Polytope of Type {25,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {25,10,4}*2000
if this polytope has a name.
Group : SmallGroup(2000,386)
Rank : 4
Schlafli Type : {25,10,4}
Number of vertices, edges, etc : 25, 125, 20, 4
Order of s0s1s2s3 : 100
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {25,10,2}*1000
5-fold quotients : {25,2,4}*400, {5,10,4}*400
10-fold quotients : {25,2,2}*200, {5,10,2}*200
25-fold quotients : {5,2,4}*80
50-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26,105)( 27,104)( 28,103)( 29,102)
( 30,101)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,120)( 37,119)
( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)
( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51, 80)( 52, 79)( 53, 78)
( 54, 77)( 55, 76)( 56,100)( 57, 99)( 58, 98)( 59, 97)( 60, 96)( 61, 95)
( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)
( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)(127,130)(128,129)
(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)
(139,143)(140,142)(151,230)(152,229)(153,228)(154,227)(155,226)(156,250)
(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)
(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)
(173,233)(174,232)(175,231)(176,205)(177,204)(178,203)(179,202)(180,201)
(181,225)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)(188,218)
(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)(196,210)
(197,209)(198,208)(199,207)(200,206)(252,255)(253,254)(256,271)(257,275)
(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)
(276,355)(277,354)(278,353)(279,352)(280,351)(281,375)(282,374)(283,373)
(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)
(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)
(300,356)(301,330)(302,329)(303,328)(304,327)(305,326)(306,350)(307,349)
(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)(315,341)
(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)(323,333)
(324,332)(325,331)(377,380)(378,379)(381,396)(382,400)(383,399)(384,398)
(385,397)(386,391)(387,395)(388,394)(389,393)(390,392)(401,480)(402,479)
(403,478)(404,477)(405,476)(406,500)(407,499)(408,498)(409,497)(410,496)
(411,495)(412,494)(413,493)(414,492)(415,491)(416,490)(417,489)(418,488)
(419,487)(420,486)(421,485)(422,484)(423,483)(424,482)(425,481)(426,455)
(427,454)(428,453)(429,452)(430,451)(431,475)(432,474)(433,473)(434,472)
(435,471)(436,470)(437,469)(438,468)(439,467)(440,466)(441,465)(442,464)
(443,463)(444,462)(445,461)(446,460)(447,459)(448,458)(449,457)(450,456);;
s1 := ( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)( 8, 29)
( 9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)( 57,104)
( 58,103)( 59,102)( 60,101)( 61,125)( 62,124)( 63,123)( 64,122)( 65,121)
( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)( 72,114)( 73,113)
( 74,112)( 75,111)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 86,100)
( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(126,156)(127,160)
(128,159)(129,158)(130,157)(131,151)(132,155)(133,154)(134,153)(135,152)
(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)(143,169)
(144,168)(145,167)(146,161)(147,165)(148,164)(149,163)(150,162)(176,235)
(177,234)(178,233)(179,232)(180,231)(181,230)(182,229)(183,228)(184,227)
(185,226)(186,250)(187,249)(188,248)(189,247)(190,246)(191,245)(192,244)
(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,237)(200,236)
(201,210)(202,209)(203,208)(204,207)(205,206)(211,225)(212,224)(213,223)
(214,222)(215,221)(216,220)(217,219)(251,281)(252,285)(253,284)(254,283)
(255,282)(256,276)(257,280)(258,279)(259,278)(260,277)(261,296)(262,300)
(263,299)(264,298)(265,297)(266,291)(267,295)(268,294)(269,293)(270,292)
(271,286)(272,290)(273,289)(274,288)(275,287)(301,360)(302,359)(303,358)
(304,357)(305,356)(306,355)(307,354)(308,353)(309,352)(310,351)(311,375)
(312,374)(313,373)(314,372)(315,371)(316,370)(317,369)(318,368)(319,367)
(320,366)(321,365)(322,364)(323,363)(324,362)(325,361)(326,335)(327,334)
(328,333)(329,332)(330,331)(336,350)(337,349)(338,348)(339,347)(340,346)
(341,345)(342,344)(376,406)(377,410)(378,409)(379,408)(380,407)(381,401)
(382,405)(383,404)(384,403)(385,402)(386,421)(387,425)(388,424)(389,423)
(390,422)(391,416)(392,420)(393,419)(394,418)(395,417)(396,411)(397,415)
(398,414)(399,413)(400,412)(426,485)(427,484)(428,483)(429,482)(430,481)
(431,480)(432,479)(433,478)(434,477)(435,476)(436,500)(437,499)(438,498)
(439,497)(440,496)(441,495)(442,494)(443,493)(444,492)(445,491)(446,490)
(447,489)(448,488)(449,487)(450,486)(451,460)(452,459)(453,458)(454,457)
(455,456)(461,475)(462,474)(463,473)(464,472)(465,471)(466,470)(467,469);;
s2 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(251,376)(252,377)(253,378)(254,379)
(255,380)(256,396)(257,397)(258,398)(259,399)(260,400)(261,391)(262,392)
(263,393)(264,394)(265,395)(266,386)(267,387)(268,388)(269,389)(270,390)
(271,381)(272,382)(273,383)(274,384)(275,385)(276,401)(277,402)(278,403)
(279,404)(280,405)(281,421)(282,422)(283,423)(284,424)(285,425)(286,416)
(287,417)(288,418)(289,419)(290,420)(291,411)(292,412)(293,413)(294,414)
(295,415)(296,406)(297,407)(298,408)(299,409)(300,410)(301,426)(302,427)
(303,428)(304,429)(305,430)(306,446)(307,447)(308,448)(309,449)(310,450)
(311,441)(312,442)(313,443)(314,444)(315,445)(316,436)(317,437)(318,438)
(319,439)(320,440)(321,431)(322,432)(323,433)(324,434)(325,435)(326,451)
(327,452)(328,453)(329,454)(330,455)(331,471)(332,472)(333,473)(334,474)
(335,475)(336,466)(337,467)(338,468)(339,469)(340,470)(341,461)(342,462)
(343,463)(344,464)(345,465)(346,456)(347,457)(348,458)(349,459)(350,460)
(351,476)(352,477)(353,478)(354,479)(355,480)(356,496)(357,497)(358,498)
(359,499)(360,500)(361,491)(362,492)(363,493)(364,494)(365,495)(366,486)
(367,487)(368,488)(369,489)(370,490)(371,481)(372,482)(373,483)(374,484)
(375,485);;
s3 := ( 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,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26,105)( 27,104)( 28,103)
( 29,102)( 30,101)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,120)
( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,113)( 44,112)
( 45,111)( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51, 80)( 52, 79)
( 53, 78)( 54, 77)( 55, 76)( 56,100)( 57, 99)( 58, 98)( 59, 97)( 60, 96)
( 61, 95)( 62, 94)( 63, 93)( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 88)
( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)(127,130)
(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)
(138,144)(139,143)(140,142)(151,230)(152,229)(153,228)(154,227)(155,226)
(156,250)(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)
(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)
(172,234)(173,233)(174,232)(175,231)(176,205)(177,204)(178,203)(179,202)
(180,201)(181,225)(182,224)(183,223)(184,222)(185,221)(186,220)(187,219)
(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)(194,212)(195,211)
(196,210)(197,209)(198,208)(199,207)(200,206)(252,255)(253,254)(256,271)
(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)
(265,267)(276,355)(277,354)(278,353)(279,352)(280,351)(281,375)(282,374)
(283,373)(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)
(291,365)(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)
(299,357)(300,356)(301,330)(302,329)(303,328)(304,327)(305,326)(306,350)
(307,349)(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)
(315,341)(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)
(323,333)(324,332)(325,331)(377,380)(378,379)(381,396)(382,400)(383,399)
(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392)(401,480)
(402,479)(403,478)(404,477)(405,476)(406,500)(407,499)(408,498)(409,497)
(410,496)(411,495)(412,494)(413,493)(414,492)(415,491)(416,490)(417,489)
(418,488)(419,487)(420,486)(421,485)(422,484)(423,483)(424,482)(425,481)
(426,455)(427,454)(428,453)(429,452)(430,451)(431,475)(432,474)(433,473)
(434,472)(435,471)(436,470)(437,469)(438,468)(439,467)(440,466)(441,465)
(442,464)(443,463)(444,462)(445,461)(446,460)(447,459)(448,458)(449,457)
(450,456);
s1 := Sym(500)!( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)
( 8, 29)( 9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)
( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)
( 24, 38)( 25, 37)( 51,110)( 52,109)( 53,108)( 54,107)( 55,106)( 56,105)
( 57,104)( 58,103)( 59,102)( 60,101)( 61,125)( 62,124)( 63,123)( 64,122)
( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)( 72,114)
( 73,113)( 74,112)( 75,111)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)
( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(126,156)
(127,160)(128,159)(129,158)(130,157)(131,151)(132,155)(133,154)(134,153)
(135,152)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)
(143,169)(144,168)(145,167)(146,161)(147,165)(148,164)(149,163)(150,162)
(176,235)(177,234)(178,233)(179,232)(180,231)(181,230)(182,229)(183,228)
(184,227)(185,226)(186,250)(187,249)(188,248)(189,247)(190,246)(191,245)
(192,244)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,237)
(200,236)(201,210)(202,209)(203,208)(204,207)(205,206)(211,225)(212,224)
(213,223)(214,222)(215,221)(216,220)(217,219)(251,281)(252,285)(253,284)
(254,283)(255,282)(256,276)(257,280)(258,279)(259,278)(260,277)(261,296)
(262,300)(263,299)(264,298)(265,297)(266,291)(267,295)(268,294)(269,293)
(270,292)(271,286)(272,290)(273,289)(274,288)(275,287)(301,360)(302,359)
(303,358)(304,357)(305,356)(306,355)(307,354)(308,353)(309,352)(310,351)
(311,375)(312,374)(313,373)(314,372)(315,371)(316,370)(317,369)(318,368)
(319,367)(320,366)(321,365)(322,364)(323,363)(324,362)(325,361)(326,335)
(327,334)(328,333)(329,332)(330,331)(336,350)(337,349)(338,348)(339,347)
(340,346)(341,345)(342,344)(376,406)(377,410)(378,409)(379,408)(380,407)
(381,401)(382,405)(383,404)(384,403)(385,402)(386,421)(387,425)(388,424)
(389,423)(390,422)(391,416)(392,420)(393,419)(394,418)(395,417)(396,411)
(397,415)(398,414)(399,413)(400,412)(426,485)(427,484)(428,483)(429,482)
(430,481)(431,480)(432,479)(433,478)(434,477)(435,476)(436,500)(437,499)
(438,498)(439,497)(440,496)(441,495)(442,494)(443,493)(444,492)(445,491)
(446,490)(447,489)(448,488)(449,487)(450,486)(451,460)(452,459)(453,458)
(454,457)(455,456)(461,475)(462,474)(463,473)(464,472)(465,471)(466,470)
(467,469);
s2 := Sym(500)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195)(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)
(213,218)(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)
(236,241)(237,242)(238,243)(239,244)(240,245)(251,376)(252,377)(253,378)
(254,379)(255,380)(256,396)(257,397)(258,398)(259,399)(260,400)(261,391)
(262,392)(263,393)(264,394)(265,395)(266,386)(267,387)(268,388)(269,389)
(270,390)(271,381)(272,382)(273,383)(274,384)(275,385)(276,401)(277,402)
(278,403)(279,404)(280,405)(281,421)(282,422)(283,423)(284,424)(285,425)
(286,416)(287,417)(288,418)(289,419)(290,420)(291,411)(292,412)(293,413)
(294,414)(295,415)(296,406)(297,407)(298,408)(299,409)(300,410)(301,426)
(302,427)(303,428)(304,429)(305,430)(306,446)(307,447)(308,448)(309,449)
(310,450)(311,441)(312,442)(313,443)(314,444)(315,445)(316,436)(317,437)
(318,438)(319,439)(320,440)(321,431)(322,432)(323,433)(324,434)(325,435)
(326,451)(327,452)(328,453)(329,454)(330,455)(331,471)(332,472)(333,473)
(334,474)(335,475)(336,466)(337,467)(338,468)(339,469)(340,470)(341,461)
(342,462)(343,463)(344,464)(345,465)(346,456)(347,457)(348,458)(349,459)
(350,460)(351,476)(352,477)(353,478)(354,479)(355,480)(356,496)(357,497)
(358,498)(359,499)(360,500)(361,491)(362,492)(363,493)(364,494)(365,495)
(366,486)(367,487)(368,488)(369,489)(370,490)(371,481)(372,482)(373,483)
(374,484)(375,485);
s3 := 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,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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