Overview
- Group
- SmallGroup(1728,31412)
- Rank
- 3
- Schläfli Type
- {6,16}
- Vertices, edges, …
- 54, 432, 144
- Order of s0s1s2
- 48
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
24-fold
27-fold
36-fold
54-fold
72-fold
108-fold
144-fold
216-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 3
48 facets
- 48 of {6}*12
18 vertex figures
- 18 of {16}*32
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 3
48 facets
- 48 of {6}*12
18 vertex figures
- 18 of {16}*32
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 9
24 facets
6 vertex figures
- 6 of {16}*32
Representations
Permutation Representation (GAP)
s0 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)(105,422)(106,418)(107,420)(108,419)(109,298)(110,300)(111,299)(112,304)(113,306)(114,305)(115,301)(116,303)(117,302)(118,316)(119,318)(120,317)(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,307)(128,309)(129,308)(130,313)(131,315)(132,314)(133,310)(134,312)(135,311)(136,271)(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)(144,275)(145,289)(146,291)(147,290)(148,295)(149,297)(150,296)(151,292)(152,294)(153,293)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)(160,283)(161,285)(162,284)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)(169,220)(170,222)(171,221)(172,235)(173,237)(174,236)(175,241)(176,243)(177,242)(178,238)(179,240)(180,239)(181,226)(182,228)(183,227)(184,232)(185,234)(186,233)(187,229)(188,231)(189,230)(190,244)(191,246)(192,245)(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,262)(200,264)(201,263)(202,268)(203,270)(204,269)(205,265)(206,267)(207,266)(208,253)(209,255)(210,254)(211,259)(212,261)(213,260)(214,256)(215,258)(216,257)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)(537,854)(538,850)(539,852)(540,851)(541,730)(542,732)(543,731)(544,736)(545,738)(546,737)(547,733)(548,735)(549,734)(550,748)(551,750)(552,749)(553,754)(554,756)(555,755)(556,751)(557,753)(558,752)(559,739)(560,741)(561,740)(562,745)(563,747)(564,746)(565,742)(566,744)(567,743)(568,703)(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)(576,707)(577,721)(578,723)(579,722)(580,727)(581,729)(582,728)(583,724)(584,726)(585,725)(586,712)(587,714)(588,713)(589,718)(590,720)(591,719)(592,715)(593,717)(594,716)(595,649)(596,651)(597,650)(598,655)(599,657)(600,656)(601,652)(602,654)(603,653)(604,667)(605,669)(606,668)(607,673)(608,675)(609,674)(610,670)(611,672)(612,671)(613,658)(614,660)(615,659)(616,664)(617,666)(618,665)(619,661)(620,663)(621,662)(622,676)(623,678)(624,677)(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,694)(632,696)(633,695)(634,700)(635,702)(636,701)(637,697)(638,699)(639,698)(640,685)(641,687)(642,686)(643,691)(644,693)(645,692)(646,688)(647,690)(648,689);; s1 := ( 1,229)( 2,227)( 3,234)( 4,226)( 5,233)( 6,231)( 7,232)( 8,230)( 9,228)( 10,220)( 11,218)( 12,225)( 13,217)( 14,224)( 15,222)( 16,223)( 17,221)( 18,219)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)( 24,240)( 25,241)( 26,239)( 27,237)( 28,256)( 29,254)( 30,261)( 31,253)( 32,260)( 33,258)( 34,259)( 35,257)( 36,255)( 37,247)( 38,245)( 39,252)( 40,244)( 41,251)( 42,249)( 43,250)( 44,248)( 45,246)( 46,265)( 47,263)( 48,270)( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,310)( 56,308)( 57,315)( 58,307)( 59,314)( 60,312)( 61,313)( 62,311)( 63,309)( 64,301)( 65,299)( 66,306)( 67,298)( 68,305)( 69,303)( 70,304)( 71,302)( 72,300)( 73,319)( 74,317)( 75,324)( 76,316)( 77,323)( 78,321)( 79,322)( 80,320)( 81,318)( 82,283)( 83,281)( 84,288)( 85,280)( 86,287)( 87,285)( 88,286)( 89,284)( 90,282)( 91,274)( 92,272)( 93,279)( 94,271)( 95,278)( 96,276)( 97,277)( 98,275)( 99,273)(100,292)(101,290)(102,297)(103,289)(104,296)(105,294)(106,295)(107,293)(108,291)(109,391)(110,389)(111,396)(112,388)(113,395)(114,393)(115,394)(116,392)(117,390)(118,382)(119,380)(120,387)(121,379)(122,386)(123,384)(124,385)(125,383)(126,381)(127,400)(128,398)(129,405)(130,397)(131,404)(132,402)(133,403)(134,401)(135,399)(136,418)(137,416)(138,423)(139,415)(140,422)(141,420)(142,421)(143,419)(144,417)(145,409)(146,407)(147,414)(148,406)(149,413)(150,411)(151,412)(152,410)(153,408)(154,427)(155,425)(156,432)(157,424)(158,431)(159,429)(160,430)(161,428)(162,426)(163,337)(164,335)(165,342)(166,334)(167,341)(168,339)(169,340)(170,338)(171,336)(172,328)(173,326)(174,333)(175,325)(176,332)(177,330)(178,331)(179,329)(180,327)(181,346)(182,344)(183,351)(184,343)(185,350)(186,348)(187,349)(188,347)(189,345)(190,364)(191,362)(192,369)(193,361)(194,368)(195,366)(196,367)(197,365)(198,363)(199,355)(200,353)(201,360)(202,352)(203,359)(204,357)(205,358)(206,356)(207,354)(208,373)(209,371)(210,378)(211,370)(212,377)(213,375)(214,376)(215,374)(216,372)(433,769)(434,767)(435,774)(436,766)(437,773)(438,771)(439,772)(440,770)(441,768)(442,760)(443,758)(444,765)(445,757)(446,764)(447,762)(448,763)(449,761)(450,759)(451,778)(452,776)(453,783)(454,775)(455,782)(456,780)(457,781)(458,779)(459,777)(460,796)(461,794)(462,801)(463,793)(464,800)(465,798)(466,799)(467,797)(468,795)(469,787)(470,785)(471,792)(472,784)(473,791)(474,789)(475,790)(476,788)(477,786)(478,805)(479,803)(480,810)(481,802)(482,809)(483,807)(484,808)(485,806)(486,804)(487,850)(488,848)(489,855)(490,847)(491,854)(492,852)(493,853)(494,851)(495,849)(496,841)(497,839)(498,846)(499,838)(500,845)(501,843)(502,844)(503,842)(504,840)(505,859)(506,857)(507,864)(508,856)(509,863)(510,861)(511,862)(512,860)(513,858)(514,823)(515,821)(516,828)(517,820)(518,827)(519,825)(520,826)(521,824)(522,822)(523,814)(524,812)(525,819)(526,811)(527,818)(528,816)(529,817)(530,815)(531,813)(532,832)(533,830)(534,837)(535,829)(536,836)(537,834)(538,835)(539,833)(540,831)(541,661)(542,659)(543,666)(544,658)(545,665)(546,663)(547,664)(548,662)(549,660)(550,652)(551,650)(552,657)(553,649)(554,656)(555,654)(556,655)(557,653)(558,651)(559,670)(560,668)(561,675)(562,667)(563,674)(564,672)(565,673)(566,671)(567,669)(568,688)(569,686)(570,693)(571,685)(572,692)(573,690)(574,691)(575,689)(576,687)(577,679)(578,677)(579,684)(580,676)(581,683)(582,681)(583,682)(584,680)(585,678)(586,697)(587,695)(588,702)(589,694)(590,701)(591,699)(592,700)(593,698)(594,696)(595,742)(596,740)(597,747)(598,739)(599,746)(600,744)(601,745)(602,743)(603,741)(604,733)(605,731)(606,738)(607,730)(608,737)(609,735)(610,736)(611,734)(612,732)(613,751)(614,749)(615,756)(616,748)(617,755)(618,753)(619,754)(620,752)(621,750)(622,715)(623,713)(624,720)(625,712)(626,719)(627,717)(628,718)(629,716)(630,714)(631,706)(632,704)(633,711)(634,703)(635,710)(636,708)(637,709)(638,707)(639,705)(640,724)(641,722)(642,729)(643,721)(644,728)(645,726)(646,727)(647,725)(648,723);; s2 := ( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)( 32,466)( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)( 40,477)( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)( 56,515)( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)( 64,523)( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)( 72,526)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)( 88,491)( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)( 