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Polytope of Type {18,12}

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