Polytope of Type {208,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {208,4}*1664b
if this polytope has a name.
Group : SmallGroup(1664,6458)
Rank : 3
Schlafli Type : {208,4}
Number of vertices, edges, etc : 208, 416, 4
Order of s0s1s2 : 208
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {104,4}*832a
4-fold quotients : {52,4}*416, {104,2}*416
8-fold quotients : {52,2}*208, {26,4}*208
13-fold quotients : {16,4}*128b
16-fold quotients : {26,2}*104
26-fold quotients : {8,4}*64a
32-fold quotients : {13,2}*52
52-fold quotients : {4,4}*32, {8,2}*32
104-fold quotients : {2,4}*16, {4,2}*16
208-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,417)( 2,429)( 3,428)( 4,427)( 5,426)( 6,425)( 7,424)( 8,423)
( 9,422)( 10,421)( 11,420)( 12,419)( 13,418)( 14,430)( 15,442)( 16,441)
( 17,440)( 18,439)( 19,438)( 20,437)( 21,436)( 22,435)( 23,434)( 24,433)
( 25,432)( 26,431)( 27,456)( 28,468)( 29,467)( 30,466)( 31,465)( 32,464)
( 33,463)( 34,462)( 35,461)( 36,460)( 37,459)( 38,458)( 39,457)( 40,443)
( 41,455)( 42,454)( 43,453)( 44,452)( 45,451)( 46,450)( 47,449)( 48,448)
( 49,447)( 50,446)( 51,445)( 52,444)( 53,482)( 54,494)( 55,493)( 56,492)
( 57,491)( 58,490)( 59,489)( 60,488)( 61,487)( 62,486)( 63,485)( 64,484)
( 65,483)( 66,469)( 67,481)( 68,480)( 69,479)( 70,478)( 71,477)( 72,476)
( 73,475)( 74,474)( 75,473)( 76,472)( 77,471)( 78,470)( 79,495)( 80,507)
( 81,506)( 82,505)( 83,504)( 84,503)( 85,502)( 86,501)( 87,500)( 88,499)
( 89,498)( 90,497)( 91,496)( 92,508)( 93,520)( 94,519)( 95,518)( 96,517)
( 97,516)( 98,515)( 99,514)(100,513)(101,512)(102,511)(103,510)(104,509)
(105,547)(106,559)(107,558)(108,557)(109,556)(110,555)(111,554)(112,553)
(113,552)(114,551)(115,550)(116,549)(117,548)(118,560)(119,572)(120,571)
(121,570)(122,569)(123,568)(124,567)(125,566)(126,565)(127,564)(128,563)
(129,562)(130,561)(131,521)(132,533)(133,532)(134,531)(135,530)(136,529)
(137,528)(138,527)(139,526)(140,525)(141,524)(142,523)(143,522)(144,534)
(145,546)(146,545)(147,544)(148,543)(149,542)(150,541)(151,540)(152,539)
(153,538)(154,537)(155,536)(156,535)(157,612)(158,624)(159,623)(160,622)
(161,621)(162,620)(163,619)(164,618)(165,617)(166,616)(167,615)(168,614)
(169,613)(170,599)(171,611)(172,610)(173,609)(174,608)(175,607)(176,606)
(177,605)(178,604)(179,603)(180,602)(181,601)(182,600)(183,586)(184,598)
(185,597)(186,596)(187,595)(188,594)(189,593)(190,592)(191,591)(192,590)
(193,589)(194,588)(195,587)(196,573)(197,585)(198,584)(199,583)(200,582)
(201,581)(202,580)(203,579)(204,578)(205,577)(206,576)(207,575)(208,574)
(209,625)(210,637)(211,636)(212,635)(213,634)(214,633)(215,632)(216,631)
(217,630)(218,629)(219,628)(220,627)(221,626)(222,638)(223,650)(224,649)
(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)(232,641)
(233,640)(234,639)(235,664)(236,676)(237,675)(238,674)(239,673)(240,672)
(241,671)(242,670)(243,669)(244,668)(245,667)(246,666)(247,665)(248,651)
(249,663)(250,662)(251,661)(252,660)(253,659)(254,658)(255,657)(256,656)
(257,655)(258,654)(259,653)(260,652)(261,690)(262,702)(263,701)(264,700)
(265,699)(266,698)(267,697)(268,696)(269,695)(270,694)(271,693)(272,692)
(273,691)(274,677)(275,689)(276,688)(277,687)(278,686)(279,685)(280,684)
(281,683)(282,682)(283,681)(284,680)(285,679)(286,678)(287,703)(288,715)
(289,714)(290,713)(291,712)(292,711)(293,710)(294,709)(295,708)(296,707)
(297,706)(298,705)(299,704)(300,716)(301,728)(302,727)(303,726)(304,725)
(305,724)(306,723)(307,722)(308,721)(309,720)(310,719)(311,718)(312,717)
(313,755)(314,767)(315,766)(316,765)(317,764)(318,763)(319,762)(320,761)
(321,760)(322,759)(323,758)(324,757)(325,756)(326,768)(327,780)(328,779)
(329,778)(330,777)(331,776)(332,775)(333,774)(334,773)(335,772)(336,771)
(337,770)(338,769)(339,729)(340,741)(341,740)(342,739)(343,738)(344,737)
(345,736)(346,735)(347,734)(348,733)(349,732)(350,731)(351,730)(352,742)
(353,754)(354,753)(355,752)(356,751)(357,750)(358,749)(359,748)(360,747)
(361,746)(362,745)(363,744)(364,743)(365,820)(366,832)(367,831)(368,830)
(369,829)(370,828)(371,827)(372,826)(373,825)(374,824)(375,823)(376,822)
(377,821)(378,807)(379,819)(380,818)(381,817)(382,816)(383,815)(384,814)
(385,813)(386,812)(387,811)(388,810)(389,809)(390,808)(391,794)(392,806)
(393,805)(394,804)(395,803)(396,802)(397,801)(398,800)(399,799)(400,798)
(401,797)(402,796)(403,795)(404,781)(405,793)(406,792)(407,791)(408,790)
(409,789)(410,788)(411,787)(412,786)(413,785)(414,784)(415,783)(416,782);;
s1 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 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 := ( 1,209)( 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);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(832)!( 1,417)( 2,429)( 3,428)( 4,427)( 5,426)( 6,425)( 7,424)
( 8,423)( 9,422)( 10,421)( 11,420)( 12,419)( 13,418)( 14,430)( 15,442)
( 16,441)( 17,440)( 18,439)( 19,438)( 20,437)( 21,436)( 22,435)( 23,434)
( 24,433)( 25,432)( 26,431)( 27,456)( 28,468)( 29,467)( 30,466)( 31,465)
( 32,464)( 33,463)( 34,462)( 35,461)( 36,460)( 37,459)( 38,458)( 39,457)
( 40,443)( 41,455)( 42,454)( 43,453)( 44,452)( 45,451)( 46,450)( 47,449)
( 48,448)( 49,447)( 50,446)( 51,445)( 52,444)( 53,482)( 54,494)( 55,493)
( 56,492)( 57,491)( 58,490)( 59,489)( 60,488)( 61,487)( 62,486)( 63,485)
( 64,484)( 65,483)( 66,469)( 67,481)( 68,480)( 69,479)( 70,478)( 71,477)
( 72,476)( 73,475)( 74,474)( 75,473)( 76,472)( 77,471)( 78,470)( 79,495)
( 80,507)( 81,506)( 82,505)( 83,504)( 84,503)( 85,502)( 86,501)( 87,500)
( 88,499)( 89,498)( 90,497)( 91,496)( 92,508)( 93,520)( 94,519)( 95,518)
( 96,517)( 97,516)( 98,515)( 99,514)(100,513)(101,512)(102,511)(103,510)
(104,509)(105,547)(106,559)(107,558)(108,557)(109,556)(110,555)(111,554)
(112,553)(113,552)(114,551)(115,550)(116,549)(117,548)(118,560)(119,572)
(120,571)(121,570)(122,569)(123,568)(124,567)(125,566)(126,565)(127,564)
