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Polytope of Type {52,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,16}*1664b
if this polytope has a name.
Group : SmallGroup(1664,6457)
Rank : 3
Schlafli Type : {52,16}
Number of vertices, edges, etc : 52, 416, 16
Order of s0s1s2 : 208
Order of s0s1s2s1 : 4
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 : {52,8}*832a
   4-fold quotients : {52,4}*416, {26,8}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {4,16}*128b
   16-fold quotients : {26,2}*104
   26-fold quotients : {4,8}*64a
   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)( 53,261)( 54,273)( 55,272)( 56,271)
( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)( 64,263)
( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)( 72,281)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,291)
( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)( 96,309)
( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)(104,301)
(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)(157,378)(158,390)(159,389)(160,388)
(161,387)(162,386)(163,385)(164,384)(165,383)(166,382)(167,381)(168,380)
(169,379)(170,365)(171,377)(172,376)(173,375)(174,374)(175,373)(176,372)
(177,371)(178,370)(179,369)(180,368)(181,367)(182,366)(183,404)(184,416)
(185,415)(186,414)(187,413)(188,412)(189,411)(190,410)(191,409)(192,408)
(193,407)(194,406)(195,405)(196,391)(197,403)(198,402)(199,401)(200,400)
(201,399)(202,398)(203,397)(204,396)(205,395)(206,394)(207,393)(208,392)
(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)(469,677)(470,689)(471,688)(472,687)
(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)
(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)(488,697)
(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)(496,715)
(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)(504,707)
(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)(512,725)
(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)(520,717)
(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)(573,794)(574,806)(575,805)(576,804)
(577,803)(578,802)(579,801)(580,800)(581,799)(582,798)(583,797)(584,796)
(585,795)(586,781)(587,793)(588,792)(589,791)(590,790)(591,789)(592,788)
(593,787)(594,786)(595,785)(596,784)(597,783)(598,782)(599,820)(600,832)
(601,831)(602,830)(603,829)(604,828)(605,827)(606,826)(607,825)(608,824)
(609,823)(610,822)(611,821)(612,807)(613,819)(614,818)(615,817)(616,816)
(617,815)(618,814)(619,813)(620,812)(621,811)(622,810)(623,809)(624,808);;
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, 41)( 28, 40)( 29, 52)( 30, 51)
( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)
( 39, 42)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)
( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 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)(157,184)(158,183)(159,195)(160,194)
(161,193)(162,192)(163,191)(164,190)(165,189)(166,188)(167,187)(168,186)
(169,185)(170,197)(171,196)(172,208)(173,207)(174,206)(175,205)(176,204)
(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(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)
(235,301)(236,300)(237,312)(238,311)(239,310)(240,309)(241,308)(242,307)
(243,306)(244,305)(245,304)(246,303)(247,302)(248,288)(249,287)(250,299)
(251,298)(252,297)(253,296)(254,295)(255,294)(256,293)(257,292)(258,291)
(259,290)(260,289)(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)
(443,561)(444,560)(445,572)(446,571)(447,570)(448,569)(449,568)(450,567)
(451,566)(452,565)(453,564)(454,563)(455,562)(456,548)(457,547)(458,559)
(459,558)(460,557)(461,556)(462,555)(463,554)(464,553)(465,552)(466,551)
(467,550)(468,549)(469,574)(470,573)(471,585)(472,584)(473,583)(474,582)
(475,581)(476,580)(477,579)(478,578)(479,577)(480,576)(481,575)(482,587)
(483,586)(484,598)(485,597)(486,596)(487,595)(488,594)(489,593)(490,592)
(491,591)(492,590)(493,589)(494,588)(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)
(651,808)(652,807)(653,819)(654,818)(655,817)(656,816)(657,815)(658,814)
(659,813)(660,812)(661,811)(662,810)(663,809)(664,821)(665,820)(666,832)
(667,831)(668,830)(669,829)(670,828)(671,827)(672,826)(673,825)(674,824)
(675,823)(676,822)(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)(703,756)(704,755)(705,767)(706,766)
(707,765)(708,764)(709,763)(710,762)(711,761)(712,760)(713,759)(714,758)
(715,757)(716,769)(717,768)(718,780)(719,779)(720,778)(721,777)(722,776)
(723,775)(724,774)(725,773)(726,772)(727,771)(728,770);;
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)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)( 32,461)
( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)( 40,443)
( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)( 48,451)
( 49,452)( 50,453)( 51,454)( 52,455)( 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)( 79,495)( 80,496)
( 81,497)( 82,498)( 83,499)( 84,500)( 85,501)( 86,502)( 87,503)( 88,504)
( 89,505)( 90,506)( 91,507)( 92,508)( 93,509)( 94,510)( 95,511)( 96,512)
( 97,513)( 98,514)( 99,515)(100,516)(101,517)(102,518)(103,519)(104,520)
(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)(235,664)(236,665)(237,666)(238,667)(239,668)(240,669)
(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)(248,651)
(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)(256,659)
(257,660)(258,661)(259,662)(260,663)(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)(287,703)(288,704)
(289,705)(290,706)(291,707)(292,708)(293,709)(294,710)(295,711)(296,712)
(297,713)(298,714)(299,715)(300,716)(301,717)(302,718)(303,719)(304,720)
(305,721)(306,722)(307,723)(308,724)(309,725)(310,726)(311,727)(312,728)
(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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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)( 53,261)( 54,273)( 55,272)
( 56,271)( 57,270)( 58,269)( 59,268)( 60,267)( 61,266)( 62,265)( 63,264)
( 64,263)( 65,262)( 66,274)( 67,286)( 68,285)( 69,284)( 70,283)( 71,282)
( 72,281)( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,275)( 79,287)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,291)( 89,290)( 90,289)( 91,288)( 92,300)( 93,312)( 94,311)( 95,310)
( 96,309)( 97,308)( 98,307)( 99,306)(100,305)(101,304)(102,303)(103,302)
(104,301)(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)(157,378)(158,390)(159,389)
(160,388)(161,387)(162,386)(163,385)(164,384)(165,383)(166,382)(167,381)
(168,380)(169,379)(170,365)(171,377)(172,376)(173,375)(174,374)(175,373)
(176,372)(177,371)(178,370)(179,369)(180,368)(181,367)(182,366)(183,404)
(184,416)(185,415)(186,414)(187,413)(188,412)(189,411)(190,410)(191,409)
(192,408)(193,407)(194,406)(195,405)(196,391)(197,403)(198,402)(199,401)
(200,400)(201,399)(202,398)(203,397)(204,396)(205,395)(206,394)(207,393)
(208,392)(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)(469,677)(470,689)(471,688)
(472,687)(473,686)(474,685)(475,684)(476,683)(477,682)(478,681)(479,680)
(480,679)(481,678)(482,690)(483,702)(484,701)(485,700)(486,699)(487,698)
(488,697)(489,696)(490,695)(491,694)(492,693)(493,692)(494,691)(495,703)
(496,715)(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)
(504,707)(505,706)(506,705)(507,704)(508,716)(509,728)(510,727)(511,726)
(512,725)(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)
(520,717)(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)(573,794)(574,806)(575,805)
(576,804)(577,803)(578,802)(579,801)(580,800)(581,799)(582,798)(583,797)
(584,796)(585,795)(586,781)(587,793)(588,792)(589,791)(590,790)(591,789)
(592,788)(593,787)(594,786)(595,785)(596,784)(597,783)(598,782)(599,820)
(600,832)(601,831)(602,830)(603,829)(604,828)(605,827)(606,826)(607,825)
(608,824)(609,823)(610,822)(611,821)(612,807)(613,819)(614,818)(615,817)
(616,816)(617,815)(618,814)(619,813)(620,812)(621,811)(622,810)(623,809)
(624,808);
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, 41)( 28, 40)( 29, 52)
( 30, 51)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)
( 38, 43)( 39, 42)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)
( 66, 67)( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 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)(157,184)(158,183)(159,195)
(160,194)(161,193)(162,192)(163,191)(164,190)(165,189)(166,188)(167,187)
(168,186)(169,185)(170,197)(171,196)(172,208)(173,207)(174,206)(175,205)
(176,204)(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(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)(235,301)(236,300)(237,312)(238,311)(239,310)(240,309)(241,308)
(242,307)(243,306)(244,305)(245,304)(246,303)(247,302)(248,288)(249,287)
(250,299)(251,298)(252,297)(253,296)(254,295)(255,294)(256,293)(257,292)
(258,291)(259,290)(260,289)(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)(443,561)(444,560)(445,572)(446,571)(447,570)(448,569)(449,568)
(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,548)(457,547)
(458,559)(459,558)(460,557)(461,556)(462,555)(463,554)(464,553)(465,552)
(466,551)(467,550)(468,549)(469,574)(470,573)(471,585)(472,584)(473,583)
(474,582)(475,581)(476,580)(477,579)(478,578)(479,577)(480,576)(481,575)
(482,587)(483,586)(484,598)(485,597)(486,596)(487,595)(488,594)(489,593)
(490,592)(491,591)(492,590)(493,589)(494,588)(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)(651,808)(652,807)(653,819)(654,818)(655,817)(656,816)(657,815)
(658,814)(659,813)(660,812)(661,811)(662,810)(663,809)(664,821)(665,820)
(666,832)(667,831)(668,830)(669,829)(670,828)(671,827)(672,826)(673,825)
(674,824)(675,823)(676,822)(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)(703,756)(704,755)(705,767)
(706,766)(707,765)(708,764)(709,763)(710,762)(711,761)(712,760)(713,759)
(714,758)(715,757)(716,769)(717,768)(718,780)(719,779)(720,778)(721,777)
(722,776)(723,775)(724,774)(725,773)(726,772)(727,771)(728,770);
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)( 27,456)( 28,457)( 29,458)( 30,459)( 31,460)
( 32,461)( 33,462)( 34,463)( 35,464)( 36,465)( 37,466)( 38,467)( 39,468)
( 40,443)( 41,444)( 42,445)( 43,446)( 44,447)( 45,448)( 46,449)( 47,450)
( 48,451)( 49,452)( 50,453)( 51,454)( 52,455)( 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)( 79,495)
( 80,496)( 81,497)( 82,498)( 83,499)( 84,500)( 85,501)( 86,502)( 87,503)
( 88,504)( 89,505)( 90,506)( 91,507)( 92,508)( 93,509)( 94,510)( 95,511)
( 96,512)( 97,513)( 98,514)( 99,515)(100,516)(101,517)(102,518)(103,519)
(104,520)(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)(235,664)(236,665)(237,666)(238,667)(239,668)
(240,669)(241,670)(242,671)(243,672)(244,673)(245,674)(246,675)(247,676)
(248,651)(249,652)(250,653)(251,654)(252,655)(253,656)(254,657)(255,658)
(256,659)(257,660)(258,661)(259,662)(260,663)(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)(287,703)
(288,704)(289,705)(290,706)(291,707)(292,708)(293,709)(294,710)(295,711)
(296,712)(297,713)(298,714)(299,715)(300,716)(301,717)(302,718)(303,719)
(304,720)(305,721)(306,722)(307,723)(308,724)(309,725)(310,726)(311,727)
(312,728)(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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >; 
 
References : None.
to this polytope