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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}*1664a
Also Known As : {52,16|2}. if this polytope has another name.
Group : SmallGroup(1664,6423)
Rank : 3
Schlafli Type : {52,16}
Number of vertices, edges, etc : 52, 416, 16
Order of s0s1s2 : 208
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {52,8}*832a, {26,16}*832
   4-fold quotients : {52,4}*416, {26,8}*416
   8-fold quotients : {52,2}*208, {26,4}*208
   13-fold quotients : {4,16}*128a
   16-fold quotients : {26,2}*104
   26-fold quotients : {4,8}*64a, {2,16}*64
   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)
(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)(112,319)
(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)(120,337)
(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)(128,329)
(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)(136,347)
(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)(144,352)
(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,354)(156,353)(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)(469,677)(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)
(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)(528,735)
(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)(536,753)
(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)(544,745)
(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)(552,763)
(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)(560,768)
(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)(568,773)
(569,772)(570,771)(571,770)(572,769)(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, 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)(625,782)(626,781)
(627,793)(628,792)(629,791)(630,790)(631,789)(632,788)(633,787)(634,786)
(635,785)(636,784)(637,783)(638,795)(639,794)(640,806)(641,805)(642,804)
(643,803)(644,802)(645,801)(646,800)(647,799)(648,798)(649,797)(650,796)
(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)(677,730)(678,729)(679,741)(680,740)(681,739)(682,738)
(683,737)(684,736)(685,735)(686,734)(687,733)(688,732)(689,731)(690,743)
(691,742)(692,754)(693,753)(694,752)(695,751)(696,750)(697,749)(698,748)
(699,747)(700,746)(701,745)(702,744)(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)( 27,456)( 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)( 53,469)( 54,470)( 55,471)( 56,472)
( 57,473)( 58,474)( 59,475)( 60,476)( 61,477)( 62,478)( 63,479)( 64,480)
( 65,481)( 66,482)( 67,483)( 68,484)( 69,485)( 70,486)( 71,487)( 72,488)
( 73,489)( 74,490)( 75,491)( 76,492)( 77,493)( 78,494)( 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)(157,599)(158,600)(159,601)(160,602)
(161,603)(162,604)(163,605)(164,606)(165,607)(166,608)(167,609)(168,610)
(169,611)(170,612)(171,613)(172,614)(173,615)(174,616)(175,617)(176,618)
(177,619)(178,620)(179,621)(180,622)(181,623)(182,624)(183,573)(184,574)
(185,575)(186,576)(187,577)(188,578)(189,579)(190,580)(191,581)(192,582)
(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)
(201,591)(202,592)(203,593)(204,594)(205,595)(206,596)(207,597)(208,598)
(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)(261,677)(262,678)(263,679)(264,680)
(265,681)(266,682)(267,683)(268,684)(269,685)(270,686)(271,687)(272,688)
(273,689)(274,690)(275,691)(276,692)(277,693)(278,694)(279,695)(280,696)
(281,697)(282,698)(283,699)(284,700)(285,701)(286,702)(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)(365,807)(366,808)(367,809)(368,810)
(369,811)(370,812)(371,813)(372,814)(373,815)(374,816)(375,817)(376,818)
(377,819)(378,820)(379,821)(380,822)(381,823)(382,824)(383,825)(384,826)
(385,827)(386,828)(387,829)(388,830)(389,831)(390,832)(391,781)(392,782)
(393,783)(394,784)(395,785)(396,786)(397,787)(398,788)(399,789)(400,790)
(401,791)(402,792)(403,793)(404,794)(405,795)(406,796)(407,797)(408,798)
(409,799)(410,800)(411,801)(412,802)(413,803)(414,804)(415,805)(416,806);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(105,313)(106,325)(107,324)(108,323)(109,322)(110,321)(111,320)
(112,319)(113,318)(114,317)(115,316)(116,315)(117,314)(118,326)(119,338)
(120,337)(121,336)(122,335)(123,334)(124,333)(125,332)(126,331)(127,330)
(128,329)(129,328)(130,327)(131,339)(132,351)(133,350)(134,349)(135,348)
(136,347)(137,346)(138,345)(139,344)(140,343)(141,342)(142,341)(143,340)
(144,352)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,354)(156,353)(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)(469,677)(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)(521,729)(522,741)(523,740)(524,739)(525,738)(526,737)(527,736)
(528,735)(529,734)(530,733)(531,732)(532,731)(533,730)(534,742)(535,754)
(536,753)(537,752)(538,751)(539,750)(540,749)(541,748)(542,747)(543,746)
(544,745)(545,744)(546,743)(547,755)(548,767)(549,766)(550,765)(551,764)
(552,763)(553,762)(554,761)(555,760)(556,759)(557,758)(558,757)(559,756)
(560,768)(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)
(568,773)(569,772)(570,771)(571,770)(572,769)(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, 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)(625,782)
(626,781)(627,793)(628,792)(629,791)(630,790)(631,789)(632,788)(633,787)
(634,786)(635,785)(636,784)(637,783)(638,795)(639,794)(640,806)(641,805)
(642,804)(643,803)(644,802)(645,801)(646,800)(647,799)(648,798)(649,797)
(650,796)(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)(677,730)(678,729)(679,741)(680,740)(681,739)
(682,738)(683,737)(684,736)(685,735)(686,734)(687,733)(688,732)(689,731)
(690,743)(691,742)(692,754)(693,753)(694,752)(695,751)(696,750)(697,749)
(698,748)(699,747)(700,746)(701,745)(702,744)(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)( 27,456)( 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)( 53,469)( 54,470)( 55,471)
( 56,472)( 57,473)( 58,474)( 59,475)( 60,476)( 61,477)( 62,478)( 63,479)
( 64,480)( 65,481)( 66,482)( 67,483)( 68,484)( 69,485)( 70,486)( 71,487)
( 72,488)( 73,489)( 74,490)( 75,491)( 76,492)( 77,493)( 78,494)( 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)(157,599)(158,600)(159,601)
(160,602)(161,603)(162,604)(163,605)(164,606)(165,607)(166,608)(167,609)
(168,610)(169,611)(170,612)(171,613)(172,614)(173,615)(174,616)(175,617)
(176,618)(177,619)(178,620)(179,621)(180,622)(181,623)(182,624)(183,573)
(184,574)(185,575)(186,576)(187,577)(188,578)(189,579)(190,580)(191,581)
(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)
(200,590)(201,591)(202,592)(203,593)(204,594)(205,595)(206,596)(207,597)
(208,598)(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)(261,677)(262,678)(263,679)
(264,680)(265,681)(266,682)(267,683)(268,684)(269,685)(270,686)(271,687)
(272,688)(273,689)(274,690)(275,691)(276,692)(277,693)(278,694)(279,695)
(280,696)(281,697)(282,698)(283,699)(284,700)(285,701)(286,702)(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)(365,807)(366,808)(367,809)
(368,810)(369,811)(370,812)(371,813)(372,814)(373,815)(374,816)(375,817)
(376,818)(377,819)(378,820)(379,821)(380,822)(381,823)(382,824)(383,825)
(384,826)(385,827)(386,828)(387,829)(388,830)(389,831)(390,832)(391,781)
(392,782)(393,783)(394,784)(395,785)(396,786)(397,787)(398,788)(399,789)
(400,790)(401,791)(402,792)(403,793)(404,794)(405,795)(406,796)(407,797)
(408,798)(409,799)(410,800)(411,801)(412,802)(413,803)(414,804)(415,805)
(416,806);
poly := sub<Sym(832)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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