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