Overview
- Group
- SmallGroup(1728,12518)
- Rank
- 3
- Schläfli Type
- {16,6}
- Vertices, edges, …
- 144, 432, 54
- 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
8-fold
12-fold
24-fold
27-fold
54-fold
108-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.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(109,163)(110,165)(111,164)(112,184)(113,186)(114,185)(115,180)(116,179)(117,178)(118,181)(119,183)(120,182)(121,175)(122,177)(123,176)(124,171)(125,170)(126,169)(127,172)(128,174)(129,173)(130,166)(131,168)(132,167)(133,189)(134,188)(135,187)(136,190)(137,192)(138,191)(139,211)(140,213)(141,212)(142,207)(143,206)(144,205)(145,208)(146,210)(147,209)(148,202)(149,204)(150,203)(151,198)(152,197)(153,196)(154,199)(155,201)(156,200)(157,193)(158,195)(159,194)(160,216)(161,215)(162,214)(217,298)(218,300)(219,299)(220,319)(221,321)(222,320)(223,315)(224,314)(225,313)(226,316)(227,318)(228,317)(229,310)(230,312)(231,311)(232,306)(233,305)(234,304)(235,307)(236,309)(237,308)(238,301)(239,303)(240,302)(241,324)(242,323)(243,322)(244,271)(245,273)(246,272)(247,292)(248,294)(249,293)(250,288)(251,287)(252,286)(253,289)(254,291)(255,290)(256,283)(257,285)(258,284)(259,279)(260,278)(261,277)(262,280)(263,282)(264,281)(265,274)(266,276)(267,275)(268,297)(269,296)(270,295)(326,327)(328,346)(329,348)(330,347)(331,342)(332,341)(333,340)(334,343)(335,345)(336,344)(338,339)(349,351)(353,354)(355,373)(356,375)(357,374)(358,369)(359,368)(360,367)(361,370)(362,372)(363,371)(365,366)(376,378)(379,406)(380,408)(381,407)(382,427)(383,429)(384,428)(385,423)(386,422)(387,421)(388,424)(389,426)(390,425)(391,418)(392,420)(393,419)(394,414)(395,413)(396,412)(397,415)(398,417)(399,416)(400,409)(401,411)(402,410)(403,432)(404,431)(405,430)(433,541)(434,543)(435,542)(436,562)(437,564)(438,563)(439,558)(440,557)(441,556)(442,559)(443,561)(444,560)(445,553)(446,555)(447,554)(448,549)(449,548)(450,547)(451,550)(452,552)(453,551)(454,544)(455,546)(456,545)(457,567)(458,566)(459,565)(460,568)(461,570)(462,569)(463,589)(464,591)(465,590)(466,585)(467,584)(468,583)(469,586)(470,588)(471,587)(472,580)(473,582)(474,581)(475,576)(476,575)(477,574)(478,577)(479,579)(480,578)(481,571)(482,573)(483,572)(484,594)(485,593)(486,592)(487,622)(488,624)(489,623)(490,643)(491,645)(492,644)(493,639)(494,638)(495,637)(496,640)(497,642)(498,641)(499,634)(500,636)(501,635)(502,630)(503,629)(504,628)(505,631)(506,633)(507,632)(508,625)(509,627)(510,626)(511,648)(512,647)(513,646)(514,595)(515,597)(516,596)(517,616)(518,618)(519,617)(520,612)(521,611)(522,610)(523,613)(524,615)(525,614)(526,607)(527,609)(528,608)(529,603)(530,602)(531,601)(532,604)(533,606)(534,605)(535,598)(536,600)(537,599)(538,621)(539,620)(540,619)(649,838)(650,840)(651,839)(652,859)(653,861)(654,860)(655,855)(656,854)(657,853)(658,856)(659,858)(660,857)(661,850)(662,852)(663,851)(664,846)(665,845)(666,844)(667,847)(668,849)(669,848)(670,841)(671,843)(672,842)(673,864)(674,863)(675,862)(676,811)(677,813)(678,812)(679,832)(680,834)(681,833)(682,828)(683,827)(684,826)(685,829)(686,831)(687,830)(688,823)(689,825)(690,824)(691,819)(692,818)(693,817)(694,820)(695,822)(696,821)(697,814)(698,816)(699,815)(700,837)(701,836)(702,835)(703,784)(704,786)(705,785)(706,805)(707,807)(708,806)(709,801)(710,800)(711,799)(712,802)(713,804)(714,803)(715,796)(716,798)(717,797)(718,792)(719,791)(720,790)(721,793)(722,795)(723,794)(724,787)(725,789)(726,788)(727,810)(728,809)(729,808)(730,757)(731,759)(732,758)(733,778)(734,780)(735,779)(736,774)(737,773)(738,772)(739,775)(740,777)(741,776)(742,769)(743,771)(744,770)(745,765)(746,764)(747,763)(748,766)(749,768)(750,767)(751,760)(752,762)(753,761)(754,783)(755,782)(756,781);; s1 := ( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)( 8,440)( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)( 16,456)( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)( 24,448)( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)( 32,463)( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)( 40,479)( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)( 48,474)( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,514)( 56,516)( 57,515)( 58,518)( 59,517)( 60,519)( 61,522)( 62,521)( 63,520)( 64,538)( 65,540)( 66,539)( 67,533)( 68,532)( 69,534)( 70,537)( 71,536)( 72,535)( 73,527)( 74,526)( 75,528)( 76,531)( 77,530)( 78,529)( 79,523)( 80,525)( 81,524)( 82,487)( 83,489)( 84,488)( 85,491)( 86,490)( 87,492)( 88,495)( 89,494)( 90,493)( 91,511)( 92,513)( 93,512)( 94,506)( 95,505)( 96,507)( 97,510)( 98,509)( 99,508)(100,500)(101,499)(102,501)(103,504)(104,503)(105,502)(106,496)(107,498)(108,497)(109,595)(110,597)(111,596)(112,599)(113,598)(114,600)(115,603)(116,602)(117,601)(118,619)(119,621)(120,620)(121,614)(122,613)(123,615)(124,618)(125,617)(126,616)(127,608)(128,607)(129,609)(130,612)(131,611)(132,610)(133,604)(134,606)(135,605)(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)(145,646)(146,648)(147,647)(148,641)(149,640)(150,642)(151,645)(152,644)(153,643)(154,635)(155,634)(156,636)(157,639)(158,638)(159,637)(160,631)(161,633)(162,632)(163,541)(164,543)(165,542)(166,545)(167,544)(168,546)(169,549)(170,548)(171,547)(172,565)(173,567)(174,566)(175,560)(176,559)(177,561)(178,564)(179,563)(180,562)(181,554)(182,553)(183,555)(184,558)(185,557)(186,556)(187,550)(188,552)(189,551)(190,568)(191,570)(192,569)(193,572)(194,571)(195,573)(196,576)(197,575)(198,574)(199,592)(200,594)(201,593)(202,587)(203,586)(204,588)(205,591)(206,590)(207,589)(208,581)(209,580)(210,582)(211,585)(212,584)(213,583)(214,577)(215,579)(216,578)(217,730)(218,732)(219,731)(220,734)(221,733)(222,735)(223,738)(224,737)(225,736)(226,754)(227,756)(228,755)(229,749)(230,748)(231,750)(232,753)(233,752)(234,751)(235,743)(236,742)(237,744)(238,747)(239,746)(240,745)(241,739)(242,741)(243,740)(244,703)(245,705)(246,704)(247,707)(248,706)(249,708)(250,711)(251,710)(252,709)(253,727)(254,729)(255,728)(256,722)(257,721)(258,723)(259,726)(260,725)(261,724)(262,716)(263,715)(264,717)(265,720)(266,719)(267,718)(268,712)(269,714)(270,713)(271,676)(272,678)(273,677)(274,680)(275,679)(276,681)(277,684)(278,683)(279,682)(280,700)(281,702)(282,701)(283,695)(284,694)(285,696)(286,699)(287,698)(288,697)(289,689)(290,688)(291,690)(292,693)(293,692)(294,691)(295,685)(296,687)(297,686)(298,649)(299,651)(300,650)(301,653)(302,652)(303,654)(304,657)(305,656)(306,655)(307,673)(308,675)(309,674)(310,668)(311,667)(312,669)(313,672)(314,671)(315,670)(316,662)(317,661)(318,663)(319,666)(320,665)(321,664)(322,658)(323,660)(324,659)(325,757)(326,759)(327,758)(328,761)(329,760)(330,762)(331,765)(332,764)(333,763)(334,781)(335,783)(336,782)(337,776)(338,775)(339,777)(340,780)(341,779)(342,778)(343,770)(344,769)(345,771)(346,774)(347,773)(348,772)(349,766)(350,768)(351,767)(352,784)(353,786)(354,785)(355,788)(356,787)(357,789)(358,792)(359,791)(360,790)(361,808)(362,810)(363,809)(364,803)(365,802)(366,804)(367,807)(368,806)(369,805)(370,797)(371,796)(372,798)(373,801)(374,800)(375,799)(376,793)(377,795)(378,794)(379,838)(380,840)(381,839)(382,842)(383,841)(384,843)(385,846)(386,845)(387,844)(388,862)(389,864)(390,863)(391,857)(392,856)(393,858)(394,861)(395,860)(396,859)(397,851)(398,850)(399,852)(400,855)(401,854)(402,853)(403,847)(404,849)(405,848)(406,811)(407,813)(408,812)(409,815)(410,814)(411,816)(412,819)(413,818)(414,817)(415,835)(416,837)(417,836)(418,830)(419,829)(420,831)(421,834)(422,833)(423,832)(424,824)(425,823)(426,825)(427,828)(428,827)(429,826)(430,820)(431,822)(432,821);; s2 := ( 1,337)( 2,338)( 3,339)( 4,335)( 5,336)( 6,334)( 7,342)( 8,340)( 9,341)( 10,330)( 11,328)( 12,329)( 13,325)( 14,326)( 15,327)( 16,332)( 17,333)( 18,331)( 19,347)( 20,348)( 21,346)( 22,345)( 23,343)( 24,344)( 25,349)( 26,350)( 27,351)( 28,364)( 29,365)( 30,366)( 31,362)( 32,363)( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)( 40,352)( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)( 48,373)( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,391)( 56,392)( 57,393)( 58,389)( 59,390)( 60,388)( 61,396)( 62,394)( 63,395)( 64,384)( 65,382)( 66,383)( 67,379)( 68,380)( 69,381)( 70,386)( 71,387)( 72,385)( 73,401)( 74,402)( 75,400)( 76,399)( 77,397)( 78,398)( 79,403)( 80,404)( 81,405)( 82,418)( 83,419)( 84,420)( 85,416)( 86,417)( 87,415)( 88,423)( 89,421)( 90,422)( 91,411)( 92,409)( 93,410)( 94,406)( 95,407)( 96,408)( 97,413)( 98,414)( 99,412)(100,428)(101,429)(102,427)(103,426)(104,424)(105,425)(106,430)(107,431)(108,432)(109,310)(110,311)(111,312)(112,308)(113,309)(114,307)(115,315)(116,313)(117,314)(118,303)(119,301)(120,302)(121,298)(122,299)(123,300)(124,305)(125,306)(126,304)(127,320)(128,321)(129,319)(130,318)(131,316)(132,317)(133,322)(134,323)(135,324)(136,283)(137,284)(138,285)(139,281)(140,282)(141,280)(142,288)(143,286)(144,287)(145,276)(146,274)(147,275)(148,271)(149,272)(150,273)(151,278)(152,279)(153,277)(154,293)(155,294)(156,292)(157,291)(158,289)(159,290)(160,295)(161,296)(162,297)(163,229)(164,230)(165,231)(166,227)(167,228)(168,226)(169,234)(170,232)(171,233)(172,222)(173,220)(174,221)(175,217)(176,218)(177,219)(178,224)(179,225)(180,223)(181,239)(182,240)(183,238)(184,237)(185,235)(186,236)(187,241)(188,242)(189,243)(190,256)(191,257)(192,258)(193,254)(194,255)(195,253)(196,261)(197,259)(198,260)(199,249)(200,247)(201,248)(202,244)(203,245)(204,246)(205,251)(206,252)(207,250)(208,266)(209,267)(210,265)(211,264)(212,262)(213,263)(214,268)(215,269)(216,270)(433,769)(434,770)(435,771)(436,767)(437,768)(438,766)(439,774)(440,772)(441,773)(442,762)(443,760)(444,761)(445,757)(446,758)(447,759)(448,764)(449,765)(450,763)(451,779)(452,780)(453,778)(454,777)(455,775)(456,776)(457,781)(458,782)(459,783)(460,796)(461,797)(462,798)(463,794)(464,795)(465,793)(466,801)(467,799)(468,800)(469,789)(470,787)(471,788)(472,784)(473,785)(474,786)(475,791)(476,792)(477,790)(478,806)(479,807)(480,805)(481,804)(482,802)(483,803)(484,808)(485,809)(486,810)(487,823)(488,824)(489,825)(490,821)(491,822)(492,820)(493,828)(494,826)(495,827)(496,816)(497,814)(498,815)(499,811)(500,812)(501,813)(502,818)(503,819)(504,817)(505,833)(506,834)(507,832)(508,831)(509,829)(510,830)(511,835)(512,836)(513,837)(514,850)(515,851)(516,852)(517,848)(518,849)(519,847)(520,855)(521,853)(522,854)(523,843)(524,841)(525,842)(526,838)(527,839)(528,840)(529,845)(530,846)(531,844)(532,860)(533,861)(534,859)(535,858)(536,856)(537,857)(538,862)(539,863)(540,864)(541,742)(542,743)(543,744)(544,740)(545,741)(546,739)(547,747)(548,745)(549,746)(550,735)(551,733)(552,734)(553,730)(554,731)(555,732)(556,737)(557,738)(558,736)(559,752)(560,753)(561,751)(562,750)(563,748)(564,749)(565,754)(566,755)(567,756)(568,715)(569,716)(570,717)(571,713)(572,714)(573,712)(574,720)(575,718)(576,719)(577,708)(578,706)(579,707)(580,703)(581,704)(582,705)(583,710)(584,711)(585,709)(586,725)(587,726)(588,724)(589,723)(590,721)(591,722)(592,727)(593,728)(594,729)(595,661)(596,662)(597,663)(598,659)(599,660)(600,658)(601,666)(602,664)(603,665)(604,654)(605,652)(606,653)(607,649)(608,650)(609,651)(610,656)(611,657)(612,655)(613,671)(614,672)(615,670)(616,669)(617,667)(618,668)(619,673)(620,674)(621,675)(622,688)(623,689)(624,690)(625,686)(626,687)(627,685)(628,693)(629,691)(630,692)(631,681)(632,679)(633,680)(634,676)(635,677)(636,678)(637,683)(638,684)(639,682)(640,698)(641,699)(642,697)(643,696)(644,694)(645,695)(646,700)(647,701)(648,702);; 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*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(864)!( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 55, 82)( 56, 84)( 57, 83)( 58,103)( 59,105)( 60,104)( 61, 99)( 62, 98)( 63, 97)( 64,100)( 65,102)( 66,101)( 67, 94)( 68, 96)( 69, 95)( 70, 90)( 71, 89)( 72, 88)( 73, 91)( 74, 93)( 75, 92)( 76, 85)( 77, 87)( 78, 86)( 79,108)( 80,107)( 81,106)(109,163)(110,165)(111,164)(112,184)(113,186)(114,185)(115,180)(116,179)(117,178)(118,181)(119,183)(120,182)(121,175)(122,177)(123,176)(124,171)(125,170)(126,169)(127,172)(128,174)(129,173)(130,166)(131,168)(132,167)(133,189)(134,188)(135,187)(136,190)(137,192)(138,191)(139,211)(140,213)(141,212)(142,207)(143,206)(144,205)(145,208)(146,210)(147,209)(148,202)(149,204)(150,203)(151,198)(152,197)(153,196)(154,199)(155,201)(156,200)(157,193)(158,195)(159,194)(160,216)(161,215)(162,214)(217,298)(218,300)(219,299)(220,319)(221,321)(222,320)(223,315)(224,314)(225,313)(226,316)(227,318)(228,317)(229,310)(230,312)(231,311)(232,306)(233,305)(234,304)(235,307)(236,309)(237,308)(238,301)(239,303)(240,302)(241,324)(242,323)(243,322)(244,271)(245,273)(246,272)(247,292)(248,294)(249,293)(250,288)(251,287)(252,286)(253,289)(254,291)(255,290)(256,283)(257,285)(258,284)(259,279)(260,278)(261,277)(262,280)(263,282)(264,281)(265,274)(266,276)(267,275)(268,297)(269,296)(270,295)(326,327)(328,346)(329,348)(330,347)(331,342)(332,341)(333,340)(334,343)(335,345)(336,344)(338,339)(349,351)(353,354)(355,373)(356,375)(357,374)(358,369)(359,368)(360,367)(361,370)(362,372)(363,371)(365,366)(376,378)(379,406)(380,408)(381,407)(382,427)(383,429)(384,428)(385,423)(386,422)(387,421)(388,424)(389,426)(390,425)(391,418)(392,420)(393,419)(394,414)(395,413)(396,412)(397,415)(398,417)(399,416)(400,409)(401,411)(402,410)(403,432)(404,431)(405,430)(433,541)(434,543)(435,542)(436,562)(437,564)(438,563)(439,558)(440,557)(441,556)(442,559)(443,561)(444,560)(445,553)(446,555)(447,554)(448,549)(449,548)(450,547)(451,550)(452,552)(453,551)(454,544)(455,546)(456,545)(457,567)(458,566)(459,565)(460,568)(461,570)(462,569)(463,589)(464,591)(465,590)(466,585)(467,584)(468,583)(469,586)(470,588)(471,587)(472,580)(473,582)(474,581)(475,576)(476,575)(477,574)(478,577)(479,579)(480,578)(481,571)(482,573)(483,572)(484,594)(485,593)(486,592)(487,622)(488,624)(489,623)(490,643)(491,645)(492,644)(493,639)(494,638)(495,637)(496,640)(497,642)(498,641)(499,634)(500,636)(501,635)(502,630)(503,629)(504,628)(505,631)(506,633)(507,632)(508,625)(509,627)(510,626)(511,648)(512,647)(513,646)(514,595)(515,597)(516,596)(517,616)(518,618)(519,617)(520,612)(521,611)(522,610)(523,613)(524,615)(525,614)(526,607)(527,609)(528,608)(529,603)(530,602)(531,601)(532,604)(533,606)(534,605)(535,598)(536,600)(537,599)(538,621)(539,620)(540,619)(649,838)(650,840)(651,839)(652,859)(653,861)(654,860)(655,855)(656,854)(657,853)(658,856)(659,858)(660,857)(661,850)(662,852)(663,851)(664,846)(665,845)(666,844)(667,847)(668,849)(669,848)(670,841)(671,843)(672,842)(673,864)(674,863)(675,862)(676,811)(677,813)(678,812)(679,832)(680,834)(681,833)(682,828)(683,827)(684,826)(685,829)(686,831)(687,830)(688,823)(689,825)(690,824)(691,819)(692,818)(693,817)(694,820)(695,822)(696,821)(697,814)(698,816)(699,815)(700,837)(701,836)(702,835)(703,784)(704,786)(705,785)(706,805)(707,807)(708,806)(709,801)(710,800)(711,799)(712,802)(713,804)(714,803)(715,796)(716,798)(717,797)(718,792)(719,791)(720,790)(721,793)(722,795)(723,794)(724,787)(725,789)(726,788)(727,810)(728,809)(729,808)(730,757)(731,759)(732,758)(733,778)(734,780)(735,779)(736,774)(737,773)(738,772)(739,775)(740,777)(741,776)(742,769)(743,771)(744,770)(745,765)(746,764)(747,763)(748,766)(749,768)(750,767)(751,760)(752,762)(753,761)(754,783)(755,782)(756,781); s1 := Sym(864)!( 1,433)( 2,435)( 3,434)( 4,437)( 5,436)( 6,438)( 7,441)( 8,440)( 9,439)( 10,457)( 11,459)( 12,458)( 13,452)( 14,451)( 15,453)( 16,456)( 17,455)( 18,454)( 19,446)( 20,445)( 21,447)( 22,450)( 23,449)( 24,448)( 25,442)( 26,444)( 27,443)( 28,460)( 29,462)( 30,461)( 31,464)( 32,463)( 33,465)( 34,468)( 35,467)( 36,466)( 37,484)( 38,486)( 39,485)( 40,479)( 41,478)( 42,480)( 43,483)( 44,482)( 45,481)( 46,473)( 47,472)( 48,474)( 49,477)( 50,476)( 51,475)( 52,469)( 53,471)( 54,470)( 55,514)( 56,516)( 57,515)( 58,518)( 59,517)( 60,519)( 61,522)( 62,521)( 63,520)( 64,538)( 65,540)( 66,539)( 67,533)( 68,532)( 69,534)( 70,537)( 71,536)( 72,535)( 73,527)( 74,526)( 75,528)( 76,531)( 77,530)( 78,529)( 79,523)( 80,525)( 81,524)( 82,487)( 83,489)( 84,488)( 85,491)( 86,490)( 87,492)( 88,495)( 89,494)( 90,493)( 91,511)( 92,513)( 93,512)( 94,506)( 95,505)( 96,507)( 97,510)( 98,509)( 99,508)(100,500)(101,499)(102,501)(103,504)(104,503)(105,502)(106,496)(107,498)(108,497)(109,595)(110,597)(111,596)(112,599)(113,598)(114,600)(115,603)(116,602)(117,601)(118,619)(119,621)(120,620)(121,614)(122,613)(123,615)(124,618)(125,617)(126,616)(127,608)(128,607)(129,609)(130,612)(131,611)(132,610)(133,604)(134,606)(135,605)(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)(145,646)(146,648)(147,647)(148,641)(149,640)(150,642)(151,645)(152,644)(153,643)(154,635)(155,634)(156,636)(157,639)(158,638)(159,637)(160,631)(161,633)(162,632)(163,541)(164,543)(165,542)(166,545)(167,544)(168,546)(169,549)(170,548)(171,547)(172,565)(173,567)(174,566)(175,560)(176,559)(177,561)(178,564)(179,563)(180,562)(181,554)(182,553)(183,555)(184,558)(185,557)(186,556)(187,550)(188,552)(189,551)(190,568)(191,570)(192,569)(193,572)(194,571)(195,573)(196,576)(197,575)(198,574)(199,592)(200,594)(201,593)(202,587)(203,586)(204,588)(205,591)(206,590)(207,589)(208,581)(209,580)(210,582)(211,585)(212,584)(213,583)(214,577)(215,579)(216,578)(217,730)(218,732)(219,731)(220,734)(221,733)(222,735)(223,738)(224,737)(225,736)(226,754)(227,756)(228,755)(229,749)(230,748)(231,750)(232,753)(233,752)(234,751)(235,743)(236,742)(237,744)(238,747)(239,746)(240,745)(241,739)(242,741)(243,740)(244,703)(245,705)(246,704)(247,707)(248,706)(249,708)(250,711)(251,710)(252,709)(253,727)(254,729)(255,728)(256,722)(257,721)(258,723)(259,726)(260,725)(261,724)(262,716)(263,715)(264,717)(265,720)(266,719)(267,718)(268,712)(269,714)(270,713)(271,676)(272,678)(273,677)(274,680)(275,679)(276,681)(277,684)(278,683)(279,682)(280,700)(281,702)(282,701)(283,695)(284,694)(285,696)(286,699)(287,698)(288,697)(289,689)(290,688)(291,690)(292,693)(293,692)(294,691)(295,685)(296,687)(297,686)(298,649)(299,651)(300,650)(301,653)(302,652)(303,654)(304,657)(305,656)(306,655)(307,673)(308,675)(309,674)(310,668)(311,667)(312,669)(313,672)(314,671)(315,670)(316,662)(317,661)(318,663)(319,666)(320,665)(321,664)(322,658)(323,660)(324,659)(325,757)(326,759)(327,758)(328,761)(329,760)(330,762)(331,765)(332,764)(333,763)(334,781)(335,783)(336,782)(337,776)(338,775)(339,777)(340,780)(341,779)(342,778)(343,770)(344,769)(345,771)(346,774)(347,773)(348,772)(349,766)(350,768)(351,767)(352,784)(353,786)(354,785)(355,788)(356,787)(357,789)(358,792)(359,791)(360,790)(361,808)(362,810)(363,809)(364,803)(365,802)(366,804)(367,807)(368,806)(369,805)(370,797)(371,796)(372,798)(373,801)(374,800)(375,799)(376,793)(377,795)(378,794)(379,838)(380,840)(381,839)(382,842)(383,841)(384,843)(385,846)(386,845)(387,844)(388,862)(389,864)(390,863)(391,857)(392,856)(393,858)(394,861)(395,860)(396,859)(397,851)(398,850)(399,852)(400,855)(401,854)(402,853)(403,847)(404,849)(405,848)(406,811)(407,813)(408,812)(409,815)(410,814)(411,816)(412,819)(413,818)(414,817)(415,835)(416,837)(417,836)(418,830)(419,829)(420,831)(421,834)(422,833)(423,832)(424,824)(425,823)(426,825)(427,828)(428,827)(429,826)(430,820)(431,822)(432,821); s2 := Sym(864)!( 1,337)( 2,338)( 3,339)( 4,335)( 5,336)( 6,334)( 7,342)( 8,340)( 9,341)( 10,330)( 11,328)( 12,329)( 13,325)( 14,326)( 15,327)( 16,332)( 17,333)( 18,331)( 19,347)( 20,348)( 21,346)( 22,345)( 23,343)( 24,344)( 25,349)( 26,350)( 27,351)( 28,364)( 29,365)( 30,366)( 31,362)( 32,363)( 33,361)( 34,369)( 35,367)( 36,368)( 37,357)( 38,355)( 39,356)( 40,352)( 41,353)( 42,354)( 43,359)( 44,360)( 45,358)( 46,374)( 47,375)( 48,373)( 49,372)( 50,370)( 51,371)( 52,376)( 53,377)( 54,378)( 55,391)( 56,392)( 57,393)( 58,389)( 59,390)( 60,388)( 61,396)( 62,394)( 63,395)( 64,384)( 65,382)( 66,383)( 67,379)( 68,380)( 69,381)( 70,386)( 71,387)( 72,385)( 73,401)( 74,402)( 75,400)( 76,399)( 77,397)( 78,398)( 79,403)( 80,404)( 81,405)( 82,418)( 83,419)( 84,420)( 85,416)( 86,417)( 87,415)( 88,423)( 89,421)( 90,422)( 91,411)( 92,409)( 93,410)( 94,406)( 95,407)( 96,408)( 97,413)( 98,414)( 99,412)(100,428)(101,429)(102,427)(103,426)(104,424)(105,425)(106,430)(107,431)(108,432)(109,310)(110,311)(111,312)(112,308)(113,309)(114,307)(115,315)(116,313)(117,314)(118,303)(119,301)(120,302)(121,298)(122,299)(123,300)(124,305)(125,306)(126,304)(127,320)(128,321)(129,319)(130,318)(131,316)(132,317)(133,322)(134,323)(135,324)(136,283)(137,284)(138,285)(139,281)(140,282)(141,280)(142,288)(143,286)(144,287)(145,276)(146,274)(147,275)(148,271)(149,272)(150,273)(151,278)(152,279)(153,277)(154,293)(155,294)(156,292)(157,291)(158,289)(159,290)(160,295)(161,296)(162,297)(163,229)(164,230)(165,231)(166,227)(167,228)(168,226)(169,234)(170,232)(171,233)(172,222)(173,220)(174,221)(175,217)(176,218)(177,219)(178,224)(179,225)(180,223)(181,239)(182,240)(183,238)(184,237)(185,235)(186,236)(187,241)(188,242)(189,243)(190,256)(191,257)(192,258)(193,254)(194,255)(195,253)(196,261)(197,259)(198,260)(199,249)(200,247)(201,248)(202,244)(203,245)(204,246)(205,251)(206,252)(207,250)(208,266)(209,267)(210,265)(211,264)(212,262)(213,263)(214,268)(215,269)(216,270)(433,769)(434,770)(435,771)(436,767)(437,768)(438,766)(439,774)(440,772)(441,773)(442,762)(443,760)(444,761)(445,757)(446,758)(447,759)(448,764)(449,765)(450,763)(451,779)(452,780)(453,778)(454,777)(455,775)(456,776)(457,781)(458,782)(459,783)(460,796)(461,797)(462,798)(463,794)(464,795)(465,793)(466,801)(467,799)(468,800)(469,789)(470,787)(471,788)(472,784)(473,785)(474,786)(475,791)(476,792)(477,790)(478,806)(479,807)(480,805)(481,804)(482,802)(483,803)(484,808)(485,809)(486,810)(487,823)(488,824)(489,825)(490,821)(491,822)(492,820)(493,828)(494,826)(495,827)(496,816)(497,814)(498,815)(499,811)(500,812)(501,813)(502,818)(503,819)(504,817)(505,833)(506,834)(507,832)(508,831)(509,829)(510,830)(511,835)(512,836)(513,837)(514,850)(515,851)(516,852)(517,848)(518,849)(519,847)(520,855)(521,853)(522,854)(523,843)(524,841)(525,842)(526,838)(527,839)(528,840)(529,845)(530,846)(531,844)(532,860)(533,861)(534,859)(535,858)(536,856)(537,857)(538,862)(539,863)(540,864)(541,742)(542,743)(543,744)(544,740)(545,741)(546,739)(547,747)(548,745)(549,746)(550,735)(551,733)(552,734)(553,730)(554,731)(555,732)(556,737)(557,738)(558,736)(559,752)(560,753)(561,751)(562,750)(563,748)(564,749)(565,754)(566,755)(567,756)(568,715)(569,716)(570,717)(571,713)(572,714)(573,712)(574,720)(575,718)(576,719)(577,708)(578,706)(579,707)(580,703)(581,704)(582,705)(583,710)(584,711)(585,709)(586,725)(587,726)(588,724)(589,723)(590,721)(591,722)(592,727)(593,728)(594,729)(595,661)(596,662)(597,663)(598,659)(599,660)(600,658)(601,666)(602,664)(603,665)(604,654)(605,652)(606,653)(607,649)(608,650)(609,651)(610,656)(611,657)(612,655)(613,671)(614,672)(615,670)(616,669)(617,667)(618,668)(619,673)(620,674)(621,675)(622,688)(623,689)(624,690)(625,686)(626,687)(627,685)(628,693)(629,691)(630,692)(631,681)(632,679)(633,680)(634,676)(635,677)(636,678)(637,683)(638,684)(639,682)(640,698)(641,699)(642,697)(643,696)(644,694)(645,695)(646,700)(647,701)(648,702); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*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 >;
References
None.
to this polytope.