Polytope of Type {250,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {250,4}*2000
Also Known As : {250,4|2}. if this polytope has another name.
Group : SmallGroup(2000,39)
Rank : 3
Schlafli Type : {250,4}
Number of vertices, edges, etc : 250, 500, 4
Order of s₀s₁s₂ : 500
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 : {250,2}*1000
   4-fold quotients : {125,2}*500
   5-fold quotients : {50,4}*400
   10-fold quotients : {50,2}*200
   20-fold quotients : {25,2}*100
   25-fold quotients : {10,4}*80
   50-fold quotients : {10,2}*40
   100-fold quotients : {5,2}*20
   125-fold quotients : {2,4}*16
   250-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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