Polytope of Type {4,104}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,104}*1664a
if this polytope has a name.
Group : SmallGroup(1664,3430)
Rank : 3
Schlafli Type : {4,104}
Number of vertices, edges, etc : 8, 416, 208
Order of s0s1s2 : 104
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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, {4,52}*832, {4,104}*832b
4-fold quotients : {4,52}*416, {2,104}*416
8-fold quotients : {2,52}*208, {4,26}*208
13-fold quotients : {4,8}*128a
16-fold quotients : {2,26}*104
26-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
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)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(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)(235,287)(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)
(469,573)(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)(495,599)(496,611)(497,610)(498,609)(499,608)(500,607)
(501,606)(502,605)(503,604)(504,603)(505,602)(506,601)(507,600)(508,612)
(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)(515,618)(516,617)
(517,616)(518,615)(519,614)(520,613)(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 := ( 1,418)( 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)( 27,444)( 28,443)( 29,455)( 30,454)( 31,453)( 32,452)
( 33,451)( 34,450)( 35,449)( 36,448)( 37,447)( 38,446)( 39,445)( 40,457)
( 41,456)( 42,468)( 43,467)( 44,466)( 45,465)( 46,464)( 47,463)( 48,462)
( 49,461)( 50,460)( 51,459)( 52,458)( 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)( 79,509)( 80,508)
( 81,520)( 82,519)( 83,518)( 84,517)( 85,516)( 86,515)( 87,514)( 88,513)
( 89,512)( 90,511)( 91,510)( 92,496)( 93,495)( 94,507)( 95,506)( 96,505)
( 97,504)( 98,503)( 99,502)(100,501)(101,500)(102,499)(103,498)(104,497)
(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)(235,652)(236,651)(237,663)(238,662)(239,661)(240,660)
(241,659)(242,658)(243,657)(244,656)(245,655)(246,654)(247,653)(248,665)
(249,664)(250,676)(251,675)(252,674)(253,673)(254,672)(255,671)(256,670)
(257,669)(258,668)(259,667)(260,666)(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)(287,717)(288,716)
(289,728)(290,727)(291,726)(292,725)(293,724)(294,723)(295,722)(296,721)
(297,720)(298,719)(299,718)(300,704)(301,703)(302,715)(303,714)(304,713)
(305,712)(306,711)(307,710)(308,709)(309,708)(310,707)(311,706)(312,705)
(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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 1,209)( 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)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 80, 91)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
( 98, 99)(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)(235,287)
(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)(469,573)(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)(495,599)(496,611)(497,610)(498,609)(499,608)
(500,607)(501,606)(502,605)(503,604)(504,603)(505,602)(506,601)(507,600)
(508,612)(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)(515,618)
(516,617)(517,616)(518,615)(519,614)(520,613)(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)!( 1,418)( 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)( 27,444)( 28,443)( 29,455)( 30,454)( 31,453)
( 32,452)( 33,451)( 34,450)( 35,449)( 36,448)( 37,447)( 38,446)( 39,445)
( 40,457)( 41,456)( 42,468)( 43,467)( 44,466)( 45,465)( 46,464)( 47,463)
( 48,462)( 49,461)( 50,460)( 51,459)( 52,458)( 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)( 79,509)
( 80,508)( 81,520)( 82,519)( 83,518)( 84,517)( 85,516)( 86,515)( 87,514)
( 88,513)( 89,512)( 90,511)( 91,510)( 92,496)( 93,495)( 94,507)( 95,506)
( 96,505)( 97,504)( 98,503)( 99,502)(100,501)(101,500)(102,499)(103,498)
(104,497)(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)(235,652)(236,651)(237,663)(238,662)(239,661)
(240,660)(241,659)(242,658)(243,657)(244,656)(245,655)(246,654)(247,653)
(248,665)(249,664)(250,676)(251,675)(252,674)(253,673)(254,672)(255,671)
(256,670)(257,669)(258,668)(259,667)(260,666)(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)(287,717)
(288,716)(289,728)(290,727)(291,726)(292,725)(293,724)(294,723)(295,722)
(296,721)(297,720)(298,719)(299,718)(300,704)(301,703)(302,715)(303,714)
(304,713)(305,712)(306,711)(307,710)(308,709)(309,708)(310,707)(311,706)
(312,705)(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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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