Polytope of Type {12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3}*1296b
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {12,3}
Number of vertices, edges, etc : 216, 324, 54
Order of s0s1s2 : 18
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,3}*648
27-fold quotients : {4,3}*48
54-fold quotients : {4,3}*24
108-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,379)( 2,381)( 3,380)( 4,385)( 5,387)( 6,386)( 7,382)( 8,384)
( 9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)( 16,391)
( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)( 24,404)
( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)( 32,414)
( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)( 40,421)
( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)( 48,425)
( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)( 56,327)
( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)( 64,334)
( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)( 72,338)
( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)( 80,348)
( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)( 88,355)
( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)
( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)
(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)(112,493)
(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)(120,497)
(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)(128,507)
(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)(136,514)
(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)(144,518)
(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)(152,528)
(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)(160,535)
(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)(168,440)
(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)(176,450)
(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)(184,457)
(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)(192,461)
(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)(200,471)
(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)(208,478)
(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)(216,482)
(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)(224,600)
(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)(232,607)
(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)(240,620)
(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)(248,630)
(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)(256,637)
(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)(264,641)
(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)(272,543)
(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)(280,550)
(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)(288,554)
(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)(296,564)
(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)(304,571)
(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)(312,584)
(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)(320,594)
(321,593)(322,589)(323,591)(324,590);;
s1 := ( 1, 2)( 4, 20)( 5, 19)( 6, 21)( 7, 11)( 8, 10)( 9, 12)( 13, 26)
( 14, 25)( 15, 27)( 16, 17)( 22, 23)( 28, 56)( 29, 55)( 30, 57)( 31, 74)
( 32, 73)( 33, 75)( 34, 65)( 35, 64)( 36, 66)( 37, 62)( 38, 61)( 39, 63)
( 40, 80)( 41, 79)( 42, 81)( 43, 71)( 44, 70)( 45, 72)( 46, 59)( 47, 58)
( 48, 60)( 49, 77)( 50, 76)( 51, 78)( 52, 68)( 53, 67)( 54, 69)( 82, 83)
( 85,101)( 86,100)( 87,102)( 88, 92)( 89, 91)( 90, 93)( 94,107)( 95,106)
( 96,108)( 97, 98)(103,104)(109,218)(110,217)(111,219)(112,236)(113,235)
(114,237)(115,227)(116,226)(117,228)(118,224)(119,223)(120,225)(121,242)
(122,241)(123,243)(124,233)(125,232)(126,234)(127,221)(128,220)(129,222)
(130,239)(131,238)(132,240)(133,230)(134,229)(135,231)(136,272)(137,271)
(138,273)(139,290)(140,289)(141,291)(142,281)(143,280)(144,282)(145,278)
(146,277)(147,279)(148,296)(149,295)(150,297)(151,287)(152,286)(153,288)
(154,275)(155,274)(156,276)(157,293)(158,292)(159,294)(160,284)(161,283)
(162,285)(163,245)(164,244)(165,246)(166,263)(167,262)(168,264)(169,254)
(170,253)(171,255)(172,251)(173,250)(174,252)(175,269)(176,268)(177,270)
(178,260)(179,259)(180,261)(181,248)(182,247)(183,249)(184,266)(185,265)
(186,267)(187,257)(188,256)(189,258)(190,299)(191,298)(192,300)(193,317)
(194,316)(195,318)(196,308)(197,307)(198,309)(199,305)(200,304)(201,306)
(202,323)(203,322)(204,324)(205,314)(206,313)(207,315)(208,302)(209,301)
(210,303)(211,320)(212,319)(213,321)(214,311)(215,310)(216,312)(325,326)
(328,344)(329,343)(330,345)(331,335)(332,334)(333,336)(337,350)(338,349)
(339,351)(340,341)(346,347)(352,380)(353,379)(354,381)(355,398)(356,397)
(357,399)(358,389)(359,388)(360,390)(361,386)(362,385)(363,387)(364,404)
(365,403)(366,405)(367,395)(368,394)(369,396)(370,383)(371,382)(372,384)
(373,401)(374,400)(375,402)(376,392)(377,391)(378,393)(406,407)(409,425)
(410,424)(411,426)(412,416)(413,415)(414,417)(418,431)(419,430)(420,432)
(421,422)(427,428)(433,542)(434,541)(435,543)(436,560)(437,559)(438,561)
(439,551)(440,550)(441,552)(442,548)(443,547)(444,549)(445,566)(446,565)
(447,567)(448,557)(449,556)(450,558)(451,545)(452,544)(453,546)(454,563)
(455,562)(456,564)(457,554)(458,553)(459,555)(460,596)(461,595)(462,597)
(463,614)(464,613)(465,615)(466,605)(467,604)(468,606)(469,602)(470,601)
(471,603)(472,620)(473,619)(474,621)(475,611)(476,610)(477,612)(478,599)
(479,598)(480,600)(481,617)(482,616)(483,618)(484,608)(485,607)(486,609)
(487,569)(488,568)(489,570)(490,587)(491,586)(492,588)(493,578)(494,577)
(495,579)(496,575)(497,574)(498,576)(499,593)(500,592)(501,594)(502,584)
(503,583)(504,585)(505,572)(506,571)(507,573)(508,590)(509,589)(510,591)
(511,581)(512,580)(513,582)(514,623)(515,622)(516,624)(517,641)(518,640)
(519,642)(520,632)(521,631)(522,633)(523,629)(524,628)(525,630)(526,647)
(527,646)(528,648)(529,638)(530,637)(531,639)(532,626)(533,625)(534,627)
(535,644)(536,643)(537,645)(538,635)(539,634)(540,636);;
s2 := ( 1,226)( 2,232)( 3,229)( 4,228)( 5,234)( 6,231)( 7,227)( 8,233)
( 9,230)( 10,217)( 11,223)( 12,220)( 13,219)( 14,225)( 15,222)( 16,218)
( 17,224)( 18,221)( 19,235)( 20,241)( 21,238)( 22,237)( 23,243)( 24,240)
( 25,236)( 26,242)( 27,239)( 28,307)( 29,313)( 30,310)( 31,309)( 32,315)
( 33,312)( 34,308)( 35,314)( 36,311)( 37,298)( 38,304)( 39,301)( 40,300)
( 41,306)( 42,303)( 43,299)( 44,305)( 45,302)( 46,316)( 47,322)( 48,319)
( 49,318)( 50,324)( 51,321)( 52,317)( 53,323)( 54,320)( 55,280)( 56,286)
( 57,283)( 58,282)( 59,288)( 60,285)( 61,281)( 62,287)( 63,284)( 64,271)
( 65,277)( 66,274)( 67,273)( 68,279)( 69,276)( 70,272)( 71,278)( 72,275)
( 73,289)( 74,295)( 75,292)( 76,291)( 77,297)( 78,294)( 79,290)( 80,296)
( 81,293)( 82,253)( 83,259)( 84,256)( 85,255)( 86,261)( 87,258)( 88,254)
( 89,260)( 90,257)( 91,244)( 92,250)( 93,247)( 94,246)( 95,252)( 96,249)
( 97,245)( 98,251)( 99,248)(100,262)(101,268)(102,265)(103,264)(104,270)
(105,267)(106,263)(107,269)(108,266)(109,118)(110,124)(111,121)(112,120)
(113,126)(114,123)(115,119)(116,125)(117,122)(128,133)(129,130)(131,135)
(136,199)(137,205)(138,202)(139,201)(140,207)(141,204)(142,200)(143,206)
(144,203)(145,190)(146,196)(147,193)(148,192)(149,198)(150,195)(151,191)
(152,197)(153,194)(154,208)(155,214)(156,211)(157,210)(158,216)(159,213)
(160,209)(161,215)(162,212)(163,172)(164,178)(165,175)(166,174)(167,180)
(168,177)(169,173)(170,179)(171,176)(182,187)(183,184)(185,189)(325,550)
(326,556)(327,553)(328,552)(329,558)(330,555)(331,551)(332,557)(333,554)
(334,541)(335,547)(336,544)(337,543)(338,549)(339,546)(340,542)(341,548)
(342,545)(343,559)(344,565)(345,562)(346,561)(347,567)(348,564)(349,560)
(350,566)(351,563)(352,631)(353,637)(354,634)(355,633)(356,639)(357,636)
(358,632)(359,638)(360,635)(361,622)(362,628)(363,625)(364,624)(365,630)
(366,627)(367,623)(368,629)(369,626)(370,640)(371,646)(372,643)(373,642)
(374,648)(375,645)(376,641)(377,647)(378,644)(379,604)(380,610)(381,607)
(382,606)(383,612)(384,609)(385,605)(386,611)(387,608)(388,595)(389,601)
(390,598)(391,597)(392,603)(393,600)(394,596)(395,602)(396,599)(397,613)
(398,619)(399,616)(400,615)(401,621)(402,618)(403,614)(404,620)(405,617)
(406,577)(407,583)(408,580)(409,579)(410,585)(411,582)(412,578)(413,584)
(414,581)(415,568)(416,574)(417,571)(418,570)(419,576)(420,573)(421,569)
(422,575)(423,572)(424,586)(425,592)(426,589)(427,588)(428,594)(429,591)
(430,587)(431,593)(432,590)(433,442)(434,448)(435,445)(436,444)(437,450)
(438,447)(439,443)(440,449)(441,446)(452,457)(453,454)(455,459)(460,523)
(461,529)(462,526)(463,525)(464,531)(465,528)(466,524)(467,530)(468,527)
(469,514)(470,520)(471,517)(472,516)(473,522)(474,519)(475,515)(476,521)
(477,518)(478,532)(479,538)(480,535)(481,534)(482,540)(483,537)(484,533)
(485,539)(486,536)(487,496)(488,502)(489,499)(490,498)(491,504)(492,501)
(493,497)(494,503)(495,500)(506,511)(507,508)(509,513);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(648)!( 1,379)( 2,381)( 3,380)( 4,385)( 5,387)( 6,386)( 7,382)
( 8,384)( 9,383)( 10,388)( 11,390)( 12,389)( 13,394)( 14,396)( 15,395)
( 16,391)( 17,393)( 18,392)( 19,397)( 20,399)( 21,398)( 22,403)( 23,405)
( 24,404)( 25,400)( 26,402)( 27,401)( 28,406)( 29,408)( 30,407)( 31,412)
( 32,414)( 33,413)( 34,409)( 35,411)( 36,410)( 37,415)( 38,417)( 39,416)
( 40,421)( 41,423)( 42,422)( 43,418)( 44,420)( 45,419)( 46,424)( 47,426)
( 48,425)( 49,430)( 50,432)( 51,431)( 52,427)( 53,429)( 54,428)( 55,325)
( 56,327)( 57,326)( 58,331)( 59,333)( 60,332)( 61,328)( 62,330)( 63,329)
( 64,334)( 65,336)( 66,335)( 67,340)( 68,342)( 69,341)( 70,337)( 71,339)
( 72,338)( 73,343)( 74,345)( 75,344)( 76,349)( 77,351)( 78,350)( 79,346)
( 80,348)( 81,347)( 82,352)( 83,354)( 84,353)( 85,358)( 86,360)( 87,359)
( 88,355)( 89,357)( 90,356)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)
( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)
(104,378)(105,377)(106,373)(107,375)(108,374)(109,487)(110,489)(111,488)
(112,493)(113,495)(114,494)(115,490)(116,492)(117,491)(118,496)(119,498)
(120,497)(121,502)(122,504)(123,503)(124,499)(125,501)(126,500)(127,505)
(128,507)(129,506)(130,511)(131,513)(132,512)(133,508)(134,510)(135,509)
(136,514)(137,516)(138,515)(139,520)(140,522)(141,521)(142,517)(143,519)
(144,518)(145,523)(146,525)(147,524)(148,529)(149,531)(150,530)(151,526)
(152,528)(153,527)(154,532)(155,534)(156,533)(157,538)(158,540)(159,539)
(160,535)(161,537)(162,536)(163,433)(164,435)(165,434)(166,439)(167,441)
(168,440)(169,436)(170,438)(171,437)(172,442)(173,444)(174,443)(175,448)
(176,450)(177,449)(178,445)(179,447)(180,446)(181,451)(182,453)(183,452)
(184,457)(185,459)(186,458)(187,454)(188,456)(189,455)(190,460)(191,462)
(192,461)(193,466)(194,468)(195,467)(196,463)(197,465)(198,464)(199,469)
(200,471)(201,470)(202,475)(203,477)(204,476)(205,472)(206,474)(207,473)
(208,478)(209,480)(210,479)(211,484)(212,486)(213,485)(214,481)(215,483)
(216,482)(217,595)(218,597)(219,596)(220,601)(221,603)(222,602)(223,598)
(224,600)(225,599)(226,604)(227,606)(228,605)(229,610)(230,612)(231,611)
(232,607)(233,609)(234,608)(235,613)(236,615)(237,614)(238,619)(239,621)
(240,620)(241,616)(242,618)(243,617)(244,622)(245,624)(246,623)(247,628)
(248,630)(249,629)(250,625)(251,627)(252,626)(253,631)(254,633)(255,632)
(256,637)(257,639)(258,638)(259,634)(260,636)(261,635)(262,640)(263,642)
(264,641)(265,646)(266,648)(267,647)(268,643)(269,645)(270,644)(271,541)
(272,543)(273,542)(274,547)(275,549)(276,548)(277,544)(278,546)(279,545)
(280,550)(281,552)(282,551)(283,556)(284,558)(285,557)(286,553)(287,555)
(288,554)(289,559)(290,561)(291,560)(292,565)(293,567)(294,566)(295,562)
(296,564)(297,563)(298,568)(299,570)(300,569)(301,574)(302,576)(303,575)
(304,571)(305,573)(306,572)(307,577)(308,579)(309,578)(310,583)(311,585)
(312,584)(313,580)(314,582)(315,581)(316,586)(317,588)(318,587)(319,592)
(320,594)(321,593)(322,589)(323,591)(324,590);
s1 := Sym(648)!( 1, 2)( 4, 20)( 5, 19)( 6, 21)( 7, 11)( 8, 10)( 9, 12)
( 13, 26)( 14, 25)( 15, 27)( 16, 17)( 22, 23)( 28, 56)( 29, 55)( 30, 57)
( 31, 74)( 32, 73)( 33, 75)( 34, 65)( 35, 64)( 36, 66)( 37, 62)( 38, 61)
( 39, 63)( 40, 80)( 41, 79)( 42, 81)( 43, 71)( 44, 70)( 45, 72)( 46, 59)
( 47, 58)( 48, 60)( 49, 77)( 50, 76)( 51, 78)( 52, 68)( 53, 67)( 54, 69)
( 82, 83)( 85,101)( 86,100)( 87,102)( 88, 92)( 89, 91)( 90, 93)( 94,107)
( 95,106)( 96,108)( 97, 98)(103,104)(109,218)(110,217)(111,219)(112,236)
(113,235)(114,237)(115,227)(116,226)(117,228)(118,224)(119,223)(120,225)
(121,242)(122,241)(123,243)(124,233)(125,232)(126,234)(127,221)(128,220)
(129,222)(130,239)(131,238)(132,240)(133,230)(134,229)(135,231)(136,272)
(137,271)(138,273)(139,290)(140,289)(141,291)(142,281)(143,280)(144,282)
(145,278)(146,277)(147,279)(148,296)(149,295)(150,297)(151,287)(152,286)
(153,288)(154,275)(155,274)(156,276)(157,293)(158,292)(159,294)(160,284)
(161,283)(162,285)(163,245)(164,244)(165,246)(166,263)(167,262)(168,264)
(169,254)(170,253)(171,255)(172,251)(173,250)(174,252)(175,269)(176,268)
(177,270)(178,260)(179,259)(180,261)(181,248)(182,247)(183,249)(184,266)
(185,265)(186,267)(187,257)(188,256)(189,258)(190,299)(191,298)(192,300)
(193,317)(194,316)(195,318)(196,308)(197,307)(198,309)(199,305)(200,304)
(201,306)(202,323)(203,322)(204,324)(205,314)(206,313)(207,315)(208,302)
(209,301)(210,303)(211,320)(212,319)(213,321)(214,311)(215,310)(216,312)
(325,326)(328,344)(329,343)(330,345)(331,335)(332,334)(333,336)(337,350)
(338,349)(339,351)(340,341)(346,347)(352,380)(353,379)(354,381)(355,398)
(356,397)(357,399)(358,389)(359,388)(360,390)(361,386)(362,385)(363,387)
(364,404)(365,403)(366,405)(367,395)(368,394)(369,396)(370,383)(371,382)
(372,384)(373,401)(374,400)(375,402)(376,392)(377,391)(378,393)(406,407)
(409,425)(410,424)(411,426)(412,416)(413,415)(414,417)(418,431)(419,430)
(420,432)(421,422)(427,428)(433,542)(434,541)(435,543)(436,560)(437,559)
(438,561)(439,551)(440,550)(441,552)(442,548)(443,547)(444,549)(445,566)
(446,565)(447,567)(448,557)(449,556)(450,558)(451,545)(452,544)(453,546)
(454,563)(455,562)(456,564)(457,554)(458,553)(459,555)(460,596)(461,595)
(462,597)(463,614)(464,613)(465,615)(466,605)(467,604)(468,606)(469,602)
(470,601)(471,603)(472,620)(473,619)(474,621)(475,611)(476,610)(477,612)
(478,599)(479,598)(480,600)(481,617)(482,616)(483,618)(484,608)(485,607)
(486,609)(487,569)(488,568)(489,570)(490,587)(491,586)(492,588)(493,578)
(494,577)(495,579)(496,575)(497,574)(498,576)(499,593)(500,592)(501,594)
(502,584)(503,583)(504,585)(505,572)(506,571)(507,573)(508,590)(509,589)
(510,591)(511,581)(512,580)(513,582)(514,623)(515,622)(516,624)(517,641)
(518,640)(519,642)(520,632)(521,631)(522,633)(523,629)(524,628)(525,630)
(526,647)(527,646)(528,648)(529,638)(530,637)(531,639)(532,626)(533,625)
(534,627)(535,644)(536,643)(537,645)(538,635)(539,634)(540,636);
s2 := Sym(648)!( 1,226)( 2,232)( 3,229)( 4,228)( 5,234)( 6,231)( 7,227)
( 8,233)( 9,230)( 10,217)( 11,223)( 12,220)( 13,219)( 14,225)( 15,222)
( 16,218)( 17,224)( 18,221)( 19,235)( 20,241)( 21,238)( 22,237)( 23,243)
( 24,240)( 25,236)( 26,242)( 27,239)( 28,307)( 29,313)( 30,310)( 31,309)
( 32,315)( 33,312)( 34,308)( 35,314)( 36,311)( 37,298)( 38,304)( 39,301)
( 40,300)( 41,306)( 42,303)( 43,299)( 44,305)( 45,302)( 46,316)( 47,322)
( 48,319)( 49,318)( 50,324)( 51,321)( 52,317)( 53,323)( 54,320)( 55,280)
( 56,286)( 57,283)( 58,282)( 59,288)( 60,285)( 61,281)( 62,287)( 63,284)
( 64,271)( 65,277)( 66,274)( 67,273)( 68,279)( 69,276)( 70,272)( 71,278)
( 72,275)( 73,289)( 74,295)( 75,292)( 76,291)( 77,297)( 78,294)( 79,290)
( 80,296)( 81,293)( 82,253)( 83,259)( 84,256)( 85,255)( 86,261)( 87,258)
( 88,254)( 89,260)( 90,257)( 91,244)( 92,250)( 93,247)( 94,246)( 95,252)
( 96,249)( 97,245)( 98,251)( 99,248)(100,262)(101,268)(102,265)(103,264)
(104,270)(105,267)(106,263)(107,269)(108,266)(109,118)(110,124)(111,121)
(112,120)(113,126)(114,123)(115,119)(116,125)(117,122)(128,133)(129,130)
(131,135)(136,199)(137,205)(138,202)(139,201)(140,207)(141,204)(142,200)
(143,206)(144,203)(145,190)(146,196)(147,193)(148,192)(149,198)(150,195)
(151,191)(152,197)(153,194)(154,208)(155,214)(156,211)(157,210)(158,216)
(159,213)(160,209)(161,215)(162,212)(163,172)(164,178)(165,175)(166,174)
(167,180)(168,177)(169,173)(170,179)(171,176)(182,187)(183,184)(185,189)
(325,550)(326,556)(327,553)(328,552)(329,558)(330,555)(331,551)(332,557)
(333,554)(334,541)(335,547)(336,544)(337,543)(338,549)(339,546)(340,542)
(341,548)(342,545)(343,559)(344,565)(345,562)(346,561)(347,567)(348,564)
(349,560)(350,566)(351,563)(352,631)(353,637)(354,634)(355,633)(356,639)
(357,636)(358,632)(359,638)(360,635)(361,622)(362,628)(363,625)(364,624)
(365,630)(366,627)(367,623)(368,629)(369,626)(370,640)(371,646)(372,643)
(373,642)(374,648)(375,645)(376,641)(377,647)(378,644)(379,604)(380,610)
(381,607)(382,606)(383,612)(384,609)(385,605)(386,611)(387,608)(388,595)
(389,601)(390,598)(391,597)(392,603)(393,600)(394,596)(395,602)(396,599)
(397,613)(398,619)(399,616)(400,615)(401,621)(402,618)(403,614)(404,620)
(405,617)(406,577)(407,583)(408,580)(409,579)(410,585)(411,582)(412,578)
(413,584)(414,581)(415,568)(416,574)(417,571)(418,570)(419,576)(420,573)
(421,569)(422,575)(423,572)(424,586)(425,592)(426,589)(427,588)(428,594)
(429,591)(430,587)(431,593)(432,590)(433,442)(434,448)(435,445)(436,444)
(437,450)(438,447)(439,443)(440,449)(441,446)(452,457)(453,454)(455,459)
(460,523)(461,529)(462,526)(463,525)(464,531)(465,528)(466,524)(467,530)
(468,527)(469,514)(470,520)(471,517)(472,516)(473,522)(474,519)(475,515)
(476,521)(477,518)(478,532)(479,538)(480,535)(481,534)(482,540)(483,537)
(484,533)(485,539)(486,536)(487,496)(488,502)(489,499)(490,498)(491,504)
(492,501)(493,497)(494,503)(495,500)(506,511)(507,508)(509,513);
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, s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope