Polytope of Type {4,148}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,148}*1184
Also Known As : {4,148|2}. if this polytope has another name.
Group : SmallGroup(1184,116)
Rank : 3
Schlafli Type : {4,148}
Number of vertices, edges, etc : 4, 296, 148
Order of s₀s₁s₂ : 148
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 : {2,148}*592, {4,74}*592
   4-fold quotients : {2,74}*296
   8-fold quotients : {2,37}*148
   37-fold quotients : {4,4}*32
   74-fold quotients : {2,4}*16, {4,2}*16
   148-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope