Polytope of Type {4,156}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,156}*1248b
if this polytope has a name.
Group : SmallGroup(1248,1233)
Rank : 3
Schlafli Type : {4,156}
Number of vertices, edges, etc : 4, 312, 156
Order of s₀s₁s₂ : 156
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) :
   2-fold quotients : {4,78}*624b
   4-fold quotients : {4,39}*312
   13-fold quotients : {4,12}*96b
   26-fold quotients : {4,6}*48c
   52-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)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624);;
s1 := (  3,  4)(  5, 49)(  6, 50)(  7, 52)(  8, 51)(  9, 45)( 10, 46)( 11, 48)
( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)
( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)( 27, 32)
( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)( 59,156)
( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)( 67,148)
( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)( 75,140)
( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)( 83,132)
( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)( 91,124)
( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)( 99,116)
(100,115)(101,109)(102,110)(103,112)(104,111)(159,160)(161,205)(162,206)
(163,208)(164,207)(165,201)(166,202)(167,204)(168,203)(169,197)(170,198)
(171,200)(172,199)(173,193)(174,194)(175,196)(176,195)(177,189)(178,190)
(179,192)(180,191)(181,185)(182,186)(183,188)(184,187)(209,261)(210,262)
(211,264)(212,263)(213,309)(214,310)(215,312)(216,311)(217,305)(218,306)
(219,308)(220,307)(221,301)(222,302)(223,304)(224,303)(225,297)(226,298)
(227,300)(228,299)(229,293)(230,294)(231,296)(232,295)(233,289)(234,290)
(235,292)(236,291)(237,285)(238,286)(239,288)(240,287)(241,281)(242,282)
(243,284)(244,283)(245,277)(246,278)(247,280)(248,279)(249,273)(250,274)
(251,276)(252,275)(253,269)(254,270)(255,272)(256,271)(257,265)(258,266)
(259,268)(260,267)(313,469)(314,470)(315,472)(316,471)(317,517)(318,518)
(319,520)(320,519)(321,513)(322,514)(323,516)(324,515)(325,509)(326,510)
(327,512)(328,511)(329,505)(330,506)(331,508)(332,507)(333,501)(334,502)
(335,504)(336,503)(337,497)(338,498)(339,500)(340,499)(341,493)(342,494)
(343,496)(344,495)(345,489)(346,490)(347,492)(348,491)(349,485)(350,486)
(351,488)(352,487)(353,481)(354,482)(355,484)(356,483)(357,477)(358,478)
(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)(365,573)(366,574)
(367,576)(368,575)(369,621)(370,622)(371,624)(372,623)(373,617)(374,618)
(375,620)(376,619)(377,613)(378,614)(379,616)(380,615)(381,609)(382,610)
(383,612)(384,611)(385,605)(386,606)(387,608)(388,607)(389,601)(390,602)
(391,604)(392,603)(393,597)(394,598)(395,600)(396,599)(397,593)(398,594)
(399,596)(400,595)(401,589)(402,590)(403,592)(404,591)(405,585)(406,586)
(407,588)(408,587)(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)
(415,580)(416,579)(417,521)(418,522)(419,524)(420,523)(421,569)(422,570)
(423,572)(424,571)(425,565)(426,566)(427,568)(428,567)(429,561)(430,562)
(431,564)(432,563)(433,557)(434,558)(435,560)(436,559)(437,553)(438,554)
(439,556)(440,555)(441,549)(442,550)(443,552)(444,551)(445,545)(446,546)
(447,548)(448,547)(449,541)(450,542)(451,544)(452,543)(453,537)(454,538)
(455,540)(456,539)(457,533)(458,534)(459,536)(460,535)(461,529)(462,530)
(463,532)(464,531)(465,525)(466,526)(467,528)(468,527);;
s2 := (  1,369)(  2,372)(  3,371)(  4,370)(  5,365)(  6,368)(  7,367)(  8,366)
(  9,413)( 10,416)( 11,415)( 12,414)( 13,409)( 14,412)( 15,411)( 16,410)
( 17,405)( 18,408)( 19,407)( 20,406)( 21,401)( 22,404)( 23,403)( 24,402)
( 25,397)( 26,400)( 27,399)( 28,398)( 29,393)( 30,396)( 31,395)( 32,394)
( 33,389)( 34,392)( 35,391)( 36,390)( 37,385)( 38,388)( 39,387)( 40,386)
( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)( 48,378)
( 49,373)( 50,376)( 51,375)( 52,374)( 53,317)( 54,320)( 55,319)( 56,318)
( 57,313)( 58,316)( 59,315)( 60,314)( 61,361)( 62,364)( 63,363)( 64,362)
( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)( 72,354)
( 73,349)( 74,352)( 75,351)( 76,350)( 77,345)( 78,348)( 79,347)( 80,346)
( 81,341)( 82,344)( 83,343)( 84,342)( 85,337)( 86,340)( 87,339)( 88,338)
( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)( 96,330)
( 97,325)( 98,328)( 99,327)(100,326)(101,321)(102,324)(103,323)(104,322)
(105,421)(106,424)(107,423)(108,422)(109,417)(110,420)(111,419)(112,418)
(113,465)(114,468)(115,467)(116,466)(117,461)(118,464)(119,463)(120,462)
(121,457)(122,460)(123,459)(124,458)(125,453)(126,456)(127,455)(128,454)
(129,449)(130,452)(131,451)(132,450)(133,445)(134,448)(135,447)(136,446)
(137,441)(138,444)(139,443)(140,442)(141,437)(142,440)(143,439)(144,438)
(145,433)(146,436)(147,435)(148,434)(149,429)(150,432)(151,431)(152,430)
(153,425)(154,428)(155,427)(156,426)(157,525)(158,528)(159,527)(160,526)
(161,521)(162,524)(163,523)(164,522)(165,569)(166,572)(167,571)(168,570)
(169,565)(170,568)(171,567)(172,566)(173,561)(174,564)(175,563)(176,562)
(177,557)(178,560)(179,559)(180,558)(181,553)(182,556)(183,555)(184,554)
(185,549)(186,552)(187,551)(188,550)(189,545)(190,548)(191,547)(192,546)
(193,541)(194,544)(195,543)(196,542)(197,537)(198,540)(199,539)(200,538)
(201,533)(202,536)(203,535)(204,534)(205,529)(206,532)(207,531)(208,530)
(209,473)(210,476)(211,475)(212,474)(213,469)(214,472)(215,471)(216,470)
(217,517)(218,520)(219,519)(220,518)(221,513)(222,516)(223,515)(224,514)
(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)(232,506)
(233,501)(234,504)(235,503)(236,502)(237,497)(238,500)(239,499)(240,498)
(241,493)(242,496)(243,495)(244,494)(245,489)(246,492)(247,491)(248,490)
(249,485)(250,488)(251,487)(252,486)(253,481)(254,484)(255,483)(256,482)
(257,477)(258,480)(259,479)(260,478)(261,577)(262,580)(263,579)(264,578)
(265,573)(266,576)(267,575)(268,574)(269,621)(270,624)(271,623)(272,622)
(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)(280,614)
(281,609)(282,612)(283,611)(284,610)(285,605)(286,608)(287,607)(288,606)
(289,601)(290,604)(291,603)(292,602)(293,597)(294,600)(295,599)(296,598)
(297,593)(298,596)(299,595)(300,594)(301,589)(302,592)(303,591)(304,590)
