Polytope of Type {612}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {612}*1224
Also Known As : 612-gon, {612}. if this polytope has another name.
Group : SmallGroup(1224,27)
Rank : 2
Schlafli Type : {612}
Number of vertices, edges, etc : 612, 612
Order of s₀s₁ : 612
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {306}*612
   3-fold quotients : {204}*408
   4-fold quotients : {153}*306
   6-fold quotients : {102}*204
   9-fold quotients : {68}*136
   12-fold quotients : {51}*102
   17-fold quotients : {36}*72
   18-fold quotients : {34}*68
   34-fold quotients : {18}*36
   36-fold quotients : {17}*34
   51-fold quotients : {12}*24
   68-fold quotients : {9}*18
   102-fold quotients : {6}*12
   153-fold quotients : {4}*8
   204-fold quotients : {3}*6
   306-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 49)(  5, 51)(  6, 50)(  7, 46)(  8, 48)(  9, 47)( 10, 43)
( 11, 45)( 12, 44)( 13, 40)( 14, 42)( 15, 41)( 16, 37)( 17, 39)( 18, 38)
( 19, 34)( 20, 36)( 21, 35)( 22, 31)( 23, 33)( 24, 32)( 25, 28)( 26, 30)
( 27, 29)( 52,105)( 53,104)( 54,103)( 55,153)( 56,152)( 57,151)( 58,150)
( 59,149)( 60,148)( 61,147)( 62,146)( 63,145)( 64,144)( 65,143)( 66,142)
( 67,141)( 68,140)( 69,139)( 70,138)( 71,137)( 72,136)( 73,135)( 74,134)
( 75,133)( 76,132)( 77,131)( 78,130)( 79,129)( 80,128)( 81,127)( 82,126)
( 83,125)( 84,124)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)( 90,118)
( 91,117)( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)( 98,110)
( 99,109)(100,108)(101,107)(102,106)(155,156)(157,202)(158,204)(159,203)
(160,199)(161,201)(162,200)(163,196)(164,198)(165,197)(166,193)(167,195)
(168,194)(169,190)(170,192)(171,191)(172,187)(173,189)(174,188)(175,184)
(176,186)(177,185)(178,181)(179,183)(180,182)(205,258)(206,257)(207,256)
(208,306)(209,305)(210,304)(211,303)(212,302)(213,301)(214,300)(215,299)
(216,298)(217,297)(218,296)(219,295)(220,294)(221,293)(222,292)(223,291)
(224,290)(225,289)(226,288)(227,287)(228,286)(229,285)(230,284)(231,283)
(232,282)(233,281)(234,280)(235,279)(236,278)(237,277)(238,276)(239,275)
(240,274)(241,273)(242,272)(243,271)(244,270)(245,269)(246,268)(247,267)
(248,266)(249,265)(250,264)(251,263)(252,262)(253,261)(254,260)(255,259)
(307,460)(308,462)(309,461)(310,508)(311,510)(312,509)(313,505)(314,507)
(315,506)(316,502)(317,504)(318,503)(319,499)(320,501)(321,500)(322,496)
(323,498)(324,497)(325,493)(326,495)(327,494)(328,490)(329,492)(330,491)
(331,487)(332,489)(333,488)(334,484)(335,486)(336,485)(337,481)(338,483)
(339,482)(340,478)(341,480)(342,479)(343,475)(344,477)(345,476)(346,472)
(347,474)(348,473)(349,469)(350,471)(351,470)(352,466)(353,468)(354,467)
(355,463)(356,465)(357,464)(358,564)(359,563)(360,562)(361,612)(362,611)
(363,610)(364,609)(365,608)(366,607)(367,606)(368,605)(369,604)(370,603)
(371,602)(372,601)(373,600)(374,599)(375,598)(376,597)(377,596)(378,595)
(379,594)(380,593)(381,592)(382,591)(383,590)(384,589)(385,588)(386,587)
(387,586)(388,585)(389,584)(390,583)(391,582)(392,581)(393,580)(394,579)
(395,578)(396,577)(397,576)(398,575)(399,574)(400,573)(401,572)(402,571)
(403,570)(404,569)(405,568)(406,567)(407,566)(408,565)(409,513)(410,512)
(411,511)(412,561)(413,560)(414,559)(415,558)(416,557)(417,556)(418,555)
(419,554)(420,553)(421,552)(422,551)(423,550)(424,549)(425,548)(426,547)
(427,546)(428,545)(429,544)(430,543)(431,542)(432,541)(433,540)(434,539)
(435,538)(436,537)(437,536)(438,535)(439,534)(440,533)(441,532)(442,531)
(443,530)(444,529)(445,528)(446,527)(447,526)(448,525)(449,524)(450,523)
(451,522)(452,521)(453,520)(454,519)(455,518)(456,517)(457,516)(458,515)
(459,514);;
s1 := (  1,361)(  2,363)(  3,362)(  4,358)(  5,360)(  6,359)(  7,406)(  8,408)
(  9,407)( 10,403)( 11,405)( 12,404)( 13,400)( 14,402)( 15,401)( 16,397)
( 17,399)( 18,398)( 19,394)( 20,396)( 21,395)( 22,391)( 23,393)( 24,392)
( 25,388)( 26,390)( 27,389)( 28,385)( 29,387)( 30,386)( 31,382)( 32,384)
( 33,383)( 34,379)( 35,381)( 36,380)( 37,376)( 38,378)( 39,377)( 40,373)
( 41,375)( 42,374)( 43,370)( 44,372)( 45,371)( 46,367)( 47,369)( 48,368)
( 49,364)( 50,366)( 51,365)( 52,310)( 53,312)( 54,311)( 55,307)( 56,309)
( 57,308)( 58,355)( 59,357)( 60,356)( 61,352)( 62,354)( 63,353)( 64,349)
( 65,351)( 66,350)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)( 72,344)
( 73,340)( 74,342)( 75,341)( 76,337)( 77,339)( 78,338)( 79,334)( 80,336)
( 81,335)( 82,331)( 83,333)( 84,332)( 85,328)( 86,330)( 87,329)( 88,325)
( 89,327)( 90,326)( 91,322)( 92,324)( 93,323)( 94,319)( 95,321)( 96,320)
( 97,316)( 98,318)( 99,317)(100,313)(101,315)(102,314)(103,414)(104,413)
(105,412)(106,411)(107,410)(108,409)(109,459)(110,458)(111,457)(112,456)
(113,455)(114,454)(115,453)(116,452)(117,451)(118,450)(119,449)(120,448)
(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,441)(128,440)
(129,439)(130,438)(131,437)(132,436)(133,435)(134,434)(135,433)(136,432)
(137,431)(138,430)(139,429)(140,428)(141,427)(142,426)(143,425)(144,424)
(145,423)(146,422)(147,421)(148,420)(149,419)(150,418)(151,417)(152,416)
(153,415)(154,514)(155,516)(156,515)(157,511)(158,513)(159,512)(160,559)
(161,561)(162,560)(163,556)(164,558)(165,557)(166,553)(167,555)(168,554)
(169,550)(170,552)(171,551)(172,547)(173,549)(174,548)(175,544)(176,546)
(177,545)(178,541)(179,543)(180,542)(181,538)(182,540)(183,539)(184,535)
(185,537)(186,536)(187,532)(188,534)(189,533)(190,529)(191,531)(192,530)
(193,526)(194,528)(195,527)(196,523)(197,525)(198,524)(199,520)(200,522)
(201,521)(202,517)(203,519)(204,518)(205,463)(206,465)(207,464)(208,460)
(209,462)(210,461)(211,508)(212,510)(213,509)(214,505)(215,507)(216,506)
(217,502)(218,504)(219,503)(220,499)(221,501)(222,500)(223,496)(224,498)
(225,497)(226,493)(227,495)(228,494)(229,490)(230,492)(231,491)(232,487)
(233,489)(234,488)(235,484)(236,486)(237,485)(238,481)(239,483)(240,482)
(241,478)(242,480)(243,479)(244,475)(245,477)(246,476)(247,472)(248,474)
(249,473)(250,469)(251,471)(252,470)(253,466)(254,468)(255,467)(256,567)
(257,566)(258,565)(259,564)(260,563)(261,562)(262,612)(263,611)(264,610)
(265,609)(266,608)(267,607)(268,606)(269,605)(270,604)(271,603)(272,602)
(273,601)(274,600)(275,599)(276,598)(277,597)(278,596)(279,595)(280,594)
(281,593)(282,592)(283,591)(284,590)(285,589)(286,588)(287,587)(288,586)
(289,585)(290,584)(291,583)(292,582)(293,581)(294,580)(295,579)(296,578)
(297,577)(298,576)(299,575)(300,574)(301,573)(302,572)(303,571)(304,570)
(305,569)(306,568);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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(612)!(  2,  3)(  4, 49)(  5, 51)(  6, 50)(  7, 46)(  8, 48)(  9, 47)
( 10, 43)( 11, 45)( 12, 44)( 13, 40)( 14, 42)( 15, 41)( 16, 37)( 17, 39)
( 18, 38)( 19, 34)( 20, 36)( 21, 35)( 22, 31)( 23, 33)( 24, 32)( 25, 28)
( 26, 30)( 27, 29)( 52,105)( 53,104)( 54,103)( 55,153)( 56,152)( 57,151)
( 58,150)( 59,149)( 60,148)( 61,147)( 62,146)( 63,145)( 64,144)( 65,143)
( 66,142)( 67,141)( 68,140)( 69,139)( 70,138)( 71,137)( 72,136)( 73,135)
( 74,134)( 75,133)( 76,132)( 77,131)( 78,130)( 79,129)( 80,128)( 81,127)
( 82,126)( 83,125)( 84,124)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)
( 90,118)( 91,117)( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)
( 98,110)( 99,109)(100,108)(101,107)(102,106)(155,156)(157,202)(158,204)
(159,203)(160,199)(161,201)(162,200)(163,196)(164,198)(165,197)(166,193)
(167,195)(168,194)(169,190)(170,192)(171,191)(172,187)(173,189)(174,188)
(175,184)(176,186)(177,185)(178,181)(179,183)(180,182)(205,258)(206,257)
(207,256)(208,306)(209,305)(210,304)(211,303)(212,302)(213,301)(214,300)
(215,299)(216,298)(217,297)(218,296)(219,295)(220,294)(221,293)(222,292)
(223,291)(224,290)(225,289)(226,288)(227,287)(228,286)(229,285)(230,284)
(231,283)(232,282)(233,281)(234,280)(235,279)(236,278)(237,277)(238,276)
(239,275)(240,274)(241,273)(242,272)(243,271)(244,270)(245,269)(246,268)
(247,267)(248,266)(249,265)(250,264)(251,263)(252,262)(253,261)(254,260)
(255,259)(307,460)(308,462)(309,461)(310,508)(311,510)(312,509)(313,505)
(314,507)(315,506)(316,502)(317,504)(318,503)(319,499)(320,501)(321,500)
(322,496)(323,498)(324,497)(325,493)(326,495)(327,494)(328,490)(329,492)
(330,491)(331,487)(332,489)(333,488)(334,484)(335,486)(336,485)(337,481)
(338,483)(339,482)(340,478)(341,480)(342,479)(343,475)(344,477)(345,476)
(346,472)(347,474)(348,473)(349,469)(350,471)(351,470)(352,466)(353,468)
(354,467)(355,463)(356,465)(357,464)(358,564)(359,563)(360,562)(361,612)
(362,611)(363,610)(364,609)(365,608)(366,607)(367,606)(368,605)(369,604)
(370,603)(371,602)(372,601)(373,600)(374,599)(375,598)(376,597)(377,596)
(378,595)(379,594)(380,593)(381,592)(382,591)(383,590)(384,589)(385,588)
(386,587)(387,586)(388,585)(389,584)(390,583)(391,582)(392,581)(393,580)
(394,579)(395,578)(396,577)(397,576)(398,575)(399,574)(400,573)(401,572)
(402,571)(403,570)(404,569)(405,568)(406,567)(407,566)(408,565)(409,513)
(410,512)(411,511)(412,561)(413,560)(414,559)(415,558)(416,557)(417,556)
(418,555)(419,554)(420,553)(421,552)(422,551)(423,550)(424,549)(425,548)
(426,547)(427,546)(428,545)(429,544)(430,543)(431,542)(432,541)(433,540)
(434,539)(435,538)(436,537)(437,536)(438,535)(439,534)(440,533)(441,532)
(442,531)(443,530)(444,529)(445,528)(446,527)(447,526)(448,525)(449,524)
(450,523)(451,522)(452,521)(453,520)(454,519)(455,518)(456,517)(457,516)
(458,515)(459,514);
s1 := Sym(612)!(  1,361)(  2,363)(  3,362)(  4,358)(  5,360)(  6,359)(  7,406)
(  8,408)(  9,407)( 10,403)( 11,405)( 12,404)( 13,400)( 14,402)( 15,401)
( 16,397)( 17,399)( 18,398)( 19,394)( 20,396)( 21,395)( 22,391)( 23,393)
( 24,392)( 25,388)( 26,390)( 27,389)( 28,385)( 29,387)( 30,386)( 31,382)
( 32,384)( 33,383)( 34,379)( 35,381)( 36,380)( 37,376)( 38,378)( 39,377)
( 40,373)( 41,375)( 42,374)( 43,370)( 44,372)( 45,371)( 46,367)( 47,369)
( 48,368)( 49,364)( 50,366)( 51,365)( 52,310)( 53,312)( 54,311)( 55,307)
( 56,309)( 57,308)( 58,355)( 59,357)( 60,356)( 61,352)( 62,354)( 63,353)
( 64,349)( 65,351)( 66,350)( 67,346)( 68,348)( 69,347)( 70,343)( 71,345)
( 72,344)( 73,340)( 74,342)( 75,341)( 76,337)( 77,339)( 78,338)( 79,334)
( 80,336)( 81,335)( 82,331)( 83,333)( 84,332)( 85,328)( 86,330)( 87,329)
( 88,325)( 89,327)( 90,326)( 91,322)( 92,324)( 93,323)( 94,319)( 95,321)
( 96,320)( 97,316)( 98,318)( 99,317)(100,313)(101,315)(102,314)(103,414)
(104,413)(105,412)(106,411)(107,410)(108,409)(109,459)(110,458)(111,457)
(112,456)(113,455)(114,454)(115,453)(116,452)(117,451)(118,450)(119,449)
(120,448)(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,441)
(128,440)(129,439)(130,438)(131,437)(132,436)(133,435)(134,434)(135,433)
(136,432)(137,431)(138,430)(139,429)(140,428)(141,427)(142,426)(143,425)
(144,424)(145,423)(146,422)(147,421)(148,420)(149,419)(150,418)(151,417)
(152,416)(153,415)(154,514)(155,516)(156,515)(157,511)(158,513)(159,512)
(160,559)(161,561)(162,560)(163,556)(164,558)(165,557)(166,553)(167,555)
(168,554)(169,550)(170,552)(171,551)(172,547)(173,549)(174,548)(175,544)
(176,546)(177,545)(178,541)(179,543)(180,542)(181,538)(182,540)(183,539)
(184,535)(185,537)(186,536)(187,532)(188,534)(189,533)(190,529)(191,531)
(192,530)(193,526)(194,528)(195,527)(196,523)(197,525)(198,524)(199,520)
(200,522)(201,521)(202,517)(203,519)(204,518)(205,463)(206,465)(207,464)
(208,460)(209,462)(210,461)(211,508)(212,510)(213,509)(214,505)(215,507)
(216,506)(217,502)(218,504)(219,503)(220,499)(221,501)(222,500)(223,496)
(224,498)(225,497)(226,493)(227,495)(228,494)(229,490)(230,492)(231,491)
(232,487)(233,489)(234,488)(235,484)(236,486)(237,485)(238,481)(239,483)
(240,482)(241,478)(242,480)(243,479)(244,475)(245,477)(246,476)(247,472)
(248,474)(249,473)(250,469)(251,471)(252,470)(253,466)(254,468)(255,467)
(256,567)(257,566)(258,565)(259,564)(260,563)(261,562)(262,612)(263,611)
(264,610)(265,609)(266,608)(267,607)(268,606)(269,605)(270,604)(271,603)
(272,602)(273,601)(274,600)(275,599)(276,598)(277,597)(278,596)(279,595)
(280,594)(281,593)(282,592)(283,591)(284,590)(285,589)(286,588)(287,587)
(288,586)(289,585)(290,584)(291,583)(292,582)(293,581)(294,580)(295,579)
(296,578)(297,577)(298,576)(299,575)(300,574)(301,573)(302,572)(303,571)
(304,570)(305,569)(306,568);
poly := sub<Sym(612)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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*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