Polytope of Type {104,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {104,8}*1664c
Also Known As : {104,8|2}. if this polytope has another name.
Group : SmallGroup(1664,3566)
Rank : 3
Schlafli Type : {104,8}
Number of vertices, edges, etc : 104, 416, 8
Order of s₀s₁s₂ : 104
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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}*832a, {52,8}*832a
   4-fold quotients : {52,4}*416, {104,2}*416, {26,8}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {8,8}*128b
   16-fold quotients : {26,2}*104
   26-fold quotients : {4,8}*64a, {8,4}*64a
   32-fold quotients : {13,2}*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 := (  1,625)(  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)( 27,651)( 28,663)( 29,662)( 30,661)( 31,660)( 32,659)
( 33,658)( 34,657)( 35,656)( 36,655)( 37,654)( 38,653)( 39,652)( 40,664)
( 41,676)( 42,675)( 43,674)( 44,673)( 45,672)( 46,671)( 47,670)( 48,669)
( 49,668)( 50,667)( 51,666)( 52,665)( 53,677)( 54,689)( 55,688)( 56,687)
( 57,686)( 58,685)( 59,684)( 60,683)( 61,682)( 62,681)( 63,680)( 64,679)
( 65,678)( 66,690)( 67,702)( 68,701)( 69,700)( 70,699)( 71,698)( 72,697)
( 73,696)( 74,695)( 75,694)( 76,693)( 77,692)( 78,691)( 79,703)( 80,715)
( 81,714)( 82,713)( 83,712)( 84,711)( 85,710)( 86,709)( 87,708)( 88,707)
( 89,706)( 90,705)( 91,704)( 92,716)( 93,728)( 94,727)( 95,726)( 96,725)
( 97,724)( 98,723)( 99,722)(100,721)(101,720)(102,719)(103,718)(104,717)
(105,768)(106,780)(107,779)(108,778)(109,777)(110,776)(111,775)(112,774)
(113,773)(114,772)(115,771)(116,770)(117,769)(118,755)(119,767)(120,766)
(121,765)(122,764)(123,763)(124,762)(125,761)(126,760)(127,759)(128,758)
(129,757)(130,756)(131,742)(132,754)(133,753)(134,752)(135,751)(136,750)
(137,749)(138,748)(139,747)(140,746)(141,745)(142,744)(143,743)(144,729)
(145,741)(146,740)(147,739)(148,738)(149,737)(150,736)(151,735)(152,734)
(153,733)(154,732)(155,731)(156,730)(157,820)(158,832)(159,831)(160,830)
(161,829)(162,828)(163,827)(164,826)(165,825)(166,824)(167,823)(168,822)
(169,821)(170,807)(171,819)(172,818)(173,817)(174,816)(175,815)(176,814)
(177,813)(178,812)(179,811)(180,810)(181,809)(182,808)(183,794)(184,806)
(185,805)(186,804)(187,803)(188,802)(189,801)(190,800)(191,799)(192,798)
(193,797)(194,796)(195,795)(196,781)(197,793)(198,792)(199,791)(200,790)
(201,789)(202,788)(203,787)(204,786)(205,785)(206,784)(207,783)(208,782)
(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)(235,443)(236,455)(237,454)(238,453)(239,452)(240,451)
(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)(248,456)
(249,468)(250,467)(251,466)(252,465)(253,464)(254,463)(255,462)(256,461)
(257,460)(258,459)(259,458)(260,457)(261,469)(262,481)(263,480)(264,479)
(265,478)(266,477)(267,476)(268,475)(269,474)(270,473)(271,472)(272,471)
(273,470)(274,482)(275,494)(276,493)(277,492)(278,491)(279,490)(280,489)
(281,488)(282,487)(283,486)(284,485)(285,484)(286,483)(287,495)(288,507)
(289,506)(290,505)(291,504)(292,503)(293,502)(294,501)(295,500)(296,499)
(297,498)(298,497)(299,496)(300,508)(301,520)(302,519)(303,518)(304,517)
(305,516)(306,515)(307,514)(308,513)(309,512)(310,511)(311,510)(312,509)
(313,560)(314,572)(315,571)(316,570)(317,569)(318,568)(319,567)(320,566)
(321,565)(322,564)(323,563)(324,562)(325,561)(326,547)(327,559)(328,558)
(329,557)(330,556)(331,555)(332,554)(333,553)(334,552)(335,551)(336,550)
(337,549)(338,548)(339,534)(340,546)(341,545)(342,544)(343,543)(344,542)
(345,541)(346,540)(347,539)(348,538)(349,537)(350,536)(351,535)(352,521)
(353,533)(354,532)(355,531)(356,530)(357,529)(358,528)(359,527)(360,526)
(361,525)(362,524)(363,523)(364,522)(365,612)(366,624)(367,623)(368,622)
(369,621)(370,620)(371,619)(372,618)(373,617)(374,616)(375,615)(376,614)
(377,613)(378,599)(379,611)(380,610)(381,609)(382,608)(383,607)(384,606)
(385,605)(386,604)(387,603)(388,602)(389,601)(390,600)(391,586)(392,598)
(393,597)(394,596)(395,595)(396,594)(397,593)(398,592)(399,591)(400,590)
(401,589)(402,588)(403,587)(404,573)(405,585)(406,584)(407,583)(408,582)
(409,581)(410,580)(411,579)(412,578)(413,577)(414,576)(415,575)(416,574);;
