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