Polytope of Type {104,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {104,8}*1664b
if this polytope has a 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 : 4
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}*832b
   4-fold quotients : {52,4}*416, {104,2}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {8,8}*128c
   16-fold quotients : {26,2}*104
   26-fold quotients : {8,4}*64a, {4,8}*64b
   32-fold quotients : {13,2}*52
   52-fold quotients : {4,4}*32, {8,2}*32
   104-fold quotients : {2,4}*16, {4,2}*16
   208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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