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 := (  1,209)(  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);;
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, 
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*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*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*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)!(  1,625)(  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)( 27,651)( 28,663)( 29,662)( 30,661)( 31,660)
( 32,659)( 33,658)( 34,657)( 35,656)( 36,655)( 37,654)( 38,653)( 39,652)
( 40,664)( 41,676)( 42,675)( 43,674)( 44,673)( 45,672)( 46,671)( 47,670)
( 48,669)( 49,668)( 50,667)( 51,666)( 52,665)( 53,677)( 54,689)( 55,688)
( 56,687)( 57,686)( 58,685)( 59,684)( 60,683)( 61,682)( 62,681)( 63,680)
( 64,679)( 65,678)( 66,690)( 67,702)( 68,701)( 69,700)( 70,699)( 71,698)
( 72,697)( 73,696)( 74,695)( 75,694)( 76,693)( 77,692)( 78,691)( 79,703)
( 80,715)( 81,714)( 82,713)( 83,712)( 84,711)( 85,710)( 86,709)( 87,708)
( 88,707)( 89,706)( 90,705)( 91,704)( 92,716)( 93,728)( 94,727)( 95,726)
( 96,725)( 97,724)( 98,723)( 99,722)(100,721)(101,720)(102,719)(103,718)
(104,717)(105,768)(106,780)(107,779)(108,778)(109,777)(110,776)(111,775)
(112,774)(113,773)(114,772)(115,771)(116,770)(117,769)(118,755)(119,767)
(120,766)(121,765)(122,764)(123,763)(124,762)(125,761)(126,760)(127,759)
(128,758)(129,757)(130,756)(131,742)(132,754)(133,753)(134,752)(135,751)
(136,750)(137,749)(138,748)(139,747)(140,746)(141,745)(142,744)(143,743)
(144,729)(145,741)(146,740)(147,739)(148,738)(149,737)(150,736)(151,735)
(152,734)(153,733)(154,732)(155,731)(156,730)(157,820)(158,832)(159,831)
(160,830)(161,829)(162,828)(163,827)(164,826)(165,825)(166,824)(167,823)
(168,822)(169,821)(170,807)(171,819)(172,818)(173,817)(174,816)(175,815)
(176,814)(177,813)(178,812)(179,811)(180,810)(181,809)(182,808)(183,794)
(184,806)(185,805)(186,804)(187,803)(188,802)(189,801)(190,800)(191,799)
(192,798)(193,797)(194,796)(195,795)(196,781)(197,793)(198,792)(199,791)
(200,790)(201,789)(202,788)(203,787)(204,786)(205,785)(206,784)(207,783)
(208,782)(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)(235,443)(236,455)(237,454)(238,453)(239,452)
(240,451)(241,450)(242,449)(243,448)(244,447)(245,446)(246,445)(247,444)
(248,456)(249,468)(250,467)(251,466)(252,465)(253,464)(254,463)(255,462)
(256,461)(257,460)(258,459)(259,458)(260,457)(261,469)(262,481)(263,480)
(264,479)(265,478)(266,477)(267,476)(268,475)(269,474)(270,473)(271,472)
(272,471)(273,470)(274,482)(275,494)(276,493)(277,492)(278,491)(279,490)
(280,489)(281,488)(282,487)(283,486)(284,485)(285,484)(286,483)(287,495)
(288,507)(289,506)(290,505)(291,504)(292,503)(293,502)(294,501)(295,500)
(296,499)(297,498)(298,497)(299,496)(300,508)(301,520)(302,519)(303,518)
(304,517)(305,516)(306,515)(307,514)(308,513)(309,512)(310,511)(311,510)
(312,509)(313,560)(314,572)(315,571)(316,570)(317,569)(318,568)(319,567)
(320,566)(321,565)(322,564)(323,563)(324,562)(325,561)(326,547)(327,559)
(328,558)(329,557)(330,556)(331,555)(332,554)(333,553)(334,552)(335,551)
(336,550)(337,549)(338,548)(339,534)(340,546)(341,545)(342,544)(343,543)
(344,542)(345,541)(346,540)(347,539)(348,538)(349,537)(350,536)(351,535)
(352,521)(353,533)(354,532)(355,531)(356,530)(357,529)(358,528)(359,527)
(360,526)(361,525)(362,524)(363,523)(364,522)(365,612)(366,624)(367,623)
(368,622)(369,621)(370,620)(371,619)(372,618)(373,617)(374,616)(375,615)
(376,614)(377,613)(378,599)(379,611)(380,610)(381,609)(382,608)(383,607)
(384,606)(385,605)(386,604)(387,603)(388,602)(389,601)(390,600)(391,586)
(392,598)(393,597)(394,596)(395,595)(396,594)(397,593)(398,592)(399,591)
(400,590)(401,589)(402,588)(403,587)(404,573)(405,585)(406,584)(407,583)
(408,582)(409,581)(410,580)(411,579)(412,578)(413,577)(414,576)(415,575)
(416,574);
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)!(  1,209)(  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);
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, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope