Polytope of Type {4,152}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,152}*1216a
Also Known As : {4,152|2}. if this polytope has another name.
Group : SmallGroup(1216,685)
Rank : 3
Schlafli Type : {4,152}
Number of vertices, edges, etc : 4, 304, 152
Order of s₀s₁s₂ : 152
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,76}*608, {2,152}*608
   4-fold quotients : {2,76}*304, {4,38}*304
   8-fold quotients : {2,38}*152
   16-fold quotients : {2,19}*76
   19-fold quotients : {4,8}*64a
   38-fold quotients : {4,4}*32, {2,8}*32
   76-fold quotients : {2,4}*16, {4,2}*16
   152-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope