Polytope of Type {16,52}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,52}*1664b
if this polytope has a name.
Group : SmallGroup(1664,6457)
Rank : 3
Schlafli Type : {16,52}
Number of vertices, edges, etc : 16, 416, 52
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 : {8,52}*832a
4-fold quotients : {4,52}*416, {8,26}*416
8-fold quotients : {2,52}*208, {4,26}*208
13-fold quotients : {16,4}*128b
16-fold quotients : {2,26}*104
26-fold quotients : {8,4}*64a
32-fold quotients : {2,13}*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)( 2,418)( 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);;
s1 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)( 81,103)
( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)
( 90, 94)( 91, 93)(105,131)(106,143)(107,142)(108,141)(109,140)(110,139)
(111,138)(112,137)(113,136)(114,135)(115,134)(116,133)(117,132)(118,144)
(119,156)(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)
(127,148)(128,147)(129,146)(130,145)(157,183)(158,195)(159,194)(160,193)
(161,192)(162,191)(163,190)(164,189)(165,188)(166,187)(167,186)(168,185)
(169,184)(170,196)(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)
(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(209,261)(210,273)
(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)(218,265)
(219,264)(220,263)(221,262)(222,274)(223,286)(224,285)(225,284)(226,283)
(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)(234,275)
(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)(250,298)
(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)(258,290)
(259,289)(260,288)(313,391)(314,403)(315,402)(316,401)(317,400)(318,399)
(319,398)(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)(326,404)
(327,416)(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)
(335,408)(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)(342,375)
(343,374)(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)(350,367)
(351,366)(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)
(359,384)(360,383)(361,382)(362,381)(363,380)(364,379)(417,521)(418,533)
(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)(426,525)
(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)(433,544)(434,543)
(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)(441,536)(442,535)
(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)(450,566)
(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)(458,558)
(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)(466,550)
(467,549)(468,548)(469,573)(470,585)(471,584)(472,583)(473,582)(474,581)
(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)(482,586)
(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)
(491,590)(492,589)(493,588)(494,587)(495,612)(496,624)(497,623)(498,622)
(499,621)(500,620)(501,619)(502,618)(503,617)(504,616)(505,615)(506,614)
(507,613)(508,599)(509,611)(510,610)(511,609)(512,608)(513,607)(514,606)
(515,605)(516,604)(517,603)(518,602)(519,601)(520,600)(625,794)(626,806)
(627,805)(628,804)(629,803)(630,802)(631,801)(632,800)(633,799)(634,798)
(635,797)(636,796)(637,795)(638,781)(639,793)(640,792)(641,791)(642,790)
(643,789)(644,788)(645,787)(646,786)(647,785)(648,784)(649,783)(650,782)
(651,807)(652,819)(653,818)(654,817)(655,816)(656,815)(657,814)(658,813)
(659,812)(660,811)(661,810)(662,809)(663,808)(664,820)(665,832)(666,831)
(667,830)(668,829)(669,828)(670,827)(671,826)(672,825)(673,824)(674,823)
(675,822)(676,821)(677,742)(678,754)(679,753)(680,752)(681,751)(682,750)
(683,749)(684,748)(685,747)(686,746)(687,745)(688,744)(689,743)(690,729)
(691,741)(692,740)(693,739)(694,738)(695,737)(696,736)(697,735)(698,734)
(699,733)(700,732)(701,731)(702,730)(703,755)(704,767)(705,766)(706,765)
(707,764)(708,763)(709,762)(710,761)(711,760)(712,759)(713,758)(714,757)
(715,756)(716,768)(717,780)(718,779)(719,778)(720,777)(721,776)(722,775)
(723,774)(724,773)(725,772)(726,771)(727,770)(728,769);;
s2 := ( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)( 8,216)
( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)( 32,244)
( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)( 40,249)
( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)( 48,254)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)( 56,272)
( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)( 64,264)
( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)( 72,282)
( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)( 80,287)
( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)( 88,292)
( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)( 96,310)
( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)(104,302)
(105,327)(106,326)(107,338)(108,337)(109,336)(110,335)(111,334)(112,333)
(113,332)(114,331)(115,330)(116,329)(117,328)(118,314)(119,313)(120,325)
(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)(128,317)
(129,316)(130,315)(131,353)(132,352)(133,364)(134,363)(135,362)(136,361)
(137,360)(138,359)(139,358)(140,357)(141,356)(142,355)(143,354)(144,340)
(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)(152,345)
(153,344)(154,343)(155,342)(156,341)(157,379)(158,378)(159,390)(160,389)
(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)(176,373)
(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,405)(184,404)
(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)(192,409)
(193,408)(194,407)(195,406)(196,392)(197,391)(198,403)(199,402)(200,401)
(201,400)(202,399)(203,398)(204,397)(205,396)(206,395)(207,394)(208,393)
(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)(424,632)
(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)(432,650)
(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)(440,642)
(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)(448,660)
(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)(456,665)
(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)(464,670)
(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)(472,688)
(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)(480,680)
(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)(488,698)
(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)(496,703)
(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)(504,708)
(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)(512,726)
(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)(520,718)
(521,743)(522,742)(523,754)(524,753)(525,752)(526,751)(527,750)(528,749)
(529,748)(530,747)(531,746)(532,745)(533,744)(534,730)(535,729)(536,741)
(537,740)(538,739)(539,738)(540,737)(541,736)(542,735)(543,734)(544,733)
(545,732)(546,731)(547,769)(548,768)(549,780)(550,779)(551,778)(552,777)
(553,776)(554,775)(555,774)(556,773)(557,772)(558,771)(559,770)(560,756)
(561,755)(562,767)(563,766)(564,765)(565,764)(566,763)(567,762)(568,761)
(569,760)(570,759)(571,758)(572,757)(573,795)(574,794)(575,806)(576,805)
(577,804)(578,803)(579,802)(580,801)(581,800)(582,799)(583,798)(584,797)
(585,796)(586,782)(587,781)(588,793)(589,792)(590,791)(591,790)(592,789)
(593,788)(594,787)(595,786)(596,785)(597,784)(598,783)(599,821)(600,820)
(601,832)(602,831)(603,830)(604,829)(605,828)(606,827)(607,826)(608,825)
(609,824)(610,823)(611,822)(612,808)(613,807)(614,819)(615,818)(616,817)
(617,816)(618,815)(619,814)(620,813)(621,812)(622,811)(623,810)(624,809);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(832)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)
( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)
( 38, 42)( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)
( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)
( 89, 95)( 90, 94)( 91, 93)(105,131)(106,143)(107,142)(108,141)(109,140)
(110,139)(111,138)(112,137)(113,136)(114,135)(115,134)(116,133)(117,132)
(118,144)(119,156)(120,155)(121,154)(122,153)(123,152)(124,151)(125,150)
(126,149)(127,148)(128,147)(129,146)(130,145)(157,183)(158,195)(159,194)
(160,193)(161,192)(162,191)(163,190)(164,189)(165,188)(166,187)(167,186)
(168,185)(169,184)(170,196)(171,208)(172,207)(173,206)(174,205)(175,204)
(176,203)(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(209,261)
(210,273)(211,272)(212,271)(213,270)(214,269)(215,268)(216,267)(217,266)
(218,265)(219,264)(220,263)(221,262)(222,274)(223,286)(224,285)(225,284)
(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)(232,277)(233,276)
(234,275)(235,300)(236,312)(237,311)(238,310)(239,309)(240,308)(241,307)
(242,306)(243,305)(244,304)(245,303)(246,302)(247,301)(248,287)(249,299)
(250,298)(251,297)(252,296)(253,295)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,288)(313,391)(314,403)(315,402)(316,401)(317,400)
(318,399)(319,398)(320,397)(321,396)(322,395)(323,394)(324,393)(325,392)
(326,404)(327,416)(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)
(334,409)(335,408)(336,407)(337,406)(338,405)(339,365)(340,377)(341,376)
(342,375)(343,374)(344,373)(345,372)(346,371)(347,370)(348,369)(349,368)
(350,367)(351,366)(352,378)(353,390)(354,389)(355,388)(356,387)(357,386)
(358,385)(359,384)(360,383)(361,382)(362,381)(363,380)(364,379)(417,521)
(418,533)(419,532)(420,531)(421,530)(422,529)(423,528)(424,527)(425,526)
(426,525)(427,524)(428,523)(429,522)(430,534)(431,546)(432,545)(433,544)
(434,543)(435,542)(436,541)(437,540)(438,539)(439,538)(440,537)(441,536)
(442,535)(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)
(450,566)(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)
(458,558)(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)
(466,550)(467,549)(468,548)(469,573)(470,585)(471,584)(472,583)(473,582)
(474,581)(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)
(482,586)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)
(490,591)(491,590)(492,589)(493,588)(494,587)(495,612)(496,624)(497,623)
(498,622)(499,621)(500,620)(501,619)(502,618)(503,617)(504,616)(505,615)
(506,614)(507,613)(508,599)(509,611)(510,610)(511,609)(512,608)(513,607)
(514,606)(515,605)(516,604)(517,603)(518,602)(519,601)(520,600)(625,794)
(626,806)(627,805)(628,804)(629,803)(630,802)(631,801)(632,800)(633,799)
(634,798)(635,797)(636,796)(637,795)(638,781)(639,793)(640,792)(641,791)
(642,790)(643,789)(644,788)(645,787)(646,786)(647,785)(648,784)(649,783)
(650,782)(651,807)(652,819)(653,818)(654,817)(655,816)(656,815)(657,814)
(658,813)(659,812)(660,811)(661,810)(662,809)(663,808)(664,820)(665,832)
(666,831)(667,830)(668,829)(669,828)(670,827)(671,826)(672,825)(673,824)
(674,823)(675,822)(676,821)(677,742)(678,754)(679,753)(680,752)(681,751)
(682,750)(683,749)(684,748)(685,747)(686,746)(687,745)(688,744)(689,743)
(690,729)(691,741)(692,740)(693,739)(694,738)(695,737)(696,736)(697,735)
(698,734)(699,733)(700,732)(701,731)(702,730)(703,755)(704,767)(705,766)
(706,765)(707,764)(708,763)(709,762)(710,761)(711,760)(712,759)(713,758)
(714,757)(715,756)(716,768)(717,780)(718,779)(719,778)(720,777)(721,776)
(722,775)(723,774)(724,773)(725,772)(726,771)(727,770)(728,769);
s2 := Sym(832)!( 1,210)( 2,209)( 3,221)( 4,220)( 5,219)( 6,218)( 7,217)
( 8,216)( 9,215)( 10,214)( 11,213)( 12,212)( 13,211)( 14,223)( 15,222)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,230)( 21,229)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,236)( 28,235)( 29,247)( 30,246)( 31,245)
( 32,244)( 33,243)( 34,242)( 35,241)( 36,240)( 37,239)( 38,238)( 39,237)
( 40,249)( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)
( 48,254)( 49,253)( 50,252)( 51,251)( 52,250)( 53,262)( 54,261)( 55,273)
( 56,272)( 57,271)( 58,270)( 59,269)( 60,268)( 61,267)( 62,266)( 63,265)
( 64,264)( 65,263)( 66,275)( 67,274)( 68,286)( 69,285)( 70,284)( 71,283)
( 72,282)( 73,281)( 74,280)( 75,279)( 76,278)( 77,277)( 78,276)( 79,288)
( 80,287)( 81,299)( 82,298)( 83,297)( 84,296)( 85,295)( 86,294)( 87,293)
( 88,292)( 89,291)( 90,290)( 91,289)( 92,301)( 93,300)( 94,312)( 95,311)
( 96,310)( 97,309)( 98,308)( 99,307)(100,306)(101,305)(102,304)(103,303)
(104,302)(105,327)(106,326)(107,338)(108,337)(109,336)(110,335)(111,334)
(112,333)(113,332)(114,331)(115,330)(116,329)(117,328)(118,314)(119,313)
(120,325)(121,324)(122,323)(123,322)(124,321)(125,320)(126,319)(127,318)
(128,317)(129,316)(130,315)(131,353)(132,352)(133,364)(134,363)(135,362)
(136,361)(137,360)(138,359)(139,358)(140,357)(141,356)(142,355)(143,354)
(144,340)(145,339)(146,351)(147,350)(148,349)(149,348)(150,347)(151,346)
(152,345)(153,344)(154,343)(155,342)(156,341)(157,379)(158,378)(159,390)
(160,389)(161,388)(162,387)(163,386)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,380)(170,366)(171,365)(172,377)(173,376)(174,375)(175,374)
(176,373)(177,372)(178,371)(179,370)(180,369)(181,368)(182,367)(183,405)
(184,404)(185,416)(186,415)(187,414)(188,413)(189,412)(190,411)(191,410)
(192,409)(193,408)(194,407)(195,406)(196,392)(197,391)(198,403)(199,402)
(200,401)(201,400)(202,399)(203,398)(204,397)(205,396)(206,395)(207,394)
(208,393)(417,626)(418,625)(419,637)(420,636)(421,635)(422,634)(423,633)
(424,632)(425,631)(426,630)(427,629)(428,628)(429,627)(430,639)(431,638)
(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)(439,643)
(440,642)(441,641)(442,640)(443,652)(444,651)(445,663)(446,662)(447,661)
(448,660)(449,659)(450,658)(451,657)(452,656)(453,655)(454,654)(455,653)
(456,665)(457,664)(458,676)(459,675)(460,674)(461,673)(462,672)(463,671)
(464,670)(465,669)(466,668)(467,667)(468,666)(469,678)(470,677)(471,689)
(472,688)(473,687)(474,686)(475,685)(476,684)(477,683)(478,682)(479,681)
(480,680)(481,679)(482,691)(483,690)(484,702)(485,701)(486,700)(487,699)
(488,698)(489,697)(490,696)(491,695)(492,694)(493,693)(494,692)(495,704)
(496,703)(497,715)(498,714)(499,713)(500,712)(501,711)(502,710)(503,709)
(504,708)(505,707)(506,706)(507,705)(508,717)(509,716)(510,728)(511,727)
(512,726)(513,725)(514,724)(515,723)(516,722)(517,721)(518,720)(519,719)
(520,718)(521,743)(522,742)(523,754)(524,753)(525,752)(526,751)(527,750)
(528,749)(529,748)(530,747)(531,746)(532,745)(533,744)(534,730)(535,729)
(536,741)(537,740)(538,739)(539,738)(540,737)(541,736)(542,735)(543,734)
(544,733)(545,732)(546,731)(547,769)(548,768)(549,780)(550,779)(551,778)
(552,777)(553,776)(554,775)(555,774)(556,773)(557,772)(558,771)(559,770)
(560,756)(561,755)(562,767)(563,766)(564,765)(565,764)(566,763)(567,762)
(568,761)(569,760)(570,759)(571,758)(572,757)(573,795)(574,794)(575,806)
(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,799)(583,798)
(584,797)(585,796)(586,782)(587,781)(588,793)(589,792)(590,791)(591,790)
(592,789)(593,788)(594,787)(595,786)(596,785)(597,784)(598,783)(599,821)
(600,820)(601,832)(602,831)(603,830)(604,829)(605,828)(606,827)(607,826)
(608,825)(609,824)(610,823)(611,822)(612,808)(613,807)(614,819)(615,818)
(616,817)(617,816)(618,815)(619,814)(620,813)(621,812)(622,811)(623,810)
(624,809);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope