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