Polytope of Type {6,12} with group SmallGroup(1296,2061)

Overview

Group: SmallGroup(1296,2061)
Rank: 3
Schläfli Type: {6,12}
Vertices, edges, …: 54, 324, 108
Order of s₀s₁s₂: 12
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

{6,6}*648g

3-fold

6-fold

9-fold

12-fold

{6,6}*108

18-fold

27-fold

36-fold

54-fold

81-fold

{2,4}*16

108-fold

162-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=<(s0*s1*s2*s1)^2> of order 3

36 facets

36 of {6}*12

18 vertex figures

18 of {12}*24

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

48 facets

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

18 vertex figures

18 of {12}*24

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

36 facets

36 of {6}*12

24 vertex figures

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

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

36 facets

36 of {6}*12

18 vertex figures

18 of {12}*24

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

36 facets

36 of {6}*12

18 vertex figures

18 of {12}*24

P/N, where N=<(s0*s1*s2*s1)^2, (s1*s2)^4> of order 9

12 facets

12 of {6}*12

10 vertex figures

6 of {4}*8
4 of {12}*24

P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2> of order 9

20 facets

8 of {6}*12
12 of {2}*4

6 vertex figures

6 of {12}*24

Representations

Permutation Representation (GAP)

s0 := (  1,487)(  2,489)(  3,488)(  4,490)(  5,492)(  6,491)(  7,493)(  8,495)(  9,494)( 10,505)( 11,507)( 12,506)( 13,508)( 14,510)( 15,509)( 16,511)( 17,513)( 18,512)( 19,496)( 20,498)( 21,497)( 22,499)( 23,501)( 24,500)( 25,502)( 26,504)( 27,503)( 28,541)( 29,543)( 30,542)( 31,544)( 32,546)( 33,545)( 34,547)( 35,549)( 36,548)( 37,559)( 38,561)( 39,560)( 40,562)( 41,564)( 42,563)( 43,565)( 44,567)( 45,566)( 46,550)( 47,552)( 48,551)( 49,553)( 50,555)( 51,554)( 52,556)( 53,558)( 54,557)( 55,514)( 56,516)( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)( 64,532)( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)( 72,539)( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)( 80,531)( 81,530)( 82,568)( 83,570)( 84,569)( 85,571)( 86,573)( 87,572)( 88,574)( 89,576)( 90,575)( 91,586)( 92,588)( 93,587)( 94,589)( 95,591)( 96,590)( 97,592)( 98,594)( 99,593)(100,577)(101,579)(102,578)(103,580)(104,582)(105,581)(106,583)(107,585)(108,584)(109,622)(110,624)(111,623)(112,625)(113,627)(114,626)(115,628)(116,630)(117,629)(118,640)(119,642)(120,641)(121,643)(122,645)(123,644)(124,646)(125,648)(126,647)(127,631)(128,633)(129,632)(130,634)(131,636)(132,635)(133,637)(134,639)(135,638)(136,595)(137,597)(138,596)(139,598)(140,600)(141,599)(142,601)(143,603)(144,602)(145,613)(146,615)(147,614)(148,616)(149,618)(150,617)(151,619)(152,621)(153,620)(154,604)(155,606)(156,605)(157,607)(158,609)(159,608)(160,610)(161,612)(162,611)(163,406)(164,408)(165,407)(166,409)(167,411)(168,410)(169,412)(170,414)(171,413)(172,424)(173,426)(174,425)(175,427)(176,429)(177,428)(178,430)(179,432)(180,431)(181,415)(182,417)(183,416)(184,418)(185,420)(186,419)(187,421)(188,423)(189,422)(190,460)(191,462)(192,461)(193,463)(194,465)(195,464)(196,466)(197,468)(198,467)(199,478)(200,480)(201,479)(202,481)(203,483)(204,482)(205,484)(206,486)(207,485)(208,469)(209,471)(210,470)(211,472)(212,474)(213,473)(214,475)(215,477)(216,476)(217,433)(218,435)(219,434)(220,436)(221,438)(222,437)(223,439)(224,441)(225,440)(226,451)(227,453)(228,452)(229,454)(230,456)(231,455)(232,457)(233,459)(234,458)(235,442)(236,444)(237,443)(238,445)(239,447)(240,446)(241,448)(242,450)(243,449)(244,325)(245,327)(246,326)(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,343)(254,345)(255,344)(256,346)(257,348)(258,347)(259,349)(260,351)(261,350)(262,334)(263,336)(264,335)(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)(271,379)(272,381)(273,380)(274,382)(275,384)(276,383)(277,385)(278,387)(279,386)(280,397)(281,399)(282,398)(283,400)(284,402)(285,401)(286,403)(287,405)(288,404)(289,388)(290,390)(291,389)(292,391)(293,393)(294,392)(295,394)(296,396)(297,395)(298,352)(299,354)(300,353)(301,355)(302,357)(303,356)(304,358)(305,360)(306,359)(307,370)(308,372)(309,371)(310,373)(311,375)(312,374)(313,376)(314,378)(315,377)(316,361)(317,363)(318,362)(319,364)(320,366)(321,365)(322,367)(323,369)(324,368);;
s1 := (  1,523)(  2,524)(  3,525)(  4,531)(  5,529)(  6,530)(  7,527)(  8,528)(  9,526)( 10,514)( 11,515)( 12,516)( 13,522)( 14,520)( 15,521)( 16,518)( 17,519)( 18,517)( 19,532)( 20,533)( 21,534)( 22,540)( 23,538)( 24,539)( 25,536)( 26,537)( 27,535)( 28,496)( 29,497)( 30,498)( 31,504)( 32,502)( 33,503)( 34,500)( 35,501)( 36,499)( 37,487)( 38,488)( 39,489)( 40,495)( 41,493)( 42,494)( 43,491)( 44,492)( 45,490)( 46,505)( 47,506)( 48,507)( 49,513)( 50,511)( 51,512)( 52,509)( 53,510)( 54,508)( 55,550)( 56,551)( 57,552)( 58,558)( 59,556)( 60,557)( 61,554)( 62,555)( 63,553)( 64,541)( 65,542)( 66,543)( 67,549)( 68,547)( 69,548)( 70,545)( 71,546)( 72,544)( 73,559)( 74,560)( 75,561)( 76,567)( 77,565)( 78,566)( 79,563)( 80,564)( 81,562)( 82,604)( 83,605)( 84,606)( 85,612)( 86,610)( 87,611)( 88,608)( 89,609)( 90,607)( 91,595)( 92,596)( 93,597)( 94,603)( 95,601)( 96,602)( 97,599)( 98,600)( 99,598)(100,613)(101,614)(102,615)(103,621)(104,619)(105,620)(106,617)(107,618)(108,616)(109,577)(110,578)(111,579)(112,585)(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)(120,570)(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)(128,587)(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)(136,631)(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)(144,634)(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)(152,627)(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)(161,645)(162,643)(163,361)(164,362)(165,363)(166,369)(167,367)(168,368)(169,365)(170,366)(171,364)(172,352)(173,353)(174,354)(175,360)(176,358)(177,359)(178,356)(179,357)(180,355)(181,370)(182,371)(183,372)(184,378)(185,376)(186,377)(187,374)(188,375)(189,373)(190,334)(191,335)(192,336)(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,325)(200,326)(201,327)(202,333)(203,331)(204,332)(205,329)(206,330)(207,328)(208,343)(209,344)(210,345)(211,351)(212,349)(213,350)(214,347)(215,348)(216,346)(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)(224,393)(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)(232,383)(233,384)(234,382)(235,397)(236,398)(237,399)(238,405)(239,403)(240,404)(241,401)(242,402)(243,400)(244,442)(245,443)(246,444)(247,450)(248,448)(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)(256,441)(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)(264,453)(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,415)(272,416)(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)(279,418)(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)(288,409)(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)(295,428)(296,429)(297,427)(298,469)(299,470)(300,471)(301,477)(302,475)(303,476)(304,473)(305,474)(306,472)(307,460)(308,461)(309,462)(310,468)(311,466)(312,467)(313,464)(314,465)(315,463)(316,478)(317,479)(318,480)(319,486)(320,484)(321,485)(322,482)(323,483)(324,481);;
s2 := (  1,166)(  2,168)(  3,167)(  4,163)(  5,165)(  6,164)(  7,169)(  8,171)(  9,170)( 10,184)( 11,186)( 12,185)( 13,181)( 14,183)( 15,182)( 16,187)( 17,189)( 18,188)( 19,175)( 20,177)( 21,176)( 22,172)( 23,174)( 24,173)( 25,178)( 26,180)( 27,179)( 28,193)( 29,195)( 30,194)( 31,190)( 32,192)( 33,191)( 34,196)( 35,198)( 36,197)( 37,211)( 38,213)( 39,212)( 40,208)( 41,210)( 42,209)( 43,214)( 44,216)( 45,215)( 46,202)( 47,204)( 48,203)( 49,199)( 50,201)( 51,200)( 52,205)( 53,207)( 54,206)( 55,220)( 56,222)( 57,221)( 58,217)( 59,219)( 60,218)( 61,223)( 62,225)( 63,224)( 64,238)( 65,240)( 66,239)( 67,235)( 68,237)( 69,236)( 70,241)( 71,243)( 72,242)( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,232)( 80,234)( 81,233)( 82,247)( 83,249)( 84,248)( 85,244)( 86,246)( 87,245)( 88,250)( 89,252)( 90,251)( 91,265)( 92,267)( 93,266)( 94,262)( 95,264)( 96,263)( 97,268)( 98,270)( 99,269)(100,256)(101,258)(102,257)(103,253)(104,255)(105,254)(106,259)(107,261)(108,260)(109,274)(110,276)(111,275)(112,271)(113,273)(114,272)(115,277)(116,279)(117,278)(118,292)(119,294)(120,293)(121,289)(122,291)(123,290)(124,295)(125,297)(126,296)(127,283)(128,285)(129,284)(130,280)(131,282)(132,281)(133,286)(134,288)(135,287)(136,301)(137,303)(138,302)(139,298)(140,300)(141,299)(142,304)(143,306)(144,305)(145,319)(146,321)(147,320)(148,316)(149,318)(150,317)(151,322)(152,324)(153,323)(154,310)(155,312)(156,311)(157,307)(158,309)(159,308)(160,313)(161,315)(162,314)(325,571)(326,573)(327,572)(328,568)(329,570)(330,569)(331,574)(332,576)(333,575)(334,589)(335,591)(336,590)(337,586)(338,588)(339,587)(340,592)(341,594)(342,593)(343,580)(344,582)(345,581)(346,577)(347,579)(348,578)(349,583)(350,585)(351,584)(352,598)(353,600)(354,599)(355,595)(356,597)(357,596)(358,601)(359,603)(360,602)(361,616)(362,618)(363,617)(364,613)(365,615)(366,614)(367,619)(368,621)(369,620)(370,607)(371,609)(372,608)(373,604)(374,606)(375,605)(376,610)(377,612)(378,611)(379,625)(380,627)(381,626)(382,622)(383,624)(384,623)(385,628)(386,630)(387,629)(388,643)(389,645)(390,644)(391,640)(392,642)(393,641)(394,646)(395,648)(396,647)(397,634)(398,636)(399,635)(400,631)(401,633)(402,632)(403,637)(404,639)(405,638)(406,490)(407,492)(408,491)(409,487)(410,489)(411,488)(412,493)(413,495)(414,494)(415,508)(416,510)(417,509)(418,505)(419,507)(420,506)(421,511)(422,513)(423,512)(424,499)(425,501)(426,500)(427,496)(428,498)(429,497)(430,502)(431,504)(432,503)(433,517)(434,519)(435,518)(436,514)(437,516)(438,515)(439,520)(440,522)(441,521)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)(448,538)(449,540)(450,539)(451,526)(452,528)(453,527)(454,523)(455,525)(456,524)(457,529)(458,531)(459,530)(460,544)(461,546)(462,545)(463,541)(464,543)(465,542)(466,547)(467,549)(468,548)(469,562)(470,564)(471,563)(472,559)(473,561)(474,560)(475,565)(476,567)(477,566)(478,553)(479,555)(480,554)(481,550)(482,552)(483,551)(484,556)(485,558)(486,557);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(648)!(  1,487)(  2,489)(  3,488)(  4,490)(  5,492)(  6,491)(  7,493)(  8,495)(  9,494)( 10,505)( 11,507)( 12,506)( 13,508)( 14,510)( 15,509)( 16,511)( 17,513)( 18,512)( 19,496)( 20,498)( 21,497)( 22,499)( 23,501)( 24,500)( 25,502)( 26,504)( 27,503)( 28,541)( 29,543)( 30,542)( 31,544)( 32,546)( 33,545)( 34,547)( 35,549)( 36,548)( 37,559)( 38,561)( 39,560)( 40,562)( 41,564)( 42,563)( 43,565)( 44,567)( 45,566)( 46,550)( 47,552)( 48,551)( 49,553)( 50,555)( 51,554)( 52,556)( 53,558)( 54,557)( 55,514)( 56,516)( 57,515)( 58,517)( 59,519)( 60,518)( 61,520)( 62,522)( 63,521)( 64,532)( 65,534)( 66,533)( 67,535)( 68,537)( 69,536)( 70,538)( 71,540)( 72,539)( 73,523)( 74,525)( 75,524)( 76,526)( 77,528)( 78,527)( 79,529)( 80,531)( 81,530)( 82,568)( 83,570)( 84,569)( 85,571)( 86,573)( 87,572)( 88,574)( 89,576)( 90,575)( 91,586)( 92,588)( 93,587)( 94,589)( 95,591)( 96,590)( 97,592)( 98,594)( 99,593)(100,577)(101,579)(102,578)(103,580)(104,582)(105,581)(106,583)(107,585)(108,584)(109,622)(110,624)(111,623)(112,625)(113,627)(114,626)(115,628)(116,630)(117,629)(118,640)(119,642)(120,641)(121,643)(122,645)(123,644)(124,646)(125,648)(126,647)(127,631)(128,633)(129,632)(130,634)(131,636)(132,635)(133,637)(134,639)(135,638)(136,595)(137,597)(138,596)(139,598)(140,600)(141,599)(142,601)(143,603)(144,602)(145,613)(146,615)(147,614)(148,616)(149,618)(150,617)(151,619)(152,621)(153,620)(154,604)(155,606)(156,605)(157,607)(158,609)(159,608)(160,610)(161,612)(162,611)(163,406)(164,408)(165,407)(166,409)(167,411)(168,410)(169,412)(170,414)(171,413)(172,424)(173,426)(174,425)(175,427)(176,429)(177,428)(178,430)(179,432)(180,431)(181,415)(182,417)(183,416)(184,418)(185,420)(186,419)(187,421)(188,423)(189,422)(190,460)(191,462)(192,461)(193,463)(194,465)(195,464)(196,466)(197,468)(198,467)(199,478)(200,480)(201,479)(202,481)(203,483)(204,482)(205,484)(206,486)(207,485)(208,469)(209,471)(210,470)(211,472)(212,474)(213,473)(214,475)(215,477)(216,476)(217,433)(218,435)(219,434)(220,436)(221,438)(222,437)(223,439)(224,441)(225,440)(226,451)(227,453)(228,452)(229,454)(230,456)(231,455)(232,457)(233,459)(234,458)(235,442)(236,444)(237,443)(238,445)(239,447)(240,446)(241,448)(242,450)(243,449)(244,325)(245,327)(246,326)(247,328)(248,330)(249,329)(250,331)(251,333)(252,332)(253,343)(254,345)(255,344)(256,346)(257,348)(258,347)(259,349)(260,351)(261,350)(262,334)(263,336)(264,335)(265,337)(266,339)(267,338)(268,340)(269,342)(270,341)(271,379)(272,381)(273,380)(274,382)(275,384)(276,383)(277,385)(278,387)(279,386)(280,397)(281,399)(282,398)(283,400)(284,402)(285,401)(286,403)(287,405)(288,404)(289,388)(290,390)(291,389)(292,391)(293,393)(294,392)(295,394)(296,396)(297,395)(298,352)(299,354)(300,353)(301,355)(302,357)(303,356)(304,358)(305,360)(306,359)(307,370)(308,372)(309,371)(310,373)(311,375)(312,374)(313,376)(314,378)(315,377)(316,361)(317,363)(318,362)(319,364)(320,366)(321,365)(322,367)(323,369)(324,368);
s1 := Sym(648)!(  1,523)(  2,524)(  3,525)(  4,531)(  5,529)(  6,530)(  7,527)(  8,528)(  9,526)( 10,514)( 11,515)( 12,516)( 13,522)( 14,520)( 15,521)( 16,518)( 17,519)( 18,517)( 19,532)( 20,533)( 21,534)( 22,540)( 23,538)( 24,539)( 25,536)( 26,537)( 27,535)( 28,496)( 29,497)( 30,498)( 31,504)( 32,502)( 33,503)( 34,500)( 35,501)( 36,499)( 37,487)( 38,488)( 39,489)( 40,495)( 41,493)( 42,494)( 43,491)( 44,492)( 45,490)( 46,505)( 47,506)( 48,507)( 49,513)( 50,511)( 51,512)( 52,509)( 53,510)( 54,508)( 55,550)( 56,551)( 57,552)( 58,558)( 59,556)( 60,557)( 61,554)( 62,555)( 63,553)( 64,541)( 65,542)( 66,543)( 67,549)( 68,547)( 69,548)( 70,545)( 71,546)( 72,544)( 73,559)( 74,560)( 75,561)( 76,567)( 77,565)( 78,566)( 79,563)( 80,564)( 81,562)( 82,604)( 83,605)( 84,606)( 85,612)( 86,610)( 87,611)( 88,608)( 89,609)( 90,607)( 91,595)( 92,596)( 93,597)( 94,603)( 95,601)( 96,602)( 97,599)( 98,600)( 99,598)(100,613)(101,614)(102,615)(103,621)(104,619)(105,620)(106,617)(107,618)(108,616)(109,577)(110,578)(111,579)(112,585)(113,583)(114,584)(115,581)(116,582)(117,580)(118,568)(119,569)(120,570)(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,586)(128,587)(129,588)(130,594)(131,592)(132,593)(133,590)(134,591)(135,589)(136,631)(137,632)(138,633)(139,639)(140,637)(141,638)(142,635)(143,636)(144,634)(145,622)(146,623)(147,624)(148,630)(149,628)(150,629)(151,626)(152,627)(153,625)(154,640)(155,641)(156,642)(157,648)(158,646)(159,647)(160,644)(161,645)(162,643)(163,361)(164,362)(165,363)(166,369)(167,367)(168,368)(169,365)(170,366)(171,364)(172,352)(173,353)(174,354)(175,360)(176,358)(177,359)(178,356)(179,357)(180,355)(181,370)(182,371)(183,372)(184,378)(185,376)(186,377)(187,374)(188,375)(189,373)(190,334)(191,335)(192,336)(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,325)(200,326)(201,327)(202,333)(203,331)(204,332)(205,329)(206,330)(207,328)(208,343)(209,344)(210,345)(211,351)(212,349)(213,350)(214,347)(215,348)(216,346)(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)(224,393)(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)(232,383)(233,384)(234,382)(235,397)(236,398)(237,399)(238,405)(239,403)(240,404)(241,401)(242,402)(243,400)(244,442)(245,443)(246,444)(247,450)(248,448)(249,449)(250,446)(251,447)(252,445)(253,433)(254,434)(255,435)(256,441)(257,439)(258,440)(259,437)(260,438)(261,436)(262,451)(263,452)(264,453)(265,459)(266,457)(267,458)(268,455)(269,456)(270,454)(271,415)(272,416)(273,417)(274,423)(275,421)(276,422)(277,419)(278,420)(279,418)(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)(288,409)(289,424)(290,425)(291,426)(292,432)(293,430)(294,431)(295,428)(296,429)(297,427)(298,469)(299,470)(300,471)(301,477)(302,475)(303,476)(304,473)(305,474)(306,472)(307,460)(308,461)(309,462)(310,468)(311,466)(312,467)(313,464)(314,465)(315,463)(316,478)(317,479)(318,480)(319,486)(320,484)(321,485)(322,482)(323,483)(324,481);
s2 := Sym(648)!(  1,166)(  2,168)(  3,167)(  4,163)(  5,165)(  6,164)(  7,169)(  8,171)(  9,170)( 10,184)( 11,186)( 12,185)( 13,181)( 14,183)( 15,182)( 16,187)( 17,189)( 18,188)( 19,175)( 20,177)( 21,176)( 22,172)( 23,174)( 24,173)( 25,178)( 26,180)( 27,179)( 28,193)( 29,195)( 30,194)( 31,190)( 32,192)( 33,191)( 34,196)( 35,198)( 36,197)( 37,211)( 38,213)( 39,212)( 40,208)( 41,210)( 42,209)( 43,214)( 44,216)( 45,215)( 46,202)( 47,204)( 48,203)( 49,199)( 50,201)( 51,200)( 52,205)( 53,207)( 54,206)( 55,220)( 56,222)( 57,221)( 58,217)( 59,219)( 60,218)( 61,223)( 62,225)( 63,224)( 64,238)( 65,240)( 66,239)( 67,235)( 68,237)( 69,236)( 70,241)( 71,243)( 72,242)( 73,229)( 74,231)( 75,230)( 76,226)( 77,228)( 78,227)( 79,232)( 80,234)( 81,233)( 82,247)( 83,249)( 84,248)( 85,244)( 86,246)( 87,245)( 88,250)( 89,252)( 90,251)( 91,265)( 92,267)( 93,266)( 94,262)( 95,264)( 96,263)( 97,268)( 98,270)( 99,269)(100,256)(101,258)(102,257)(103,253)(104,255)(105,254)(106,259)(107,261)(108,260)(109,274)(110,276)(111,275)(112,271)(113,273)(114,272)(115,277)(116,279)(117,278)(118,292)(119,294)(120,293)(121,289)(122,291)(123,290)(124,295)(125,297)(126,296)(127,283)(128,285)(129,284)(130,280)(131,282)(132,281)(133,286)(134,288)(135,287)(136,301)(137,303)(138,302)(139,298)(140,300)(141,299)(142,304)(143,306)(144,305)(145,319)(146,321)(147,320)(148,316)(149,318)(150,317)(151,322)(152,324)(153,323)(154,310)(155,312)(156,311)(157,307)(158,309)(159,308)(160,313)(161,315)(162,314)(325,571)(326,573)(327,572)(328,568)(329,570)(330,569)(331,574)(332,576)(333,575)(334,589)(335,591)(336,590)(337,586)(338,588)(339,587)(340,592)(341,594)(342,593)(343,580)(344,582)(345,581)(346,577)(347,579)(348,578)(349,583)(350,585)(351,584)(352,598)(353,600)(354,599)(355,595)(356,597)(357,596)(358,601)(359,603)(360,602)(361,616)(362,618)(363,617)(364,613)(365,615)(366,614)(367,619)(368,621)(369,620)(370,607)(371,609)(372,608)(373,604)(374,606)(375,605)(376,610)(377,612)(378,611)(379,625)(380,627)(381,626)(382,622)(383,624)(384,623)(385,628)(386,630)(387,629)(388,643)(389,645)(390,644)(391,640)(392,642)(393,641)(394,646)(395,648)(396,647)(397,634)(398,636)(399,635)(400,631)(401,633)(402,632)(403,637)(404,639)(405,638)(406,490)(407,492)(408,491)(409,487)(410,489)(411,488)(412,493)(413,495)(414,494)(415,508)(416,510)(417,509)(418,505)(419,507)(420,506)(421,511)(422,513)(423,512)(424,499)(425,501)(426,500)(427,496)(428,498)(429,497)(430,502)(431,504)(432,503)(433,517)(434,519)(435,518)(436,514)(437,516)(438,515)(439,520)(440,522)(441,521)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)(448,538)(449,540)(450,539)(451,526)(452,528)(453,527)(454,523)(455,525)(456,524)(457,529)(458,531)(459,530)(460,544)(461,546)(462,545)(463,541)(464,543)(465,542)(466,547)(467,549)(468,548)(469,562)(470,564)(471,563)(472,559)(473,561)(474,560)(475,565)(476,567)(477,566)(478,553)(479,555)(480,554)(481,550)(482,552)(483,551)(484,556)(485,558)(486,557);
poly := sub<Sym(648)|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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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 >;

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