Polytope of Type {12,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,3}*1296d
if this polytope has a name.
Group : SmallGroup(1296,2061)
Rank : 4
Schlafli Type : {12,6,3}
Number of vertices, edges, etc : 36, 108, 27, 3
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 6
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6,3}*648d
3-fold quotients : {12,6,3}*432b
6-fold quotients : {6,6,3}*216b
9-fold quotients : {12,2,3}*144, {4,6,3}*144
18-fold quotients : {2,6,3}*72, {6,2,3}*72
27-fold quotients : {4,2,3}*48
36-fold quotients : {3,2,3}*36
54-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
3 facets:
3 of 3-fold non-regular quotient of {12,6}*432b
12 vertex figures:
12 of {6,3}*36
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 3.
3 facets:
3 of 3-fold non-regular quotient of {12,6}*432b
20 vertex figures:
8 of {6,3}*36
12 of {2,3}*12
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)(123,125)(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)(141,143)(146,147)(148,151)(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)(163,244)(164,246)(165,245)(166,250)(167,252)(168,251)(169,247)(170,249)(171,248)(172,253)(173,255)(174,254)(175,259)(176,261)(177,260)(178,256)(179,258)(180,257)(181,262)(182,264)(183,263)(184,268)(185,270)(186,269)(187,265)(188,267)(189,266)(190,271)(191,273)(192,272)(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,280)(200,282)(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)(208,289)(209,291)(210,290)(211,295)(212,297)(213,296)(214,292)(215,294)(216,293)(217,298)(218,300)(219,299)(220,304)(221,306)(222,305)(223,301)(224,303)(225,302)(226,307)(227,309)(228,308)(229,313)(230,315)(231,314)(232,310)(233,312)(234,311)(235,316)(236,318)(237,317)(238,322)(239,324)(240,323)(241,319)(242,321)(243,320)(325,406)(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)(334,415)(335,417)(336,416)(337,421)(338,423)(339,422)(340,418)(341,420)(342,419)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)(352,433)(353,435)(354,434)(355,439)(356,441)(357,440)(358,436)(359,438)(360,437)(361,442)(362,444)(363,443)(364,448)(365,450)(366,449)(367,445)(368,447)(369,446)(370,451)(371,453)(372,452)(373,457)(374,459)(375,458)(376,454)(377,456)(378,455)(379,460)(380,462)(381,461)(382,466)(383,468)(384,467)(385,463)(386,465)(387,464)(388,469)(389,471)(390,470)(391,475)(392,477)(393,476)(394,472)(395,474)(396,473)(397,478)(398,480)(399,479)(400,484)(401,486)(402,485)(403,481)(404,483)(405,482)(488,489)(490,493)(491,495)(492,494)(497,498)(499,502)(500,504)(501,503)(506,507)(508,511)(509,513)(510,512)(515,516)(517,520)(518,522)(519,521)(524,525)(526,529)(527,531)(528,530)(533,534)(535,538)(536,540)(537,539)(542,543)(544,547)(545,549)(546,548)(551,552)(553,556)(554,558)(555,557)(560,561)(562,565)(563,567)(564,566)(569,570)(571,574)(572,576)(573,575)(578,579)(580,583)(581,585)(582,584)(587,588)(589,592)(590,594)(591,593)(596,597)(598,601)(599,603)(600,602)(605,606)(607,610)(608,612)(609,611)(614,615)(616,619)(617,621)(618,620)(623,624)(625,628)(626,630)(627,629)(632,633)(634,637)(635,639)(636,638)(641,642)(643,646)(644,648)(645,647);;
s1 := ( 1,328)( 2,329)( 3,330)( 4,325)( 5,326)( 6,327)( 7,331)( 8,332)( 9,333)( 10,337)( 11,338)( 12,339)( 13,334)( 14,335)( 15,336)( 16,340)( 17,341)( 18,342)( 19,346)( 20,347)( 21,348)( 22,343)( 23,344)( 24,345)( 25,349)( 26,350)( 27,351)( 28,382)( 29,383)( 30,384)( 31,379)( 32,380)( 33,381)( 34,385)( 35,386)( 36,387)( 37,391)( 38,392)( 39,393)( 40,388)( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,400)( 47,401)( 48,402)( 49,397)( 50,398)( 51,399)( 52,403)( 53,404)( 54,405)( 55,355)( 56,356)( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)( 64,364)( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)( 72,369)( 73,373)( 74,374)( 75,375)( 76,370)( 77,371)( 78,372)( 79,376)( 80,377)( 81,378)( 82,409)( 83,410)( 84,411)( 85,406)( 86,407)( 87,408)( 88,412)( 89,413)( 90,414)( 91,418)( 92,419)( 93,420)( 94,415)( 95,416)( 96,417)( 97,421)( 98,422)( 99,423)(100,427)(101,428)(102,429)(103,424)(104,425)(105,426)(106,430)(107,431)(108,432)(109,463)(110,464)(111,465)(112,460)(113,461)(114,462)(115,466)(116,467)(117,468)(118,472)(119,473)(120,474)(121,469)(122,470)(123,471)(124,475)(125,476)(126,477)(127,481)(128,482)(129,483)(130,478)(131,479)(132,480)(133,484)(134,485)(135,486)(136,436)(137,437)(138,438)(139,433)(140,434)(141,435)(142,439)(143,440)(144,441)(145,445)(146,446)(147,447)(148,442)(149,443)(150,444)(151,448)(152,449)(153,450)(154,454)(155,455)(156,456)(157,451)(158,452)(159,453)(160,457)(161,458)(162,459)(163,571)(164,572)(165,573)(166,568)(167,569)(168,570)(169,574)(170,575)(171,576)(172,580)(173,581)(174,582)(175,577)(176,578)(177,579)(178,583)(179,584)(180,585)(181,589)(182,590)(183,591)(184,586)(185,587)(186,588)(187,592)(188,593)(189,594)(190,625)(191,626)(192,627)(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,634)(200,635)(201,636)(202,631)(203,632)(204,633)(205,637)(206,638)(207,639)(208,643)(209,644)(210,645)(211,640)(212,641)(213,642)(214,646)(215,647)(216,648)(217,598)(218,599)(219,600)(220,595)(221,596)(222,597)(223,601)(224,602)(225,603)(226,607)(227,608)(228,609)(229,604)(230,605)(231,606)(232,610)(233,611)(234,612)(235,616)(236,617)(237,618)(238,613)(239,614)(240,615)(241,619)(242,620)(243,621)(244,490)(245,491)(246,492)(247,487)(248,488)(249,489)(250,493)(251,494)(252,495)(253,499)(254,500)(255,501)(256,496)(257,497)(258,498)(259,502)(260,503)(261,504)(262,508)(263,509)(264,510)(265,505)(266,506)(267,507)(268,511)(269,512)(270,513)(271,544)(272,545)(273,546)(274,541)(275,542)(276,543)(277,547)(278,548)(279,549)(280,553)(281,554)(282,555)(283,550)(284,551)(285,552)(286,556)(287,557)(288,558)(289,562)(290,563)(291,564)(292,559)(293,560)(294,561)(295,565)(296,566)(297,567)(298,517)(299,518)(300,519)(301,514)(302,515)(303,516)(304,520)(305,521)(306,522)(307,526)(308,527)(309,528)(310,523)(311,524)(312,525)(313,529)(314,530)(315,531)(316,535)(317,536)(318,537)(319,532)(320,533)(321,534)(322,538)(323,539)(324,540);;
s2 := ( 1,514)( 2,516)( 3,515)( 4,518)( 5,517)( 6,519)( 7,522)( 8,521)( 9,520)( 10,532)( 11,534)( 12,533)( 13,536)( 14,535)( 15,537)( 16,540)( 17,539)( 18,538)( 19,523)( 20,525)( 21,524)( 22,527)( 23,526)( 24,528)( 25,531)( 26,530)( 27,529)( 28,487)( 29,489)( 30,488)( 31,491)( 32,490)( 33,492)( 34,495)( 35,494)( 36,493)( 37,505)( 38,507)( 39,506)( 40,509)( 41,508)( 42,510)( 43,513)( 44,512)( 45,511)( 46,496)( 47,498)( 48,497)( 49,500)( 50,499)( 51,501)( 52,504)( 53,503)( 54,502)( 55,541)( 56,543)( 57,542)( 58,545)( 59,544)( 60,546)( 61,549)( 62,548)( 63,547)( 64,559)( 65,561)( 66,560)( 67,563)( 68,562)( 69,564)( 70,567)( 71,566)( 72,565)( 73,550)( 74,552)( 75,551)( 76,554)( 77,553)( 78,555)( 79,558)( 80,557)( 81,556)( 82,595)( 83,597)( 84,596)( 85,599)( 86,598)( 87,600)( 88,603)( 89,602)( 90,601)( 91,613)( 92,615)( 93,614)( 94,617)( 95,616)( 96,618)( 97,621)( 98,620)( 99,619)(100,604)(101,606)(102,605)(103,608)(104,607)(105,609)(106,612)(107,611)(108,610)(109,568)(110,570)(111,569)(112,572)(113,571)(114,573)(115,576)(116,575)(117,574)(118,586)(119,588)(120,587)(121,590)(122,589)(123,591)(124,594)(125,593)(126,592)(127,577)(128,579)(129,578)(130,581)(131,580)(132,582)(133,585)(134,584)(135,583)(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)(145,640)(146,642)(147,641)(148,644)(149,643)(150,645)(151,648)(152,647)(153,646)(154,631)(155,633)(156,632)(157,635)(158,634)(159,636)(160,639)(161,638)(162,637)(163,433)(164,435)(165,434)(166,437)(167,436)(168,438)(169,441)(170,440)(171,439)(172,451)(173,453)(174,452)(175,455)(176,454)(177,456)(178,459)(179,458)(180,457)(181,442)(182,444)(183,443)(184,446)(185,445)(186,447)(187,450)(188,449)(189,448)(190,406)(191,408)(192,407)(193,410)(194,409)(195,411)(196,414)(197,413)(198,412)(199,424)(200,426)(201,425)(202,428)(203,427)(204,429)(205,432)(206,431)(207,430)(208,415)(209,417)(210,416)(211,419)(212,418)(213,420)(214,423)(215,422)(216,421)(217,460)(218,462)(219,461)(220,464)(221,463)(222,465)(223,468)(224,467)(225,466)(226,478)(227,480)(228,479)(229,482)(230,481)(231,483)(232,486)(233,485)(234,484)(235,469)(236,471)(237,470)(238,473)(239,472)(240,474)(241,477)(242,476)(243,475)(244,352)(245,354)(246,353)(247,356)(248,355)(249,357)(250,360)(251,359)(252,358)(253,370)(254,372)(255,371)(256,374)(257,373)(258,375)(259,378)(260,377)(261,376)(262,361)(263,363)(264,362)(265,365)(266,364)(267,366)(268,369)(269,368)(270,367)(271,325)(272,327)(273,326)(274,329)(275,328)(276,330)(277,333)(278,332)(279,331)(280,343)(281,345)(282,344)(283,347)(284,346)(285,348)(286,351)(287,350)(288,349)(289,334)(290,336)(291,335)(292,338)(293,337)(294,339)(295,342)(296,341)(297,340)(298,379)(299,381)(300,380)(301,383)(302,382)(303,384)(304,387)(305,386)(306,385)(307,397)(308,399)(309,398)(310,401)(311,400)(312,402)(313,405)(314,404)(315,403)(316,388)(317,390)(318,389)(319,392)(320,391)(321,393)(322,396)(323,395)(324,394);;
s3 := ( 1,496)( 2,498)( 3,497)( 4,499)( 5,501)( 6,500)( 7,502)( 8,504)( 9,503)( 10,487)( 11,489)( 12,488)( 13,490)( 14,492)( 15,491)( 16,493)( 17,495)( 18,494)( 19,505)( 20,507)( 21,506)( 22,508)( 23,510)( 24,509)( 25,511)( 26,513)( 27,512)( 28,550)( 29,552)( 30,551)( 31,553)( 32,555)( 33,554)( 34,556)( 35,558)( 36,557)( 37,541)( 38,543)( 39,542)( 40,544)( 41,546)( 42,545)( 43,547)( 44,549)( 45,548)( 46,559)( 47,561)( 48,560)( 49,562)( 50,564)( 51,563)( 52,565)( 53,567)( 54,566)( 55,523)( 56,525)( 57,524)( 58,526)( 59,528)( 60,527)( 61,529)( 62,531)( 63,530)( 64,514)( 65,516)( 66,515)( 67,517)( 68,519)( 69,518)( 70,520)( 71,522)( 72,521)( 73,532)( 74,534)( 75,533)( 76,535)( 77,537)( 78,536)( 79,538)( 80,540)( 81,539)( 82,577)( 83,579)( 84,578)( 85,580)( 86,582)( 87,581)( 88,583)( 89,585)( 90,584)( 91,568)( 92,570)( 93,569)( 94,571)( 95,573)( 96,572)( 97,574)( 98,576)( 99,575)(100,586)(101,588)(102,587)(103,589)(104,591)(105,590)(106,592)(107,594)(108,593)(109,631)(110,633)(111,632)(112,634)(113,636)(114,635)(115,637)(116,639)(117,638)(118,622)(119,624)(120,623)(121,625)(122,627)(123,626)(124,628)(125,630)(126,629)(127,640)(128,642)(129,641)(130,643)(131,645)(132,644)(133,646)(134,648)(135,647)(136,604)(137,606)(138,605)(139,607)(140,609)(141,608)(142,610)(143,612)(144,611)(145,595)(146,597)(147,596)(148,598)(149,600)(150,599)(151,601)(152,603)(153,602)(154,613)(155,615)(156,614)(157,616)(158,618)(159,617)(160,619)(161,621)(162,620)(163,415)(164,417)(165,416)(166,418)(167,420)(168,419)(169,421)(170,423)(171,422)(172,406)(173,408)(174,407)(175,409)(176,411)(177,410)(178,412)(179,414)(180,413)(181,424)(182,426)(183,425)(184,427)(185,429)(186,428)(187,430)(188,432)(189,431)(190,469)(191,471)(192,470)(193,472)(194,474)(195,473)(196,475)(197,477)(198,476)(199,460)(200,462)(201,461)(202,463)(203,465)(204,464)(205,466)(206,468)(207,467)(208,478)(209,480)(210,479)(211,481)(212,483)(213,482)(214,484)(215,486)(216,485)(217,442)(218,444)(219,443)(220,445)(221,447)(222,446)(223,448)(224,450)(225,449)(226,433)(227,435)(228,434)(229,436)(230,438)(231,437)(232,439)(233,441)(234,440)(235,451)(236,453)(237,452)(238,454)(239,456)(240,455)(241,457)(242,459)(243,458)(244,334)(245,336)(246,335)(247,337)(248,339)(249,338)(250,340)(251,342)(252,341)(253,325)(254,327)(255,326)(256,328)(257,330)(258,329)(259,331)(260,333)(261,332)(262,343)(263,345)(264,344)(265,346)(266,348)(267,347)(268,349)(269,351)(270,350)(271,388)(272,390)(273,389)(274,391)(275,393)(276,392)(277,394)(278,396)(279,395)(280,379)(281,381)(282,380)(283,382)(284,384)(285,383)(286,385)(287,387)(288,386)(289,397)(290,399)(291,398)(292,400)(293,402)(294,401)(295,403)(296,405)(297,404)(298,361)(299,363)(300,362)(301,364)(302,366)(303,365)(304,367)(305,369)(306,368)(307,352)(308,354)(309,353)(310,355)(311,357)(312,356)(313,358)(314,360)(315,359)(316,370)(317,372)(318,371)(319,373)(320,375)(321,374)(322,376)(323,378)(324,377);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(648)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(110,111)(112,115)(113,117)(114,116)(119,120)(121,124)(122,126)(123,125)(128,129)(130,133)(131,135)(132,134)(137,138)(139,142)(140,144)(141,143)(146,147)(148,151)(149,153)(150,152)(155,156)(157,160)(158,162)(159,161)(163,244)(164,246)(165,245)(166,250)(167,252)(168,251)(169,247)(170,249)(171,248)(172,253)(173,255)(174,254)(175,259)(176,261)(177,260)(178,256)(179,258)(180,257)(181,262)(182,264)(183,263)(184,268)(185,270)(186,269)(187,265)(188,267)(189,266)(190,271)(191,273)(192,272)(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,280)(200,282)(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)(208,289)(209,291)(210,290)(211,295)(212,297)(213,296)(214,292)(215,294)(216,293)(217,298)(218,300)(219,299)(220,304)(221,306)(222,305)(223,301)(224,303)(225,302)(226,307)(227,309)(228,308)(229,313)(230,315)(231,314)(232,310)(233,312)(234,311)(235,316)(236,318)(237,317)(238,322)(239,324)(240,323)(241,319)(242,321)(243,320)(325,406)(326,408)(327,407)(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)(334,415)(335,417)(336,416)(337,421)(338,423)(339,422)(340,418)(341,420)(342,419)(343,424)(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)(352,433)(353,435)(354,434)(355,439)(356,441)(357,440)(358,436)(359,438)(360,437)(361,442)(362,444)(363,443)(364,448)(365,450)(366,449)(367,445)(368,447)(369,446)(370,451)(371,453)(372,452)(373,457)(374,459)(375,458)(376,454)(377,456)(378,455)(379,460)(380,462)(381,461)(382,466)(383,468)(384,467)(385,463)(386,465)(387,464)(388,469)(389,471)(390,470)(391,475)(392,477)(393,476)(394,472)(395,474)(396,473)(397,478)(398,480)(399,479)(400,484)(401,486)(402,485)(403,481)(404,483)(405,482)(488,489)(490,493)(491,495)(492,494)(497,498)(499,502)(500,504)(501,503)(506,507)(508,511)(509,513)(510,512)(515,516)(517,520)(518,522)(519,521)(524,525)(526,529)(527,531)(528,530)(533,534)(535,538)(536,540)(537,539)(542,543)(544,547)(545,549)(546,548)(551,552)(553,556)(554,558)(555,557)(560,561)(562,565)(563,567)(564,566)(569,570)(571,574)(572,576)(573,575)(578,579)(580,583)(581,585)(582,584)(587,588)(589,592)(590,594)(591,593)(596,597)(598,601)(599,603)(600,602)(605,606)(607,610)(608,612)(609,611)(614,615)(616,619)(617,621)(618,620)(623,624)(625,628)(626,630)(627,629)(632,633)(634,637)(635,639)(636,638)(641,642)(643,646)(644,648)(645,647);
s1 := Sym(648)!( 1,328)( 2,329)( 3,330)( 4,325)( 5,326)( 6,327)( 7,331)( 8,332)( 9,333)( 10,337)( 11,338)( 12,339)( 13,334)( 14,335)( 15,336)( 16,340)( 17,341)( 18,342)( 19,346)( 20,347)( 21,348)( 22,343)( 23,344)( 24,345)( 25,349)( 26,350)( 27,351)( 28,382)( 29,383)( 30,384)( 31,379)( 32,380)( 33,381)( 34,385)( 35,386)( 36,387)( 37,391)( 38,392)( 39,393)( 40,388)( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,400)( 47,401)( 48,402)( 49,397)( 50,398)( 51,399)( 52,403)( 53,404)( 54,405)( 55,355)( 56,356)( 57,357)( 58,352)( 59,353)( 60,354)( 61,358)( 62,359)( 63,360)( 64,364)( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)( 72,369)( 73,373)( 74,374)( 75,375)( 76,370)( 77,371)( 78,372)( 79,376)( 80,377)( 81,378)( 82,409)( 83,410)( 84,411)( 85,406)( 86,407)( 87,408)( 88,412)( 89,413)( 90,414)( 91,418)( 92,419)( 93,420)( 94,415)( 95,416)( 96,417)( 97,421)( 98,422)( 99,423)(100,427)(101,428)(102,429)(103,424)(104,425)(105,426)(106,430)(107,431)(108,432)(109,463)(110,464)(111,465)(112,460)(113,461)(114,462)(115,466)(116,467)(117,468)(118,472)(119,473)(120,474)(121,469)(122,470)(123,471)(124,475)(125,476)(126,477)(127,481)(128,482)(129,483)(130,478)(131,479)(132,480)(133,484)(134,485)(135,486)(136,436)(137,437)(138,438)(139,433)(140,434)(141,435)(142,439)(143,440)(144,441)(145,445)(146,446)(147,447)(148,442)(149,443)(150,444)(151,448)(152,449)(153,450)(154,454)(155,455)(156,456)(157,451)(158,452)(159,453)(160,457)(161,458)(162,459)(163,571)(164,572)(165,573)(166,568)(167,569)(168,570)(169,574)(170,575)(171,576)(172,580)(173,581)(174,582)(175,577)(176,578)(177,579)(178,583)(179,584)(180,585)(181,589)(182,590)(183,591)(184,586)(185,587)(186,588)(187,592)(188,593)(189,594)(190,625)(191,626)(192,627)(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,634)(200,635)(201,636)(202,631)(203,632)(204,633)(205,637)(206,638)(207,639)(208,643)(209,644)(210,645)(211,640)(212,641)(213,642)(214,646)(215,647)(216,648)(217,598)(218,599)(219,600)(220,595)(221,596)(222,597)(223,601)(224,602)(225,603)(226,607)(227,608)(228,609)(229,604)(230,605)(231,606)(232,610)(233,611)(234,612)(235,616)(236,617)(237,618)(238,613)(239,614)(240,615)(241,619)(242,620)(243,621)(244,490)(245,491)(246,492)(247,487)(248,488)(249,489)(250,493)(251,494)(252,495)(253,499)(254,500)(255,501)(256,496)(257,497)(258,498)(259,502)(260,503)(261,504)(262,508)(263,509)(264,510)(265,505)(266,506)(267,507)(268,511)(269,512)(270,513)(271,544)(272,545)(273,546)(274,541)(275,542)(276,543)(277,547)(278,548)(279,549)(280,553)(281,554)(282,555)(283,550)(284,551)(285,552)(286,556)(287,557)(288,558)(289,562)(290,563)(291,564)(292,559)(293,560)(294,561)(295,565)(296,566)(297,567)(298,517)(299,518)(300,519)(301,514)(302,515)(303,516)(304,520)(305,521)(306,522)(307,526)(308,527)(309,528)(310,523)(311,524)(312,525)(313,529)(314,530)(315,531)(316,535)(317,536)(318,537)(319,532)(320,533)(321,534)(322,538)(323,539)(324,540);
s2 := Sym(648)!( 1,514)( 2,516)( 3,515)( 4,518)( 5,517)( 6,519)( 7,522)( 8,521)( 9,520)( 10,532)( 11,534)( 12,533)( 13,536)( 14,535)( 15,537)( 16,540)( 17,539)( 18,538)( 19,523)( 20,525)( 21,524)( 22,527)( 23,526)( 24,528)( 25,531)( 26,530)( 27,529)( 28,487)( 29,489)( 30,488)( 31,491)( 32,490)( 33,492)( 34,495)( 35,494)( 36,493)( 37,505)( 38,507)( 39,506)( 40,509)( 41,508)( 42,510)( 43,513)( 44,512)( 45,511)( 46,496)( 47,498)( 48,497)( 49,500)( 50,499)( 51,501)( 52,504)( 53,503)( 54,502)( 55,541)( 56,543)( 57,542)( 58,545)( 59,544)( 60,546)( 61,549)( 62,548)( 63,547)( 64,559)( 65,561)( 66,560)( 67,563)( 68,562)( 69,564)( 70,567)( 71,566)( 72,565)( 73,550)( 74,552)( 75,551)( 76,554)( 77,553)( 78,555)( 79,558)( 80,557)( 81,556)( 82,595)( 83,597)( 84,596)( 85,599)( 86,598)( 87,600)( 88,603)( 89,602)( 90,601)( 91,613)( 92,615)( 93,614)( 94,617)( 95,616)( 96,618)( 97,621)( 98,620)( 99,619)(100,604)(101,606)(102,605)(103,608)(104,607)(105,609)(106,612)(107,611)(108,610)(109,568)(110,570)(111,569)(112,572)(113,571)(114,573)(115,576)(116,575)(117,574)(118,586)(119,588)(120,587)(121,590)(122,589)(123,591)(124,594)(125,593)(126,592)(127,577)(128,579)(129,578)(130,581)(131,580)(132,582)(133,585)(134,584)(135,583)(136,622)(137,624)(138,623)(139,626)(140,625)(141,627)(142,630)(143,629)(144,628)(145,640)(146,642)(147,641)(148,644)(149,643)(150,645)(151,648)(152,647)(153,646)(154,631)(155,633)(156,632)(157,635)(158,634)(159,636)(160,639)(161,638)(162,637)(163,433)(164,435)(165,434)(166,437)(167,436)(168,438)(169,441)(170,440)(171,439)(172,451)(173,453)(174,452)(175,455)(176,454)(177,456)(178,459)(179,458)(180,457)(181,442)(182,444)(183,443)(184,446)(185,445)(186,447)(187,450)(188,449)(189,448)(190,406)(191,408)(192,407)(193,410)(194,409)(195,411)(196,414)(197,413)(198,412)(199,424)(200,426)(201,425)(202,428)(203,427)(204,429)(205,432)(206,431)(207,430)(208,415)(209,417)(210,416)(211,419)(212,418)(213,420)(214,423)(215,422)(216,421)(217,460)(218,462)(219,461)(220,464)(221,463)(222,465)(223,468)(224,467)(225,466)(226,478)(227,480)(228,479)(229,482)(230,481)(231,483)(232,486)(233,485)(234,484)(235,469)(236,471)(237,470)(238,473)(239,472)(240,474)(241,477)(242,476)(243,475)(244,352)(245,354)(246,353)(247,356)(248,355)(249,357)(250,360)(251,359)(252,358)(253,370)(254,372)(255,371)(256,374)(257,373)(258,375)(259,378)(260,377)(261,376)(262,361)(263,363)(264,362)(265,365)(266,364)(267,366)(268,369)(269,368)(270,367)(271,325)(272,327)(273,326)(274,329)(275,328)(276,330)(277,333)(278,332)(279,331)(280,343)(281,345)(282,344)(283,347)(284,346)(285,348)(286,351)(287,350)(288,349)(289,334)(290,336)(291,335)(292,338)(293,337)(294,339)(295,342)(296,341)(297,340)(298,379)(299,381)(300,380)(301,383)(302,382)(303,384)(304,387)(305,386)(306,385)(307,397)(308,399)(309,398)(310,401)(311,400)(312,402)(313,405)(314,404)(315,403)(316,388)(317,390)(318,389)(319,392)(320,391)(321,393)(322,396)(323,395)(324,394);
s3 := Sym(648)!( 1,496)( 2,498)( 3,497)( 4,499)( 5,501)( 6,500)( 7,502)( 8,504)( 9,503)( 10,487)( 11,489)( 12,488)( 13,490)( 14,492)( 15,491)( 16,493)( 17,495)( 18,494)( 19,505)( 20,507)( 21,506)( 22,508)( 23,510)( 24,509)( 25,511)( 26,513)( 27,512)( 28,550)( 29,552)( 30,551)( 31,553)( 32,555)( 33,554)( 34,556)( 35,558)( 36,557)( 37,541)( 38,543)( 39,542)( 40,544)( 41,546)( 42,545)( 43,547)( 44,549)( 45,548)( 46,559)( 47,561)( 48,560)( 49,562)( 50,564)( 51,563)( 52,565)( 53,567)( 54,566)( 55,523)( 56,525)( 57,524)( 58,526)( 59,528)( 60,527)( 61,529)( 62,531)( 63,530)( 64,514)( 65,516)( 66,515)( 67,517)( 68,519)( 69,518)( 70,520)( 71,522)( 72,521)( 73,532)( 74,534)( 75,533)( 76,535)( 77,537)( 78,536)( 79,538)( 80,540)( 81,539)( 82,577)( 83,579)( 84,578)( 85,580)( 86,582)( 87,581)( 88,583)( 89,585)( 90,584)( 91,568)( 92,570)( 93,569)( 94,571)( 95,573)( 96,572)( 97,574)( 98,576)( 99,575)(100,586)(101,588)(102,587)(103,589)(104,591)(105,590)(106,592)(107,594)(108,593)(109,631)(110,633)(111,632)(112,634)(113,636)(114,635)(115,637)(116,639)(117,638)(118,622)(119,624)(120,623)(121,625)(122,627)(123,626)(124,628)(125,630)(126,629)(127,640)(128,642)(129,641)(130,643)(131,645)(132,644)(133,646)(134,648)(135,647)(136,604)(137,606)(138,605)(139,607)(140,609)(141,608)(142,610)(143,612)(144,611)(145,595)(146,597)(147,596)(148,598)(149,600)(150,599)(151,601)(152,603)(153,602)(154,613)(155,615)(156,614)(157,616)(158,618)(159,617)(160,619)(161,621)(162,620)(163,415)(164,417)(165,416)(166,418)(167,420)(168,419)(169,421)(170,423)(171,422)(172,406)(173,408)(174,407)(175,409)(176,411)(177,410)(178,412)(179,414)(180,413)(181,424)(182,426)(183,425)(184,427)(185,429)(186,428)(187,430)(188,432)(189,431)(190,469)(191,471)(192,470)(193,472)(194,474)(195,473)(196,475)(197,477)(198,476)(199,460)(200,462)(201,461)(202,463)(203,465)(204,464)(205,466)(206,468)(207,467)(208,478)(209,480)(210,479)(211,481)(212,483)(213,482)(214,484)(215,486)(216,485)(217,442)(218,444)(219,443)(220,445)(221,447)(222,446)(223,448)(224,450)(225,449)(226,433)(227,435)(228,434)(229,436)(230,438)(231,437)(232,439)(233,441)(234,440)(235,451)(236,453)(237,452)(238,454)(239,456)(240,455)(241,457)(242,459)(243,458)(244,334)(245,336)(246,335)(247,337)(248,339)(249,338)(250,340)(251,342)(252,341)(253,325)(254,327)(255,326)(256,328)(257,330)(258,329)(259,331)(260,333)(261,332)(262,343)(263,345)(264,344)(265,346)(266,348)(267,347)(268,349)(269,351)(270,350)(271,388)(272,390)(273,389)(274,391)(275,393)(276,392)(277,394)(278,396)(279,395)(280,379)(281,381)(282,380)(283,382)(284,384)(285,383)(286,385)(287,387)(288,386)(289,397)(290,399)(291,398)(292,400)(293,402)(294,401)(295,403)(296,405)(297,404)(298,361)(299,363)(300,362)(301,364)(302,366)(303,365)(304,367)(305,369)(306,368)(307,352)(308,354)(309,353)(310,355)(311,357)(312,356)(313,358)(314,360)(315,359)(316,370)(317,372)(318,371)(319,373)(320,375)(321,374)(322,376)(323,378)(324,377);
poly := sub<Sym(648)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*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 >;
References : None.
to this polytope