(305,585)(306,588)(307,587)(308,586)(309,581)(310,584)(311,583)(312,582);;
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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(624)!(  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)(613,615)(614,616)(617,619)(618,620)(621,623)
(622,624);
s1 := Sym(624)!(  3,  4)(  5, 49)(  6, 50)(  7, 52)(  8, 51)(  9, 45)( 10, 46)
( 11, 48)( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)
( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)
( 27, 32)( 28, 31)( 53,105)( 54,106)( 55,108)( 56,107)( 57,153)( 58,154)
( 59,156)( 60,155)( 61,149)( 62,150)( 63,152)( 64,151)( 65,145)( 66,146)
( 67,148)( 68,147)( 69,141)( 70,142)( 71,144)( 72,143)( 73,137)( 74,138)
( 75,140)( 76,139)( 77,133)( 78,134)( 79,136)( 80,135)( 81,129)( 82,130)
( 83,132)( 84,131)( 85,125)( 86,126)( 87,128)( 88,127)( 89,121)( 90,122)
( 91,124)( 92,123)( 93,117)( 94,118)( 95,120)( 96,119)( 97,113)( 98,114)
( 99,116)(100,115)(101,109)(102,110)(103,112)(104,111)(159,160)(161,205)
(162,206)(163,208)(164,207)(165,201)(166,202)(167,204)(168,203)(169,197)
(170,198)(171,200)(172,199)(173,193)(174,194)(175,196)(176,195)(177,189)
(178,190)(179,192)(180,191)(181,185)(182,186)(183,188)(184,187)(209,261)
(210,262)(211,264)(212,263)(213,309)(214,310)(215,312)(216,311)(217,305)
(218,306)(219,308)(220,307)(221,301)(222,302)(223,304)(224,303)(225,297)
(226,298)(227,300)(228,299)(229,293)(230,294)(231,296)(232,295)(233,289)
(234,290)(235,292)(236,291)(237,285)(238,286)(239,288)(240,287)(241,281)
(242,282)(243,284)(244,283)(245,277)(246,278)(247,280)(248,279)(249,273)
(250,274)(251,276)(252,275)(253,269)(254,270)(255,272)(256,271)(257,265)
(258,266)(259,268)(260,267)(313,469)(314,470)(315,472)(316,471)(317,517)
(318,518)(319,520)(320,519)(321,513)(322,514)(323,516)(324,515)(325,509)
(326,510)(327,512)(328,511)(329,505)(330,506)(331,508)(332,507)(333,501)
(334,502)(335,504)(336,503)(337,497)(338,498)(339,500)(340,499)(341,493)
(342,494)(343,496)(344,495)(345,489)(346,490)(347,492)(348,491)(349,485)
(350,486)(351,488)(352,487)(353,481)(354,482)(355,484)(356,483)(357,477)
(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)(365,573)
(366,574)(367,576)(368,575)(369,621)(370,622)(371,624)(372,623)(373,617)
(374,618)(375,620)(376,619)(377,613)(378,614)(379,616)(380,615)(381,609)
(382,610)(383,612)(384,611)(385,605)(386,606)(387,608)(388,607)(389,601)
(390,602)(391,604)(392,603)(393,597)(394,598)(395,600)(396,599)(397,593)
(398,594)(399,596)(400,595)(401,589)(402,590)(403,592)(404,591)(405,585)
(406,586)(407,588)(408,587)(409,581)(410,582)(411,584)(412,583)(413,577)
(414,578)(415,580)(416,579)(417,521)(418,522)(419,524)(420,523)(421,569)
(422,570)(423,572)(424,571)(425,565)(426,566)(427,568)(428,567)(429,561)
(430,562)(431,564)(432,563)(433,557)(434,558)(435,560)(436,559)(437,553)
(438,554)(439,556)(440,555)(441,549)(442,550)(443,552)(444,551)(445,545)
(446,546)(447,548)(448,547)(449,541)(450,542)(451,544)(452,543)(453,537)
(454,538)(455,540)(456,539)(457,533)(458,534)(459,536)(460,535)(461,529)
(462,530)(463,532)(464,531)(465,525)(466,526)(467,528)(468,527);
s2 := Sym(624)!(  1,369)(  2,372)(  3,371)(  4,370)(  5,365)(  6,368)(  7,367)
(  8,366)(  9,413)( 10,416)( 11,415)( 12,414)( 13,409)( 14,412)( 15,411)
( 16,410)( 17,405)( 18,408)( 19,407)( 20,406)( 21,401)( 22,404)( 23,403)
( 24,402)( 25,397)( 26,400)( 27,399)( 28,398)( 29,393)( 30,396)( 31,395)
( 32,394)( 33,389)( 34,392)( 35,391)( 36,390)( 37,385)( 38,388)( 39,387)
( 40,386)( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)
( 48,378)( 49,373)( 50,376)( 51,375)( 52,374)( 53,317)( 54,320)( 55,319)
( 56,318)( 57,313)( 58,316)( 59,315)( 60,314)( 61,361)( 62,364)( 63,363)
( 64,362)( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)
( 72,354)( 73,349)( 74,352)( 75,351)( 76,350)( 77,345)( 78,348)( 79,347)
( 80,346)( 81,341)( 82,344)( 83,343)( 84,342)( 85,337)( 86,340)( 87,339)
( 88,338)( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)
( 96,330)( 97,325)( 98,328)( 99,327)(100,326)(101,321)(102,324)(103,323)
(104,322)(105,421)(106,424)(107,423)(108,422)(109,417)(110,420)(111,419)
(112,418)(113,465)(114,468)(115,467)(116,466)(117,461)(118,464)(119,463)
(120,462)(121,457)(122,460)(123,459)(124,458)(125,453)(126,456)(127,455)
(128,454)(129,449)(130,452)(131,451)(132,450)(133,445)(134,448)(135,447)
(136,446)(137,441)(138,444)(139,443)(140,442)(141,437)(142,440)(143,439)
(144,438)(145,433)(146,436)(147,435)(148,434)(149,429)(150,432)(151,431)
(152,430)(153,425)(154,428)(155,427)(156,426)(157,525)(158,528)(159,527)
(160,526)(161,521)(162,524)(163,523)(164,522)(165,569)(166,572)(167,571)
(168,570)(169,565)(170,568)(171,567)(172,566)(173,561)(174,564)(175,563)
(176,562)(177,557)(178,560)(179,559)(180,558)(181,553)(182,556)(183,555)
(184,554)(185,549)(186,552)(187,551)(188,550)(189,545)(190,548)(191,547)
(192,546)(193,541)(194,544)(195,543)(196,542)(197,537)(198,540)(199,539)
(200,538)(201,533)(202,536)(203,535)(204,534)(205,529)(206,532)(207,531)
(208,530)(209,473)(210,476)(211,475)(212,474)(213,469)(214,472)(215,471)
(216,470)(217,517)(218,520)(219,519)(220,518)(221,513)(222,516)(223,515)
(224,514)(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)
(232,506)(233,501)(234,504)(235,503)(236,502)(237,497)(238,500)(239,499)
(240,498)(241,493)(242,496)(243,495)(244,494)(245,489)(246,492)(247,491)
(248,490)(249,485)(250,488)(251,487)(252,486)(253,481)(254,484)(255,483)
(256,482)(257,477)(258,480)(259,479)(260,478)(261,577)(262,580)(263,579)
(264,578)(265,573)(266,576)(267,575)(268,574)(269,621)(270,624)(271,623)
(272,622)(273,617)(274,620)(275,619)(276,618)(277,613)(278,616)(279,615)
(280,614)(281,609)(282,612)(283,611)(284,610)(285,605)(286,608)(287,607)
(288,606)(289,601)(290,604)(291,603)(292,602)(293,597)(294,600)(295,599)
(296,598)(297,593)(298,596)(299,595)(300,594)(301,589)(302,592)(303,591)
(304,590)(305,585)(306,588)(307,587)(308,586)(309,581)(310,584)(311,583)
(312,582);
poly := sub<Sym(624)|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*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope