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.
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,
s3*s1*s2*s1*s2*s3*s1*s2*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, s3*s1*s2*s1*s2*s3*s1*s2*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