Polytope of Type {12,6} with group SmallGroup(1728,46303)

Overview

Group: SmallGroup(1728,46303)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 144, 432, 72
Order of s₀s₁s₂: 24
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,6}*864c

3-fold

6-fold

8-fold

{6,6}*216d

9-fold

{12,6}*192b

12-fold

18-fold

24-fold

36-fold

48-fold

72-fold

144-fold

216-fold

{2,2}*8

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=<s1*s0*(s1*s2)^2*s1*s0*s2*s1> of order 2

36 facets

36 of {12}*24

96 vertex figures

48 of {6}*12
48 of {3}*6

P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2> of order 2

36 facets

36 of {12}*24

72 vertex figures

72 of {6}*12

P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3

24 facets

24 of {12}*24

60 vertex figures

42 of {6}*12
18 of {2}*4

P/N, where N=<(s0*s1)^4> of order 3

30 facets

9 of {4}*8
21 of {12}*24

48 vertex figures

48 of {6}*12

P/N, where N=<(s0*s1)^4*(s2*s1*s0)^2*(s2*s1)^2> of order 3

24 facets

24 of {12}*24

48 vertex figures

48 of {6}*12

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 3

24 facets

24 of {12}*24

48 vertex figures

48 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle