Polytope of Type {4,208}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,208}*1664b
if this polytope has a name.
Group : SmallGroup(1664,6458)
Rank : 3
Schlafli Type : {4,208}
Number of vertices, edges, etc : 4, 416, 208
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 : {4,104}*832a
4-fold quotients : {4,52}*416, {2,104}*416
8-fold quotients : {2,52}*208, {4,26}*208
13-fold quotients : {4,16}*128b
16-fold quotients : {2,26}*104
26-fold quotients : {4,8}*64a
32-fold quotients : {2,13}*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)( 2,210)( 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)( 53,261)( 54,262)( 55,263)( 56,264)
( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)( 64,272)
( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)
( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)( 80,288)
( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)( 88,296)
( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)( 96,304)
( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)(104,312)
(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)(157,378)(158,379)(159,380)(160,381)
(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)(168,389)
(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)(176,371)
(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,404)(184,405)
(185,406)(186,407)(187,408)(188,409)(189,410)(190,411)(191,412)(192,413)
(193,414)(194,415)(195,416)(196,391)(197,392)(198,393)(199,394)(200,395)
(201,396)(202,397)(203,398)(204,399)(205,400)(206,401)(207,402)(208,403)
(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)(469,677)(470,678)(471,679)(472,680)
(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)(480,688)
(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)(488,696)
(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)(496,704)
(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)(504,712)
(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)(512,720)
(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)(520,728)
(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)(573,794)(574,795)(575,796)(576,797)
(577,798)(578,799)(579,800)(580,801)(581,802)(582,803)(583,804)(584,805)
(585,806)(586,781)(587,782)(588,783)(589,784)(590,785)(591,786)(592,787)
(593,788)(594,789)(595,790)(596,791)(597,792)(598,793)(599,820)(600,821)
(601,822)(602,823)(603,824)(604,825)(605,826)(606,827)(607,828)(608,829)
(609,830)(610,831)(611,832)(612,807)(613,808)(614,809)(615,810)(616,811)
(617,812)(618,813)(619,814)(620,815)(621,816)(622,817)(623,818)(624,819);;
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 := ( 1,418)( 2,417)( 3,429)( 4,428)( 5,427)( 6,426)( 7,425)( 8,424)
( 9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)( 16,442)
( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)( 24,434)
( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)( 32,465)
( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)( 40,444)
( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)( 48,449)
( 49,448)( 50,447)( 51,446)( 52,445)( 53,483)( 54,482)( 55,494)( 56,493)
( 57,492)( 58,491)( 59,490)( 60,489)( 61,488)( 62,487)( 63,486)( 64,485)
( 65,484)( 66,470)( 67,469)( 68,481)( 69,480)( 70,479)( 71,478)( 72,477)
( 73,476)( 74,475)( 75,474)( 76,473)( 77,472)( 78,471)( 79,496)( 80,495)
( 81,507)( 82,506)( 83,505)( 84,504)( 85,503)( 86,502)( 87,501)( 88,500)
( 89,499)( 90,498)( 91,497)( 92,509)( 93,508)( 94,520)( 95,519)( 96,518)
( 97,517)( 98,516)( 99,515)(100,514)(101,513)(102,512)(103,511)(104,510)
(105,548)(106,547)(107,559)(108,558)(109,557)(110,556)(111,555)(112,554)
(113,553)(114,552)(115,551)(116,550)(117,549)(118,561)(119,560)(120,572)
(121,571)(122,570)(123,569)(124,568)(125,567)(126,566)(127,565)(128,564)
(129,563)(130,562)(131,522)(132,521)(133,533)(134,532)(135,531)(136,530)
(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)(144,535)
(145,534)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)(152,540)
(153,539)(154,538)(155,537)(156,536)(157,613)(158,612)(159,624)(160,623)
(161,622)(162,621)(163,620)(164,619)(165,618)(166,617)(167,616)(168,615)
(169,614)(170,600)(171,599)(172,611)(173,610)(174,609)(175,608)(176,607)
(177,606)(178,605)(179,604)(180,603)(181,602)(182,601)(183,587)(184,586)
(185,598)(186,597)(187,596)(188,595)(189,594)(190,593)(191,592)(192,591)
(193,590)(194,589)(195,588)(196,574)(197,573)(198,585)(199,584)(200,583)
(201,582)(202,581)(203,580)(204,579)(205,578)(206,577)(207,576)(208,575)
(209,626)(210,625)(211,637)(212,636)(213,635)(214,634)(215,633)(216,632)
(217,631)(218,630)(219,629)(220,628)(221,627)(222,639)(223,638)(224,650)
(225,649)(226,648)(227,647)(228,646)(229,645)(230,644)(231,643)(232,642)
(233,641)(234,640)(235,665)(236,664)(237,676)(238,675)(239,674)(240,673)
(241,672)(242,671)(243,670)(244,669)(245,668)(246,667)(247,666)(248,652)
(249,651)(250,663)(251,662)(252,661)(253,660)(254,659)(255,658)(256,657)
(257,656)(258,655)(259,654)(260,653)(261,691)(262,690)(263,702)(264,701)
(265,700)(266,699)(267,698)(268,697)(269,696)(270,695)(271,694)(272,693)
(273,692)(274,678)(275,677)(276,689)(277,688)(278,687)(279,686)(280,685)
(281,684)(282,683)(283,682)(284,681)(285,680)(286,679)(287,704)(288,703)
(289,715)(290,714)(291,713)(292,712)(293,711)(294,710)(295,709)(296,708)
(297,707)(298,706)(299,705)(300,717)(301,716)(302,728)(303,727)(304,726)
(305,725)(306,724)(307,723)(308,722)(309,721)(310,720)(311,719)(312,718)
(313,756)(314,755)(315,767)(316,766)(317,765)(318,764)(319,763)(320,762)
(321,761)(322,760)(323,759)(324,758)(325,757)(326,769)(327,768)(328,780)
(329,779)(330,778)(331,777)(332,776)(333,775)(334,774)(335,773)(336,772)
(337,771)(338,770)(339,730)(340,729)(341,741)(342,740)(343,739)(344,738)
(345,737)(346,736)(347,735)(348,734)(349,733)(350,732)(351,731)(352,743)
(353,742)(354,754)(355,753)(356,752)(357,751)(358,750)(359,749)(360,748)
(361,747)(362,746)(363,745)(364,744)(365,821)(366,820)(367,832)(368,831)
(369,830)(370,829)(371,828)(372,827)(373,826)(374,825)(375,824)(376,823)
(377,822)(378,808)(379,807)(380,819)(381,818)(382,817)(383,816)(384,815)
(385,814)(386,813)(387,812)(388,811)(389,810)(390,809)(391,795)(392,794)
(393,806)(394,805)(395,804)(396,803)(397,802)(398,801)(399,800)(400,799)
(401,798)(402,797)(403,796)(404,782)(405,781)(406,793)(407,792)(408,791)
(409,790)(410,789)(411,788)(412,787)(413,786)(414,785)(415,784)(416,783);;
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*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*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 53,261)( 54,262)( 55,263)
( 56,264)( 57,265)( 58,266)( 59,267)( 60,268)( 61,269)( 62,270)( 63,271)
( 64,272)( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)
( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)
( 80,288)( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)
( 88,296)( 89,297)( 90,298)( 91,299)( 92,300)( 93,301)( 94,302)( 95,303)
( 96,304)( 97,305)( 98,306)( 99,307)(100,308)(101,309)(102,310)(103,311)
(104,312)(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)(157,378)(158,379)(159,380)
(160,381)(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)
(168,389)(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)
(176,371)(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,404)
(184,405)(185,406)(186,407)(187,408)(188,409)(189,410)(190,411)(191,412)
(192,413)(193,414)(194,415)(195,416)(196,391)(197,392)(198,393)(199,394)
(200,395)(201,396)(202,397)(203,398)(204,399)(205,400)(206,401)(207,402)
(208,403)(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)(469,677)(470,678)(471,679)
(472,680)(473,681)(474,682)(475,683)(476,684)(477,685)(478,686)(479,687)
(480,688)(481,689)(482,690)(483,691)(484,692)(485,693)(486,694)(487,695)
(488,696)(489,697)(490,698)(491,699)(492,700)(493,701)(494,702)(495,703)
(496,704)(497,705)(498,706)(499,707)(500,708)(501,709)(502,710)(503,711)
(504,712)(505,713)(506,714)(507,715)(508,716)(509,717)(510,718)(511,719)
(512,720)(513,721)(514,722)(515,723)(516,724)(517,725)(518,726)(519,727)
(520,728)(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)(573,794)(574,795)(575,796)
(576,797)(577,798)(578,799)(579,800)(580,801)(581,802)(582,803)(583,804)
(584,805)(585,806)(586,781)(587,782)(588,783)(589,784)(590,785)(591,786)
(592,787)(593,788)(594,789)(595,790)(596,791)(597,792)(598,793)(599,820)
(600,821)(601,822)(602,823)(603,824)(604,825)(605,826)(606,827)(607,828)
(608,829)(609,830)(610,831)(611,832)(612,807)(613,808)(614,809)(615,810)
(616,811)(617,812)(618,813)(619,814)(620,815)(621,816)(622,817)(623,818)
(624,819);
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)!( 1,418)( 2,417)( 3,429)( 4,428)( 5,427)( 6,426)( 7,425)
( 8,424)( 9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)
( 16,442)( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)
( 24,434)( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)
( 32,465)( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)
( 40,444)( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)
( 48,449)( 49,448)( 50,447)( 51,446)( 52,445)( 53,483)( 54,482)( 55,494)
( 56,493)( 57,492)( 58,491)( 59,490)( 60,489)( 61,488)( 62,487)( 63,486)
( 64,485)( 65,484)( 66,470)( 67,469)( 68,481)( 69,480)( 70,479)( 71,478)
( 72,477)( 73,476)( 74,475)( 75,474)( 76,473)( 77,472)( 78,471)( 79,496)
( 80,495)( 81,507)( 82,506)( 83,505)( 84,504)( 85,503)( 86,502)( 87,501)
( 88,500)( 89,499)( 90,498)( 91,497)( 92,509)( 93,508)( 94,520)( 95,519)
( 96,518)( 97,517)( 98,516)( 99,515)(100,514)(101,513)(102,512)(103,511)
(104,510)(105,548)(106,547)(107,559)(108,558)(109,557)(110,556)(111,555)
(112,554)(113,553)(114,552)(115,551)(116,550)(117,549)(118,561)(119,560)
(120,572)(121,571)(122,570)(123,569)(124,568)(125,567)(126,566)(127,565)
(128,564)(129,563)(130,562)(131,522)(132,521)(133,533)(134,532)(135,531)
(136,530)(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)
(144,535)(145,534)(146,546)(147,545)(148,544)(149,543)(150,542)(151,541)
(152,540)(153,539)(154,538)(155,537)(156,536)(157,613)(158,612)(159,624)
(160,623)(161,622)(162,621)(163,620)(164,619)(165,618)(166,617)(167,616)
(168,615)(169,614)(170,600)(171,599)(172,611)(173,610)(174,609)(175,608)
(176,607)(177,606)(178,605)(179,604)(180,603)(181,602)(182,601)(183,587)
(184,586)(185,598)(186,597)(187,596)(188,595)(189,594)(190,593)(191,592)
(192,591)(193,590)(194,589)(195,588)(196,574)(197,573)(198,585)(199,584)
(200,583)(201,582)(202,581)(203,580)(204,579)(205,578)(206,577)(207,576)
(208,575)(209,626)(210,625)(211,637)(212,636)(213,635)(214,634)(215,633)
(216,632)(217,631)(218,630)(219,629)(220,628)(221,627)(222,639)(223,638)
(224,650)(225,649)(226,648)(227,647)(228,646)(229,645)(230,644)(231,643)
(232,642)(233,641)(234,640)(235,665)(236,664)(237,676)(238,675)(239,674)
(240,673)(241,672)(242,671)(243,670)(244,669)(245,668)(246,667)(247,666)
(248,652)(249,651)(250,663)(251,662)(252,661)(253,660)(254,659)(255,658)
(256,657)(257,656)(258,655)(259,654)(260,653)(261,691)(262,690)(263,702)
(264,701)(265,700)(266,699)(267,698)(268,697)(269,696)(270,695)(271,694)
(272,693)(273,692)(274,678)(275,677)(276,689)(277,688)(278,687)(279,686)
(280,685)(281,684)(282,683)(283,682)(284,681)(285,680)(286,679)(287,704)
(288,703)(289,715)(290,714)(291,713)(292,712)(293,711)(294,710)(295,709)
(296,708)(297,707)(298,706)(299,705)(300,717)(301,716)(302,728)(303,727)
(304,726)(305,725)(306,724)(307,723)(308,722)(309,721)(310,720)(311,719)
(312,718)(313,756)(314,755)(315,767)(316,766)(317,765)(318,764)(319,763)
(320,762)(321,761)(322,760)(323,759)(324,758)(325,757)(326,769)(327,768)
(328,780)(329,779)(330,778)(331,777)(332,776)(333,775)(334,774)(335,773)
(336,772)(337,771)(338,770)(339,730)(340,729)(341,741)(342,740)(343,739)
(344,738)(345,737)(346,736)(347,735)(348,734)(349,733)(350,732)(351,731)
(352,743)(353,742)(354,754)(355,753)(356,752)(357,751)(358,750)(359,749)
(360,748)(361,747)(362,746)(363,745)(364,744)(365,821)(366,820)(367,832)
(368,831)(369,830)(370,829)(371,828)(372,827)(373,826)(374,825)(375,824)
(376,823)(377,822)(378,808)(379,807)(380,819)(381,818)(382,817)(383,816)
(384,815)(385,814)(386,813)(387,812)(388,811)(389,810)(390,809)(391,795)
(392,794)(393,806)(394,805)(395,804)(396,803)(397,802)(398,801)(399,800)
(400,799)(401,798)(402,797)(403,796)(404,782)(405,781)(406,793)(407,792)
(408,791)(409,790)(410,789)(411,788)(412,787)(413,786)(414,785)(415,784)
(416,783);
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*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*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*s0*s1*s2*s1 >;
References : None.
to this polytope