Polytope of Type {4,153}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,153}*1224
if this polytope has a name.
Group : SmallGroup(1224,43)
Rank : 3
Schlafli Type : {4,153}
Number of vertices, edges, etc : 4, 306, 153
Order of s₀s₁s₂ : 153
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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) :
   3-fold quotients : {4,51}*408
   17-fold quotients : {4,9}*72
   51-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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