96,503)( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)(104,511)(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)(112,603)(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)(120,606)(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,622)(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)(144,625)(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)(152,636)(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)(168,548)(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)(176,556)(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)(192,570)(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)(200,578)(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)(224,735)(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)(232,743)(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)(248,709)(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)(256,720)(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)(272,677)(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)(280,685)(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)(288,688)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)(304,653)(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)(312,665)(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)(320,673)(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)(328,765)(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)(336,768)(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,784)(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)(360,787)(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)(368,798)(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)(384,845)(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)(392,853)(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)(408,813)(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)(416,821)(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832);; 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*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)(105,422)(106,418)(107,420)(108,419)(109,298)(110,300)(111,299)(112,304)(113,306)(114,305)(115,301)(116,303)(117,302)(118,316)(119,318)(120,317)(121,322)(122,324)(123,323)(124,319)(125,321)(126,320)(127,307)(128,309)(129,308)(130,313)(131,315)(132,314)(133,310)(134,312)(135,311)(136,271)(137,273)(138,272)(139,277)(140,279)(141,278)(142,274)(143,276)(144,275)(145,289)(146,291)(147,290)(148,295)(149,297)(150,296)(151,292)(152,294)(153,293)(154,280)(155,282)(156,281)(157,286)(158,288)(159,287)(160,283)(161,285)(162,284)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)(169,220)(170,222)(171,221)(172,235)(173,237)(174,236)(175,241)(176,243)(177,242)(178,238)(179,240)(180,239)(181,226)(182,228)(183,227)(184,232)(185,234)(186,233)(187,229)(188,231)(189,230)(190,244)(191,246)(192,245)(193,250)(194,252)(195,251)(196,247)(197,249)(198,248)(199,262)(200,264)(201,263)(202,268)(203,270)(204,269)(205,265)(206,267)(207,266)(208,253)(209,255)(210,254)(211,259)(212,261)(213,260)(214,256)(215,258)(216,257)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)(537,854)(538,850)(539,852)(540,851)(541,730)(542,732)(543,731)(544,736)(545,738)(546,737)(547,733)(548,735)(549,734)(550,748)(551,750)(552,749)(553,754)(554,756)(555,755)(556,751)(557,753)(558,752)(559,739)(560,741)(561,740)(562,745)(563,747)(564,746)(565,742)(566,744)(567,743)(568,703)(569,705)(570,704)(571,709)(572,711)(573,710)(574,706)(575,708)(576,707)(577,721)(578,723)(579,722)(580,727)(581,729)(582,728)(583,724)(584,726)(585,725)(586,712)(587,714)(588,713)(589,718)(590,720)(591,719)(592,715)(593,717)(594,716)(595,649)(596,651)(597,650)(598,655)(599,657)(600,656)(601,652)(602,654)(603,653)(604,667)(605,669)(606,668)(607,673)(608,675)(609,674)(610,670)(611,672)(612,671)(613,658)(614,660)(615,659)(616,664)(617,666)(618,665)(619,661)(620,663)(621,662)(622,676)(623,678)(624,677)(625,682)(626,684)(627,683)(628,679)(629,681)(630,680)(631,694)(632,696)(633,695)(634,700)(635,702)(636,701)(637,697)(638,699)(639,698)(640,685)(641,687)(642,686)(643,691)(644,693)(645,692)(646,688)(647,690)(648,689); s1 := Sym(864)!( 1,229)( 2,227)( 3,234)( 4,226)( 5,233)( 6,231)( 7,232)( 8,230)( 9,228)( 10,220)( 11,218)( 12,225)( 13,217)( 14,224)( 15,222)( 16,223)( 17,221)( 18,219)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)( 24,240)( 25,241)( 26,239)( 27,237)( 28,256)( 29,254)( 30,261)( 31,253)( 32,260)( 33,258)( 34,259)( 35,257)( 36,255)( 37,247)( 38,245)( 39,252)( 40,244)( 41,251)( 42,249)( 43,250)( 44,248)( 45,246)( 46,265)( 47,263)( 48,270)( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,310)( 56,308)( 57,315)( 58,307)( 59,314)( 60,312)( 61,313)( 62,311)( 63,309)( 64,301)( 65,299)( 66,306)( 67,298)( 68,305)( 69,303)( 70,304)( 71,302)( 72,300)( 73,319)( 74,317)( 75,324)( 76,316)( 77,323)( 78,321)( 79,322)( 80,320)( 81,318)( 82,283)( 83,281)( 84,288)( 85,280)( 86,287)( 87,285)( 88,286)( 89,284)( 90,282)( 91,274)( 92,272)( 93,279)( 94,271)( 95,278)( 96,276)( 97,277)( 98,275)( 99,273)(100,292)(101,290)(102,297)(103,289)(104,296)(105,294)(106,295)(107,293)(108,291)(109,391)(110,389)(111,396)(112,388)(113,395)(114,393)(115,394)(116,392)(117,390)(118,382)(119,380)(120,387)(121,379)(122,386)(123,384)(124,385)(125,383)(126,381)(127,400)(128,398)(129,405)(130,397)(131,404)(132,402)(133,403)(134,401)(135,399)(136,418)(137,416)(138,423)(139,415)(140,422)(141,420)(142,421)(143,419)(144,417)(145,409)(146,407)(147,414)(148,406)(149,413)(150,411)(151,412)(152,410)(153,408)(154,427)(155,425)(156,432)(157,424)(158,431)(159,429)(160,430)(161,428)(162,426)(163,337)(164,335)(165,342)(166,334)(167,341)(168,339)(169,340)(170,338)(171,336)(172,328)(173,326)(174,333)(175,325)(176,332)(177,330)(178,331)(179,329)(180,327)(181,346)(182,344)(183,351)(184,343)(185,350)(186,348)(187,349)(188,347)(189,345)(190,364)(191,362)(192,369)(193,361)(194,368)(195,366)(196,367)(197,365)(198,363)(199,355)(200,353)(201,360)(202,352)(203,359)(204,357)(205,358)(206,356)(207,354)(208,373)(209,371)(210,378)(211,370)(212,377)(213,375)(214,376)(215,374)(216,372)(433,769)(434,767)(435,774)(436,766)(437,773)(438,771)(439,772)(440,770)(441,768)(442,760)(443,758)(444,765)(445,757)(446,764)(447,762)(448,763)(449,761)(450,759)(451,778)(452,776)(453,783)(454,775)(455,782)(456,780)(457,781)(458,779)(459,777)(460,796)(461,794)(462,801)(463,793)(464,800)(465,798)(466,799)(467,797)(468,795)(469,787)(470,785)(471,792)(472,784)(473,791)(474,789)(475,790)(476,788)(477,786)(478,805)(479,803)(480,810)(481,802)(482,809)(483,807)(484,808)(485,806)(486,804)(487,850)(488,848)(489,855)(490,847)(491,854)(492,852)(493,853)(494,851)(495,849)(496,841)(497,839)(498,846)(499,838)(500,845)(501,843)(502,844)(503,842)(504,840)(505,859)(506,857)(507,864)(508,856)(509,863)(510,861)(511,862)(512,860)(513,858)(514,823)(515,821)(516,828)(517,820)(518,827)(519,825)(520,826)(521,824)(522,822)(523,814)(524,812)(525,819)(526,811)(527,818)(528,816)(529,817)(530,815)(531,813)(532,832)(533,830)(534,837)(535,829)(536,836)(537,834)(538,835)(539,833)(540,831)(541,661)(542,659)(543,666)(544,658)(545,665)(546,663)(547,664)(548,662)(549,660)(550,652)(551,650)(552,657)(553,649)(554,656)(555,654)(556,655)(557,653)(558,651)(559,670)(560,668)(561,675)(562,667)(563,674)(564,672)(565,673)(566,671)(567,669)(568,688)(569,686)(570,693)(571,685)(572,692)(573,690)(574,691)(575,689)(576,687)(577,679)(578,677)(579,684)(580,676)(581,683)(582,681)(583,682)(584,680)(585,678)(586,697)(587,695)(588,702)(589,694)(590,701)(591,699)(592,700)(593,698)(594,696)(595,742)(596,740)(597,747)(598,739)(599,746)(600,744)(601,745)(602,743)(603,741)(604,733)(605,731)(606,738)(607,730)(608,737)(609,735)(610,736)(611,734)(612,732)(613,751)(614,749)(615,756)(616,748)(617,755)(618,753)(619,754)(620,752)(621,750)(622,715)(623,713)(624,720)(625,712)(626,719)(627,717)(628,718)(629,716)(630,714)(631,706)(632,704)(633,711)(634,703)(635,710)(636,708)(637,709)(638,707)(639,705)(640,724)(641,722)(642,729)(643,721)(644,728)(645,726)(646,727)(647,725)(648,723); s2 := Sym(864)!( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)( 32,466)( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)( 40,477)( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,514)( 56,515)( 57,516)( 58,522)( 59,520)( 60,521)( 61,518)( 62,519)( 63,517)( 64,523)( 65,524)( 66,525)( 67,531)( 68,529)( 69,530)( 70,527)( 71,528)( 72,526)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)( 81,535)( 82,487)( 83,488)( 84,489)( 85,495)( 86,493)( 87,494)( 88,491)( 89,492)( 90,490)( 91,496)( 92,497)( 93,498)( 94,504)( 95,502)( 96,503)( 97,500)( 98,501)( 99,499)(100,505)(101,506)(102,507)(103,513)(104,511)(105,512)(106,509)(107,510)(108,508)(109,595)(110,596)(111,597)(112,603)(113,601)(114,602)(115,599)(116,600)(117,598)(118,604)(119,605)(120,606)(121,612)(122,610)(123,611)(124,608)(125,609)(126,607)(127,613)(128,614)(129,615)(130,621)(131,619)(132,620)(133,617)(134,618)(135,616)(136,622)(137,623)(138,624)(139,630)(140,628)(141,629)(142,626)(143,627)(144,625)(145,631)(146,632)(147,633)(148,639)(149,637)(150,638)(151,635)(152,636)(153,634)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)(161,645)(162,643)(163,541)(164,542)(165,543)(166,549)(167,547)(168,548)(169,545)(170,546)(171,544)(172,550)(173,551)(174,552)(175,558)(176,556)(177,557)(178,554)(179,555)(180,553)(181,559)(182,560)(183,561)(184,567)(185,565)(186,566)(187,563)(188,564)(189,562)(190,568)(191,569)(192,570)(193,576)(194,574)(195,575)(196,572)(197,573)(198,571)(199,577)(200,578)(201,579)(202,585)(203,583)(204,584)(205,581)(206,582)(207,580)(208,586)(209,587)(210,588)(211,594)(212,592)(213,593)(214,590)(215,591)(216,589)(217,730)(218,731)(219,732)(220,738)(221,736)(222,737)(223,734)(224,735)(225,733)(226,739)(227,740)(228,741)(229,747)(230,745)(231,746)(232,743)(233,744)(234,742)(235,748)(236,749)(237,750)(238,756)(239,754)(240,755)(241,752)(242,753)(243,751)(244,703)(245,704)(246,705)(247,711)(248,709)(249,710)(250,707)(251,708)(252,706)(253,712)(254,713)(255,714)(256,720)(257,718)(258,719)(259,716)(260,717)(261,715)(262,721)(263,722)(264,723)(265,729)(266,727)(267,728)(268,725)(269,726)(270,724)(271,676)(272,677)(273,678)(274,684)(275,682)(276,683)(277,680)(278,681)(279,679)(280,685)(281,686)(282,687)(283,693)(284,691)(285,692)(286,689)(287,690)(288,688)(289,694)(290,695)(291,696)(292,702)(293,700)(294,701)(295,698)(296,699)(297,697)(298,649)(299,650)(300,651)(301,657)(302,655)(303,656)(304,653)(305,654)(306,652)(307,658)(308,659)(309,660)(310,666)(311,664)(312,665)(313,662)(314,663)(315,661)(316,667)(317,668)(318,669)(319,675)(320,673)(321,674)(322,671)(323,672)(324,670)(325,757)(326,758)(327,759)(328,765)(329,763)(330,764)(331,761)(332,762)(333,760)(334,766)(335,767)(336,768)(337,774)(338,772)(339,773)(340,770)(341,771)(342,769)(343,775)(344,776)(345,777)(346,783)(347,781)(348,782)(349,779)(350,780)(351,778)(352,784)(353,785)(354,786)(355,792)(356,790)(357,791)(358,788)(359,789)(360,787)(361,793)(362,794)(363,795)(364,801)(365,799)(366,800)(367,797)(368,798)(369,796)(370,802)(371,803)(372,804)(373,810)(374,808)(375,809)(376,806)(377,807)(378,805)(379,838)(380,839)(381,840)(382,846)(383,844)(384,845)(385,842)(386,843)(387,841)(388,847)(389,848)(390,849)(391,855)(392,853)(393,854)(394,851)(395,852)(396,850)(397,856)(398,857)(399,858)(400,864)(401,862)(402,863)(403,860)(404,861)(405,859)(406,811)(407,812)(408,813)(409,819)(410,817)(411,818)(412,815)(413,816)(414,814)(415,820)(416,821)(417,822)(418,828)(419,826)(420,827)(421,824)(422,825)(423,823)(424,829)(425,830)(426,831)(427,837)(428,835)(429,836)(430,833)(431,834)(432,832); poly := sub<Sym(864)|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*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*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 >;
References
None.
to this polytope.