(128,563)(129,562)(130,561)(131,521)(132,533)(133,532)(134,531)(135,530)
(136,529)(137,528)(138,527)(139,526)(140,525)(141,524)(142,523)(143,522)
(144,534)(145,546)(146,545)(147,544)(148,543)(149,542)(150,541)(151,540)
(152,539)(153,538)(154,537)(155,536)(156,535)(157,612)(158,624)(159,623)
(160,622)(161,621)(162,620)(163,619)(164,618)(165,617)(166,616)(167,615)
(168,614)(169,613)(170,599)(171,611)(172,610)(173,609)(174,608)(175,607)
(176,606)(177,605)(178,604)(179,603)(180,602)(181,601)(182,600)(183,586)
(184,598)(185,597)(186,596)(187,595)(188,594)(189,593)(190,592)(191,591)
(192,590)(193,589)(194,588)(195,587)(196,573)(197,585)(198,584)(199,583)
(200,582)(201,581)(202,580)(203,579)(204,578)(205,577)(206,576)(207,575)
(208,574)(209,625)(210,637)(211,636)(212,635)(213,634)(214,633)(215,632)
(216,631)(217,630)(218,629)(219,628)(220,627)(221,626)(222,638)(223,650)
(224,649)(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)
(232,641)(233,640)(234,639)(235,664)(236,676)(237,675)(238,674)(239,673)
(240,672)(241,671)(242,670)(243,669)(244,668)(245,667)(246,666)(247,665)
(248,651)(249,663)(250,662)(251,661)(252,660)(253,659)(254,658)(255,657)
(256,656)(257,655)(258,654)(259,653)(260,652)(261,690)(262,702)(263,701)
(264,700)(265,699)(266,698)(267,697)(268,696)(269,695)(270,694)(271,693)
(272,692)(273,691)(274,677)(275,689)(276,688)(277,687)(278,686)(279,685)
(280,684)(281,683)(282,682)(283,681)(284,680)(285,679)(286,678)(287,703)
(288,715)(289,714)(290,713)(291,712)(292,711)(293,710)(294,709)(295,708)
(296,707)(297,706)(298,705)(299,704)(300,716)(301,728)(302,727)(303,726)
(304,725)(305,724)(306,723)(307,722)(308,721)(309,720)(310,719)(311,718)
(312,717)(313,755)(314,767)(315,766)(316,765)(317,764)(318,763)(319,762)
(320,761)(321,760)(322,759)(323,758)(324,757)(325,756)(326,768)(327,780)
(328,779)(329,778)(330,777)(331,776)(332,775)(333,774)(334,773)(335,772)
(336,771)(337,770)(338,769)(339,729)(340,741)(341,740)(342,739)(343,738)
(344,737)(345,736)(346,735)(347,734)(348,733)(349,732)(350,731)(351,730)
(352,742)(353,754)(354,753)(355,752)(356,751)(357,750)(358,749)(359,748)
(360,747)(361,746)(362,745)(363,744)(364,743)(365,820)(366,832)(367,831)
(368,830)(369,829)(370,828)(371,827)(372,826)(373,825)(374,824)(375,823)
(376,822)(377,821)(378,807)(379,819)(380,818)(381,817)(382,816)(383,815)
(384,814)(385,813)(386,812)(387,811)(388,810)(389,809)(390,808)(391,794)
(392,806)(393,805)(394,804)(395,803)(396,802)(397,801)(398,800)(399,799)
(400,798)(401,797)(402,796)(403,795)(404,781)(405,793)(406,792)(407,791)
(408,790)(409,789)(410,788)(411,787)(412,786)(413,785)(414,784)(415,783)
(416,782);
s1 := Sym(832)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)
( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 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)!( 1,209)( 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);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope