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