Polytope of Type {8,104}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,104}*1664d
if this polytope has a name.
Group : SmallGroup(1664,3800)
Rank : 3
Schlafli Type : {8,104}
Number of vertices, edges, etc : 8, 416, 104
Order of s0s1s2 : 104
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}*832b, {8,52}*832b
4-fold quotients : {4,52}*416
8-fold quotients : {2,52}*208, {4,26}*208
13-fold quotients : {8,8}*128d
16-fold quotients : {2,26}*104
26-fold quotients : {4,8}*64b, {8,4}*64b
32-fold quotients : {2,13}*52
52-fold quotients : {4,4}*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)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)( 32,448)
( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)( 40,456)
( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)( 48,464)
( 49,465)( 50,466)( 51,467)( 52,468)( 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)( 79,508)( 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)(157,612)(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)(235,651)(236,652)(237,653)(238,654)(239,655)(240,656)
(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)(248,664)
(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)(256,672)
(257,673)(258,674)(259,675)(260,676)(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)(287,716)(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)(365,820)(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)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)
( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)( 68, 90)
( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)
( 77, 81)( 78, 80)(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)(157,170)(158,182)(159,181)(160,180)
(161,179)(162,178)(163,177)(164,176)(165,175)(166,174)(167,173)(168,172)
(169,171)(183,196)(184,208)(185,207)(186,206)(187,205)(188,204)(189,203)
(190,202)(191,201)(192,200)(193,199)(194,198)(195,197)(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)
(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)(242,293)
(243,292)(244,291)(245,290)(246,289)(247,288)(248,300)(249,312)(250,311)
(251,310)(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)
(259,302)(260,301)(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)
(443,547)(444,559)(445,558)(446,557)(447,556)(448,555)(449,554)(450,553)
(451,552)(452,551)(453,550)(454,549)(455,548)(456,560)(457,572)(458,571)
(459,570)(460,569)(461,568)(462,567)(463,566)(464,565)(465,564)(466,563)
(467,562)(468,561)(469,612)(470,624)(471,623)(472,622)(473,621)(474,620)
(475,619)(476,618)(477,617)(478,616)(479,615)(480,614)(481,613)(482,599)
(483,611)(484,610)(485,609)(486,608)(487,607)(488,606)(489,605)(490,604)
(491,603)(492,602)(493,601)(494,600)(495,586)(496,598)(497,597)(498,596)
(499,595)(500,594)(501,593)(502,592)(503,591)(504,590)(505,589)(506,588)
(507,587)(508,573)(509,585)(510,584)(511,583)(512,582)(513,581)(514,580)
(515,579)(516,578)(517,577)(518,576)(519,575)(520,574)(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)
(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)
(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)
(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)
(675,809)(676,808)(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)(703,768)(704,780)(705,779)(706,778)
(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)
(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)
(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);;
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)( 53,301)( 54,300)( 55,312)( 56,311)
( 57,310)( 58,309)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,288)( 67,287)( 68,299)( 69,298)( 70,297)( 71,296)( 72,295)
( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,275)( 80,274)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,262)( 93,261)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)(104,263)
(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)(157,392)(158,391)(159,403)(160,402)
(161,401)(162,400)(163,399)(164,398)(165,397)(166,396)(167,395)(168,394)
(169,393)(170,405)(171,404)(172,416)(173,415)(174,414)(175,413)(176,412)
(177,411)(178,410)(179,409)(180,408)(181,407)(182,406)(183,366)(184,365)
(185,377)(186,376)(187,375)(188,374)(189,373)(190,372)(191,371)(192,370)
(193,369)(194,368)(195,367)(196,379)(197,378)(198,390)(199,389)(200,388)
(201,387)(202,386)(203,385)(204,384)(205,383)(206,382)(207,381)(208,380)
(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)(469,717)(470,716)(471,728)(472,727)
(473,726)(474,725)(475,724)(476,723)(477,722)(478,721)(479,720)(480,719)
(481,718)(482,704)(483,703)(484,715)(485,714)(486,713)(487,712)(488,711)
(489,710)(490,709)(491,708)(492,707)(493,706)(494,705)(495,691)(496,690)
(497,702)(498,701)(499,700)(500,699)(501,698)(502,697)(503,696)(504,695)
(505,694)(506,693)(507,692)(508,678)(509,677)(510,689)(511,688)(512,687)
(513,686)(514,685)(515,684)(516,683)(517,682)(518,681)(519,680)(520,679)
(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)(573,808)(574,807)(575,819)(576,818)
(577,817)(578,816)(579,815)(580,814)(581,813)(582,812)(583,811)(584,810)
(585,809)(586,821)(587,820)(588,832)(589,831)(590,830)(591,829)(592,828)
(593,827)(594,826)(595,825)(596,824)(597,823)(598,822)(599,782)(600,781)
(601,793)(602,792)(603,791)(604,790)(605,789)(606,788)(607,787)(608,786)
(609,785)(610,784)(611,783)(612,795)(613,794)(614,806)(615,805)(616,804)
(617,803)(618,802)(619,801)(620,800)(621,799)(622,798)(623,797)(624,796);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*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*s0*s1*s2*s1*s2*s1*s2*s0*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)( 27,443)( 28,444)( 29,445)( 30,446)( 31,447)
( 32,448)( 33,449)( 34,450)( 35,451)( 36,452)( 37,453)( 38,454)( 39,455)
( 40,456)( 41,457)( 42,458)( 43,459)( 44,460)( 45,461)( 46,462)( 47,463)
( 48,464)( 49,465)( 50,466)( 51,467)( 52,468)( 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)( 79,508)
( 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)(157,612)(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)(235,651)(236,652)(237,653)(238,654)(239,655)
(240,656)(241,657)(242,658)(243,659)(244,660)(245,661)(246,662)(247,663)
(248,664)(249,665)(250,666)(251,667)(252,668)(253,669)(254,670)(255,671)
(256,672)(257,673)(258,674)(259,675)(260,676)(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)(287,716)
(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)(365,820)(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)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)
( 60, 98)( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)
( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)
( 76, 82)( 77, 81)( 78, 80)(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)(157,170)(158,182)(159,181)
(160,180)(161,179)(162,178)(163,177)(164,176)(165,175)(166,174)(167,173)
(168,172)(169,171)(183,196)(184,208)(185,207)(186,206)(187,205)(188,204)
(189,203)(190,202)(191,201)(192,200)(193,199)(194,198)(195,197)(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)(235,287)(236,299)(237,298)(238,297)(239,296)(240,295)(241,294)
(242,293)(243,292)(244,291)(245,290)(246,289)(247,288)(248,300)(249,312)
(250,311)(251,310)(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)
(258,303)(259,302)(260,301)(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)(443,547)(444,559)(445,558)(446,557)(447,556)(448,555)(449,554)
(450,553)(451,552)(452,551)(453,550)(454,549)(455,548)(456,560)(457,572)
(458,571)(459,570)(460,569)(461,568)(462,567)(463,566)(464,565)(465,564)
(466,563)(467,562)(468,561)(469,612)(470,624)(471,623)(472,622)(473,621)
(474,620)(475,619)(476,618)(477,617)(478,616)(479,615)(480,614)(481,613)
(482,599)(483,611)(484,610)(485,609)(486,608)(487,607)(488,606)(489,605)
(490,604)(491,603)(492,602)(493,601)(494,600)(495,586)(496,598)(497,597)
(498,596)(499,595)(500,594)(501,593)(502,592)(503,591)(504,590)(505,589)
(506,588)(507,587)(508,573)(509,585)(510,584)(511,583)(512,582)(513,581)
(514,580)(515,579)(516,578)(517,577)(518,576)(519,575)(520,574)(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)(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)
(658,826)(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)
(666,818)(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)
(674,810)(675,809)(676,808)(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)(703,768)(704,780)(705,779)
(706,778)(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)
(714,770)(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)
(722,762)(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);
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)( 53,301)( 54,300)( 55,312)
( 56,311)( 57,310)( 58,309)( 59,308)( 60,307)( 61,306)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,288)( 67,287)( 68,299)( 69,298)( 70,297)( 71,296)
( 72,295)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,275)
( 80,274)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,262)( 93,261)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,268)(100,267)(101,266)(102,265)(103,264)
(104,263)(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)(157,392)(158,391)(159,403)
(160,402)(161,401)(162,400)(163,399)(164,398)(165,397)(166,396)(167,395)
(168,394)(169,393)(170,405)(171,404)(172,416)(173,415)(174,414)(175,413)
(176,412)(177,411)(178,410)(179,409)(180,408)(181,407)(182,406)(183,366)
(184,365)(185,377)(186,376)(187,375)(188,374)(189,373)(190,372)(191,371)
(192,370)(193,369)(194,368)(195,367)(196,379)(197,378)(198,390)(199,389)
(200,388)(201,387)(202,386)(203,385)(204,384)(205,383)(206,382)(207,381)
(208,380)(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)(469,717)(470,716)(471,728)
(472,727)(473,726)(474,725)(475,724)(476,723)(477,722)(478,721)(479,720)
(480,719)(481,718)(482,704)(483,703)(484,715)(485,714)(486,713)(487,712)
(488,711)(489,710)(490,709)(491,708)(492,707)(493,706)(494,705)(495,691)
(496,690)(497,702)(498,701)(499,700)(500,699)(501,698)(502,697)(503,696)
(504,695)(505,694)(506,693)(507,692)(508,678)(509,677)(510,689)(511,688)
(512,687)(513,686)(514,685)(515,684)(516,683)(517,682)(518,681)(519,680)
(520,679)(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)(573,808)(574,807)(575,819)
(576,818)(577,817)(578,816)(579,815)(580,814)(581,813)(582,812)(583,811)
(584,810)(585,809)(586,821)(587,820)(588,832)(589,831)(590,830)(591,829)
(592,828)(593,827)(594,826)(595,825)(596,824)(597,823)(598,822)(599,782)
(600,781)(601,793)(602,792)(603,791)(604,790)(605,789)(606,788)(607,787)
(608,786)(609,785)(610,784)(611,783)(612,795)(613,794)(614,806)(615,805)
(616,804)(617,803)(618,802)(619,801)(620,800)(621,799)(622,798)(623,797)
(624,796);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*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*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope