,721)
(504,720)(505,719)(506,718)(507,717)(508,703)(509,715)(510,714)(511,713)
(512,712)(513,711)(514,710)(515,709)(516,708)(517,707)(518,706)(519,705)
(520,704)(521,742)(522,754)(523,753)(524,752)(525,751)(526,750)(527,749)
(528,748)(529,747)(530,746)(531,745)(532,744)(533,743)(534,729)(535,741)
(536,740)(537,739)(538,738)(539,737)(540,736)(541,735)(542,734)(543,733)
(544,732)(545,731)(546,730)(547,768)(548,780)(549,779)(550,778)(551,777)
(552,776)(553,775)(554,774)(555,773)(556,772)(557,771)(558,770)(559,769)
(560,755)(561,767)(562,766)(563,765)(564,764)(565,763)(566,762)(567,761)
(568,760)(569,759)(570,758)(571,757)(572,756)(573,781)(574,793)(575,792)
(576,791)(577,790)(578,789)(579,788)(580,787)(581,786)(582,785)(583,784)
(584,783)(585,782)(586,794)(587,806)(588,805)(589,804)(590,803)(591,802)
(592,801)(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,807)
(600,819)(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)
(608,811)(609,810)(610,809)(611,808)(612,820)(613,832)(614,831)(615,830)
(616,829)(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)
(624,821);
s1 := Sym(832)!(  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 15)
( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)
( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)
( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79, 93)( 80, 92)
( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)
( 89, 96)( 90, 95)( 91, 94)(105,132)(106,131)(107,143)(108,142)(109,141)
(110,140)(111,139)(112,138)(113,137)(114,136)(115,135)(116,134)(117,133)
(118,145)(119,144)(120,156)(121,155)(122,154)(123,153)(124,152)(125,151)
(126,150)(127,149)(128,148)(129,147)(130,146)(157,197)(158,196)(159,208)
(160,207)(161,206)(162,205)(163,204)(164,203)(165,202)(166,201)(167,200)
(168,199)(169,198)(170,184)(171,183)(172,195)(173,194)(174,193)(175,192)
(176,191)(177,190)(178,189)(179,188)(180,187)(181,186)(182,185)(209,262)
(210,261)(211,273)(212,272)(213,271)(214,270)(215,269)(216,268)(217,267)
(218,266)(219,265)(220,264)(221,263)(222,275)(223,274)(224,286)(225,285)
(226,284)(227,283)(228,282)(229,281)(230,280)(231,279)(232,278)(233,277)
(234,276)(235,288)(236,287)(237,299)(238,298)(239,297)(240,296)(241,295)
(242,294)(243,293)(244,292)(245,291)(246,290)(247,289)(248,301)(249,300)
(250,312)(251,311)(252,310)(253,309)(254,308)(255,307)(256,306)(257,305)
(258,304)(259,303)(260,302)(313,392)(314,391)(315,403)(316,402)(317,401)
(318,400)(319,399)(320,398)(321,397)(322,396)(323,395)(324,394)(325,393)
(326,405)(327,404)(328,416)(329,415)(330,414)(331,413)(332,412)(333,411)
(334,410)(335,409)(336,408)(337,407)(338,406)(339,366)(340,365)(341,377)
(342,376)(343,375)(344,374)(345,373)(346,372)(347,371)(348,370)(349,369)
(350,368)(351,367)(352,379)(353,378)(354,390)(355,389)(356,388)(357,387)
(358,386)(359,385)(360,384)(361,383)(362,382)(363,381)(364,380)(417,522)
(418,521)(419,533)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)
(426,526)(427,525)(428,524)(429,523)(430,535)(431,534)(432,546)(433,545)
(434,544)(435,543)(436,542)(437,541)(438,540)(439,539)(440,538)(441,537)
(442,536)(443,548)(444,547)(445,559)(446,558)(447,557)(448,556)(449,555)
(450,554)(451,553)(452,552)(453,551)(454,550)(455,549)(456,561)(457,560)
(458,572)(459,571)(460,570)(461,569)(462,568)(463,567)(464,566)(465,565)
(466,564)(467,563)(468,562)(469,587)(470,586)(471,598)(472,597)(473,596)
(474,595)(475,594)(476,593)(477,592)(478,591)(479,590)(480,589)(481,588)
(482,574)(483,573)(484,585)(485,584)(486,583)(487,582)(488,581)(489,580)
(490,579)(491,578)(492,577)(493,576)(494,575)(495,613)(496,612)(497,624)
(498,623)(499,622)(500,621)(501,620)(502,619)(503,618)(504,617)(505,616)
(506,615)(507,614)(508,600)(509,599)(510,611)(511,610)(512,609)(513,608)
(514,607)(515,606)(516,605)(517,604)(518,603)(519,602)(520,601)(625,795)
(626,794)(627,806)(628,805)(629,804)(630,803)(631,802)(632,801)(633,800)
(634,799)(635,798)(636,797)(637,796)(638,782)(639,781)(640,793)(641,792)
(642,791)(643,790)(644,789)(645,788)(646,787)(647,786)(648,785)(649,784)
(650,783)(651,821)(652,820)(653,832)(654,831)(655,830)(656,829)(657,828)
(658,827)(659,826)(660,825)(661,824)(662,823)(663,822)(664,808)(665,807)
(666,819)(667,818)(668,817)(669,816)(670,815)(671,814)(672,813)(673,812)
(674,811)(675,810)(676,809)(677,743)(678,742)(679,754)(680,753)(681,752)
(682,751)(683,750)(684,749)(685,748)(686,747)(687,746)(688,745)(689,744)
(690,730)(691,729)(692,741)(693,740)(694,739)(695,738)(696,737)(697,736)
(698,735)(699,734)(700,733)(701,732)(702,731)(703,769)(704,768)(705,780)
(706,779)(707,778)(708,777)(709,776)(710,775)(711,774)(712,773)(713,772)
(714,771)(715,770)(716,756)(717,755)(718,767)(719,766)(720,765)(721,764)
(722,763)(723,762)(724,761)(725,760)(726,759)(727,758)(728,757);
s2 := 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);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
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*s2*s1*s0*s1*s0*s2*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